DE102019202009A1 - Apparatus, methods and computer program for locating a transponder - Google Patents

Abstract

Apparatus for locating a transponder. The apparatus is configured to obtain a time of arrival of one or more signals on the basis of transmission time stamps and reception time stamps of two or more signals. Further, the apparatus for obtaining a first arrival time difference based on a difference between reception time stamps obtained at a first station and describing reception times of two signals, one transmitted by the reference station and the other transmitted by the transponder, is at the first station configured. The apparatus is configured to obtain a second arrival time difference based on a difference between reception time stamps obtained at a second station and describing reception times of two signals, one transmitted by the reference station and the other transmitted by the transponder, at the second station . Furthermore, the apparatus is configured to calculate a position of the transponder on the basis of the arrival time and the at least two arrival time differences.

Description

Technical area

Embodiments according to the invention relate to an apparatus, a method and a computer program for localizing (locating) a transponder (tag).

Background of the invention

Localization systems are essential in everyday life these days. Satellite navigation [8, 18] has replaced paper road maps and enables cars and airplanes to operate autonomously. With increasing requirements in terms of logistics and manufacturing, precise information about the position becomes mandatory. Depending on the operating conditions for the localization, there are different measuring principles [12, 16, 21] and techniques [4, 20, 7]. The most common measurement techniques are time of arrival (TOA) [4] and time difference of arrival (TDOA) [20]. The difference between the two techniques is that the TOA gets the distance between two stations based on the signal propagation time and the TDOA gets it based on the time difference between the stations. Two way ranging (TWR) uses the TOA technique to obtain the distance between two stations [5]. In contrast to one-way distance determination such as For satellite-based applications, the TWR responds to the transmitted signal. It is therefore not necessary for the sending stations to be synchronous. In applications where it is necessary to obtain not only the distance but also the position of the target (the tag, the transponder) in relation to the other stations (anchors, anchors), TWR is less suitable due to the short update time. The triangle measurement (triangulation) in a two-dimensional space requires at least three distance measurements. TWR needs the distances between the transponder and each anchor before the triangle measurement. With an increasing number of transponders, the update decreases over time. In contrast to TOA, TDOA is better suited for applications with many transponders. In TDOA applications, the anchors do not respond. The multilateration is obtained by the difference in time stamps between the anchors. In geometrical terms, TOA equations are circles and TDOA are hyperboloids in two-dimensional space. Much like satellite navigation systems that are based on TOA, it is necessary that the clocks of the TDOA anchors are synchronized. The synchronization can take place via cable [1] or with an additional station [12]. Apart from the measurement technology, the measurement equipment is equally important.

Positioning in buildings is generally a challenge for HF-based localization systems. Reflections could cause interference with the main signal and lead to fading [9, 14]. The Decawave transceiver [13] is based on ultra broadband technology (UWB technology, UWB = ultra wideband) and corresponds to the IEEE802.15.4-2011 standard [10]. It supports six frequency bands with center frequencies from 3.5 GHz to 6.5 GHz and data rates of up to 6.8 Mb / s. The bandwidth varies with the selected center frequencies from 500 to 1000 MHz. In [11, 6, 19], various methods of wireless TDOA clock synchronization are presented. What they all have in common is that they use a fixed and known time interval for the synchronization signal.

It is therefore desirable to arrive at a concept that achieves a better compromise between optimizing synchronization between clocks of stations used to locate the transponder and maximizing the efficiency and accuracy of locating the transponder.

This is achieved through the subject matter of the independent claims of the present application.

Further embodiments according to the invention are defined by the subject matter of the dependent claims of the present application.

Summary of the invention

An embodiment according to this invention relates to an apparatus for locating a transponder. The apparatus is configured to obtain an arrival time of one or more signals on the basis of transmission time stamps and reception time stamps of two or more signals transmitted between a reference station and a transponder. The arrival time can be used as TOA and defines, for example, a flight time of a signal that is sent by the reference station and received by the transponder. Thus, for example, two signals are sent between the reference station and the transponder, whereby both signals have the same arrival time, since a distance between the reference station and the transponder is constant, for example during a determination of the arrival time. Therefore, it is sufficient that the apparatus receives the arrival time of only one of the two signals. A clock shift correction and / or an antenna delay correction and / or a signal power correction can be used to determine the time of arrival. According to an exemplary embodiment, the clock offset correction and / or the signal power correction can be determined in parallel with or simultaneously with the determination of the arrival time, if the arrival time is based on the transmission time stamps and reception time stamps of at least three signals. In other words, the clock shift correction and / or the signal power correction can be based on the transmit time stamps and receive time stamps of the two or more signals.

The apparatus is configured to obtain a first arrival time difference based on a difference between reception time stamps obtained at a first station and describing reception times of two signals, one transmitted by the reference station and the other transmitted by the transponder, at the first station . Further, the apparatus for obtaining a second arrival time difference based on a difference between reception time stamps obtained at a second station and describing reception time stamps of two signals, one transmitted by the reference station and the other transmitted by the transponder, is at the second station configured. The time of arrival difference can be expressed as TDOA. The two signals on which the receive timestamps obtained at the second station are based can be the same as the two signals on which the receive timestamps obtained at the first station are based, or can be different from the two signals on which the receive timestamps are based on receive time stamps obtained from the first station. The two signals received by the first station and / or the two signals received by the second station can for example be sent in a time-synchronized manner, for example in such a way that a transmission time difference is predetermined or can be calculated. Thus, the arrival time difference defines, for example, a difference in a flight time of the two signals. In other words, the reference station can have a different distance from the first station or the second station than the transponder from the first station or the second station, whereby a difference between these two distances can lead to the respective arrival time difference.

A clock offset correction and / or a signal power correction and / or an antenna delay correction can be used to determine the first arrival time difference and / or the second arrival time difference.

The apparatus is configured to calculate a position of the transponder on the basis of the arrival time and the at least two arrival time differences, which are represented, for example, by the first arrival time difference and the second arrival time difference. According to one embodiment, the apparatus is configured to receive the time of arrival from a station that calculates the time of arrival, e.g. B. the reference station or the transponder, to receive the first arrival time difference from a station that calculates the first arrival time difference, such. B. the first station, and / or to receive the second arrival time difference from a station that calculates the second arrival time difference, such as. B. the second station. Alternatively, the apparatus can be configured to receive the transmission time stamps and reception time stamps from the respective stations in order to calculate the arrival time, the first arrival time difference and / or the second arrival time difference itself. Optionally, it is possible that the apparatus is part of the transponder and / or the reference station, whereby the apparatus is configured to calculate the arrival time itself and to receive the first arrival time difference by the first station and the second arrival time difference by the second station. It is also possible that the apparatus is part of the first station and / or the second station, whereby the apparatus is configured to determine or calculate a first arrival time difference and / or the second arrival time difference itself and the arrival time difference, for example from the reference station or to receive the transponder.

Embodiments of the apparatus are based on the idea that combining time of arrival and time of arrival difference measurements is very efficient and optimizes accuracy for localizing the transponder. For example, it is advantageous that when combining TOA and TDOA a number of equations to be solved can be maximized and that at the same time errors based on the different clocks of the different stations which are used, for example, to locate the transponder, can be minimized. According to one embodiment, the apparatus is configured to generate a system of equations that includes a first equation, based on the time of arrival, a second equation based on the first time of arrival difference and solve a third equation based on a second time of arrival difference to locate the transponder. It is therefore already possible to locate the transponder with just one reference station, one transponder and two stations for a two-dimensional space. On the basis of the sending time stamps and the receiving time stamps, the first arrival time difference and / or the second arrival time difference can provide a wireless clock adjustment (a wireless clock calibration) in order to achieve a high level of accuracy.

According to one embodiment, the first arrival time difference is based on a difference between first received time stamp information from the first station and second received time stamp information from the first station. The first receive time stamp information describes, for example, with regard to a clock of the first station when the first station receives a first signal sent by the reference station, and the second receive time stamp information of the first station describes, for example, with regard to the clock of the first station, when the first station receives a signal sent by the transponder receives second signal. The second arrival time difference is based, for example, on a difference between first received time stamp information from the second station and second received time stamp information from the second station. According to one embodiment, the first receive time stamp information of the second station describes, for example with regard to a clock of the second station, when the second station receives the first signal sent by the reference station, and the second receive time stamp information of the second station describes, for example, with regard to the clock of the second station, when the second Station receives the second signal sent by the transponder. Thus, the first arrival time difference is assigned, for example, to a difference between reception time stamps of a first signal that is sent by the reference station and received by a first station and a second signal that is sent by the transponder and received by the first station. The second arrival time difference is assigned, for example, to a difference between reception time stamps of a first signal that is sent by the reference station and received by the second station and a second signal that is sent by the transponder and received by the second station. In other words, the first arrival time difference represents, for example, a time difference between reception time stamps of the first signal and the second signal by a first station, and the second arrival time difference represents, for example, a time difference between reception time stamps of the first signal and the second signal by the second station.

According to an embodiment, the first arrival time difference is calculated, for example by the apparatus or another device, using a signal power correction in order to correct the first reception time stamp information of the first station and the second reception time stamp information of the first station. The second arrival time difference is calculated using, for example, signal power correction to correct the first received time stamp information of the second station and the second received time stamp information of the second station. According to one embodiment, the signal power correction that is used to calculate the first arrival time difference and / or the second arrival time difference is configured to at least partially compensate for an influence of a signal power on time stamps of the first station and / or the second station. The signal power correction is obtained prior to the localization of the transponder, e.g. for different signal power levels, e.g. for the stations, e.g. B. the reference station, the transponder, the first station and / or the second station. According to one embodiment, the signal power correction is independent of the station that sends the signal, whereby the signal power correction is based on the first received time stamp information that corresponds to the signal sent by the reference station, and on the second received time stamp information that is assigned to the second signal sent by the transponder, can be applied, but without the need to have knowledge of the station sending the signal received by the first station and / or the second station.

According to one embodiment, the first arrival time difference and / or the second arrival time difference are calculated, for example, by the apparatus or by another device using an offset that describes a time delay between a transmission of the two signals, one by the reference station and one by the Transponder is sent. The offset represents a time synchronization, for example such that a difference in transmission times between the first signal and the second signal is predetermined or can be calculated. For example, if both signals are sent simultaneously, the offset is zero. By using the offset for the calculation of the first time difference of arrival and / or the second time of arrival difference, it is possible to have the calculation based solely on the received time stamp information of the first signal and the second signal at the first station and / or the second station, independently from the transmission time stamp information of the first signal and the second signal.

According to one embodiment, the offset is determined on the basis of the arrival time, on the basis of a first reception time stamp of the transponder and on the basis of a first transmission time stamp of the transponder. The first reception time stamp of the transponder describes, for example, when a first signal sent by the reference station is received by the transponder, and the first transmission time stamp of the transponder describes, for example, when a second signal is sent by the transponder. This exemplary embodiment is based on the basic idea that the reference station sends the first signal and the transponder sends the second signal after it has received the first signal. Thus, the arrival time describes, for example, the time that the first signal needs from the reference station to the transponder, for example the time difference between the first reception time stamp of the transponder and a first transmission time stamp of the reference station, which describes when the first signal is sent by the reference station. Thus, the offset represents, for example, a summation of the arrival time and a difference between the first transmission time stamp of the transponder and the first reception time stamp of the transponder, which describes a computing time of the transponder before the second signal is sent by the transponder. According to one exemplary embodiment, a clock shift correction and / or an antenna delay correction and / or a signal power correction are used to determine the offset. With these corrections it is possible to determine the offset very precisely and thus to achieve a very precise synchronization of a transmission of the first signal and a transmission of the second signal.

According to one embodiment, the clock shift correction used to determine the offset is based on transmission time stamps and reception time stamps, which are related to a third signal that is transmitted by the reference station and received by the transponder, e.g. B. is sent from the reference station to the transponder. Furthermore, the clock shift correction can be based on transmission time stamps and reception time stamps which are related to a first signal which is transmitted by the reference station and received by the transponder. According to one embodiment, the first signal and the third signal, which is used for clock skew correction, have the same signal power levels. Thus, the clock shift correction is based, for example, on a clock shift error which describes a time difference between a difference in transmission time stamps of the first signal and the third signal and a difference in reception time stamps of the first signal and the third signal. According to one embodiment, the clock shift correction can be determined with the same two signals that are used for determining the first arrival time difference and / or the second arrival time difference, plus the third signal, which leads to a very efficient clock shift correction, whereby a very precise synchronization can be achieved .

bestimmt.According to one embodiment, the offset K is according to $$K=TO\mathrm{A.}+\mathrm{\Delta }{T}_{1.2}^T+\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\mathrm{\Delta }{T}_{1.3}^T}\cdot \left(\mathrm{\Delta }{T}_{1.2}^T+{\mathrm{E.}}_1\right)\right)+{\mathrm{E.}}_1+2\mathrm{B.}$$

certainly.

stellt eine Differenz zwischen einem ersten Sendezeitstempel des Transponders, der beschreibt, wann ein zweites Signal durch den Transponder gesendet wird, und einem ersten Empfangszeitstempel des Transponders, der beschreibt, wann ein durch die Referenzstation gesendetes erstes Signal durch den Transponder empfangen wird, dar. Die Abweichung $C_{\mathrm{1,3}}^{RT}$

stellt eine Differenz zwischen einer Differenz von Sendezeitstempeln, die einem Senden zweier Signale mit denselben Signalleistungspegeln zugeordnet sind, die durch die Referenzstation gesendet werden, und einer Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^T$

von Empfangszeitstempeln, die einem Empfang der zwei Signale mit denselben Signalleistungspegeln durch den Transponder zugeordnet sind, dar. Die Differenz von Sendezeitstempeln stellt beispielsweise eine Differenz zwischen einem zweiten Sendezeitstempel der Referenzstation, der beschreibt, wann ein drittes Signal durch die Referenzstation gesendet wird, und einem ersten Sendezeitstempel der Referenzstation, der beschreibt, wann das erste Signal durch die Referenzstation gesendet wird, dar. Die Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^T$

von Empfangszeitstempeln stellt beispielsweise eine Differenz zwischen einem dritten Empfangszeitstempel des Transponders, der beschreibt, wann das dritte Signal, das durch die Referenzstation gesendet wird, durch den Transponder empfangen wird, und einem ersten Empfangszeitstempel des Transponders, der beschreibt, wann das durch die Referenzstation gesendete erste Signal durch den Transponder empfangen wird, dar. Das erste Signal und das dritte Signal weisen beispielsweise dieselben Signalleistungspegel auf. Der Wert E₁ stellt eine Signalleistungskorrektur dar, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, die einer Korrektur von Empfangszeitstempeln des Transponders für empfangene Signale mit einem ersten Signalleistungspegel zugeordnet ist, und der Wert B stellt eine auf den Transponder bezogene Antennenverzögerungskorrektur dar, z. B. einen vorbestimmten Wert. Die Signalleistungskorrektur korrigiert beispielsweise den ersten Empfangszeitstempel des Transponders in Abhängigkeit von dem Signalleistungspegel des ersten Signals. Da Signale, die zu demselben Sendezeitstempel durch dieselbe Station gesendet werden, zu unterschiedlichen Empfangszeitstempeln an derselben Station, die die zwei Signale empfängt, führen können, nähert die Signalleistungskorrektur beispielsweise die zwei verschiedenen Empfangszeitstempel auf einen gemeinsamen Empfangszeitstempel an, der beschreibt, wann ein Referenzsignal mit einem vorbestimmten Referenzsignalleistungspegel empfangen wird. Gemäß einem Ausführungsbeispiel kann die Antennenverzögerungskorrektur Zeitverzögerungen, die einer Station zugeordnet sind, die Signale sendet und/oder empfängt, korrigieren, wobei die Antennenzeitverzögerung beispielsweise eine Zeitdifferenz zwischen einem Empfang eines Signals durch eine Antenne der Station und einem Empfangszeitstempel darstellt, der durch eine Uhr der dem empfangenen Signal zugeordneten Station bestimmt wird. Alternativ oder zusätzlich dazu kann die Antennenverzögerungskorrektur Sendezeitstempel der Station korrigieren. Gemäß einem Ausführungsbeispiel korrigiert die Antennenverzögerungskorrektur eine Zeitverzögerung zwischen einem Sendezeitstempel eines Signals, das durch die Station gesendet wird, die durch die Uhr der Station bestimmt wird, und einer tatsächlichen Zeit, wann das Signal durch die Antenne der Station gesendet wird.The value TOA represents the arrival time, which is corrected for example with regard to the clock shift, corrected with regard to the signal power level and / or corrected with regard to the antenna delay, of the one or more signals that are sent between the reference station and the transponder. The value $\mathrm{\Delta }{T}_{1.2}^T$

represents a difference between a first transmission time stamp of the transponder, which describes when a second signal is transmitted by the transponder, and a first reception time stamp of the transponder, which describes when a first signal transmitted by the reference station is received by the transponder deviation ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T}$

represents a difference between a difference in transmission time stamps associated with transmitting two signals with the same signal power levels transmitted by the reference station and a difference $\mathrm{\Delta }{T}_{1.3}^T$

of reception time stamps, which are assigned to a reception of the two signals with the same signal power levels by the transponder. The difference in transmission time stamps represents, for example, a difference between a second transmission time stamp of the reference station, which describes when a third signal is transmitted by the reference station, and one first transmission time stamp of the reference station, which describes when the first signal is transmitted by the reference station. The difference $\mathrm{\Delta }{T}_{1.3}^T$

of receive time stamps, for example, represents a Difference between a third reception time stamp of the transponder, which describes when the third signal sent by the reference station is received by the transponder, and a first reception time stamp of the transponder, which describes when the first signal sent by the reference station is received by the transponder The first signal and the third signal have the same signal power level, for example. The value E ₁ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the transponder for received signals with a first signal power level, and the value B represents an antenna delay correction related to the transponder, e.g. B. a predetermined value. The signal power correction corrects, for example, the first reception time stamp of the transponder as a function of the signal power level of the first signal. Since signals that are sent with the same transmission time stamp by the same station can lead to different reception time stamps at the same station that receives the two signals, the signal power correction, for example, approximates the two different reception time stamps to a common reception time stamp, which describes when a reference signal is included a predetermined reference signal power level is received. According to one embodiment, the antenna delay correction can correct time delays assigned to a station that sends and / or receives signals, the antenna time delay representing, for example, a time difference between a reception of a signal by an antenna of the station and a reception time stamp indicated by a clock of the station associated with the received signal is determined. Alternatively or additionally, the antenna delay correction can correct the station's transmission time stamp. According to one embodiment, the antenna delay correction corrects a time delay between a transmission time stamp of a signal transmitted by the station, which is determined by the clock of the station, and an actual time when the signal is transmitted by the antenna of the station.

bestimmt. Der Index I, z. B. i∈[1;N], wobei N≥2, stellt eine Nummer einer Station Si dar, bei der die Empfangszeitstempel erhalten werden, die die Empfangszeiten der zwei Signale beschreiben, wobei eines durch die Referenzstation gesendet wird und eines durch den Transponder gesendet wird, und die zum Bestimmen der Differenz $\mathrm{\Delta }{T}_{\mathrm{1,2}}^{Si}$

zwischen den Empfangszeitstempeln verwendet werden. Der Wert E₃ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, dar, die einer Korrektur von Empfangszeitstempeln der Station Si für empfangene Signale mit einem ersten Signalleistungspegel zugeordnet ist. Der Wert E₄ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, dar, die einer Korrektur von Empfangszeitstempeln der Station Si für empfangene Signale mit einem zweiten Signalleistungspegel zugeordnet ist. Der Wert K stellt einen Versatz dar, der eine Zeitverzögerung zwischen einem Senden der zwei Signale beschreibt, wobei eines durch die Referenzstation gesendet wird und eines durch den Transponder gesendet wird. Die Signalleistungskorrektur E₃ korrigiert beispielsweise den ersten Empfangszeitstempel der Station Si in Abhängigkeit von dem Signalleistungspegel des ersten Signals, und die Signalleistungskorrektur E₄ korrigiert beispielsweise den Empfangszeitstempel der Station Si in Abhängigkeit von dem Signalleistungspegel des zweiten Signals. Da die Signalleistungskorrektur beispielsweise unabhängig von der Station ist, die die Signale sendet, können E₃ und E₄ auf eine Mehrzahl von Empfangszeitstempeln derselben empfangenden Station für empfangene Signale mit selben Signalleistungspegeln angewendet werden, wobei E₃ einem ersten Signalleistungspegel entspricht und E₄ einem zweiten Signalleistungspegel entspricht. Gemäß einem Ausführungsbeispiel nähert die Signalleistungskorrektur beispielsweise Empfangszeitstempel an einen einzigen gemeinsamen Empfangszeitstempel an, der beschreibt, wann ein Referenzsignal mit einem vorbestimmten Referenzsignalleistungspegel empfangen würde.According to one embodiment, the first time of arrival difference and the second time of arrival difference are according to $T\mathrm{D.}O{\mathrm{A.}}_i=\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3+K$

certainly. The index I, e.g. B. i∈ [1; N], where N≥2, represents a number of a station Si at which the reception time stamps are obtained which describe the reception times of the two signals, one being sent by the reference station and one by the transponder is sent, and the one to determine the difference $\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}$

used between receive timestamps. The value E ₃ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the station Si for received signals with a first signal power level. The value E ₄ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the station Si for received signals with a second signal power level. The value K represents an offset which describes a time delay between a transmission of the two signals, one being transmitted by the reference station and one being transmitted by the transponder. The signal power correction E ₃ corrects, for example, the first reception time stamp of the station Si depending on the signal power level of the first signal, and the signal power correction E ₄ corrects, for example, the reception time stamp of the station Si depending on the signal power level of the second signal. For example, since the signal power correction is independent of the station sending the signals, E ₃ and E _{4 can be} applied to a plurality of receive time stamps from the same receiving station for received signals with the same signal power levels, where E ₃ corresponds to a first signal power level and E _{4 to} a second Corresponds to the signal power level. According to one exemplary embodiment, the signal power correction approximates the reception time stamp, for example, to a single common reception time stamp that describes when a reference signal with a predetermined reference signal power level would be received.

According to one embodiment, the first arrival time difference is calculated, for example, by the apparatus or by another device using a clock offset correction in order to correct a difference between reception time stamps obtained at the first station and / or for signal power corrections which correct the reception time stamps obtained at the first station, to correct. Furthermore or alternatively, the second arrival time difference is calculated, for example, by the apparatus or another device using a clock offset correction in order to correct a difference between reception time stamps obtained at the second station and / or for signal power corrections which correct the reception time stamps obtained at the second station, to correct. The clock offset correction used to calculate the second time of arrival difference may be the same as e.g. The clock offset correction used to calculate the first time-of-arrival difference, or it may be different. The reception timestamps obtained at the first station and the signal power corrections corresponding to the first station are assigned to a clock of the first station, for example. The reception time stamps that are received at the second station and / or the signal power corrections that are assigned to the second station are assigned to a clock of the second station, for example. Since the clock of the first station and the clock of the second station can differ from each other, a clock offset correction is used to determine, for example, the first arrival time difference and / or the second arrival time difference, which correspond to a common clock such as a clock of the reference station, whereby the apparatus may be configured to locate the transponder based on the first time of arrival difference, the second time of arrival difference corresponding to a common clock rather than two different clocks, whereby the first time of arrival difference is comparable to the second time of arrival difference.

According to one embodiment, the clock shift correction used to calculate the first arrival time difference is based on a transmission time stamp and a reception time stamp, which are related to a third signal that is sent by the reference station and received by the first station, for example sent from the reference station to the first station becomes. Optionally or in addition to this, transmit time stamps and receive time stamps, which are related to a first signal transmitted by the reference station and received by the first station, are used to determine the clock offset correction which is used to calculate the first time difference of arrival. According to one embodiment, the clock shift correction that is used to calculate the second arrival time difference is based on a transmission time stamp and a reception time stamp, which are related to the third signal that is sent by the reference station and received by the second station, for example from the reference station the second station is sent. Optionally or in addition to this, transmit timestamps and receive timestamps related to the first signal transmitted by the reference station and received by the second station can be used to determine the clock shift correction which is used to calculate the second time difference of arrival . According to an embodiment, the first signal is transmitted by the reference station and received by the first station and / or the second station, and the third signal is transmitted by the reference station and received by the first station and / or the second station, the first signal and the third signal have the same signal power levels. Thus, the clock shift correction is based, for example, on a clock shift error which describes a time difference between a difference in transmission time stamps of the first signal and the third signal and a difference in reception time stamps of the first signal and the third signal. According to one embodiment, the clock shift correction can be determined with the same two signals as are used to determine the arrival time, which leads to a very efficient clock shift correction, whereby a very precise synchronization can be achieved.

berechnet. Der Index I, z. B. i∈[1;N], wobei N≥2, stellt eine Nummer einer Station Si dar, bei der die Empfangszeitstempel, die die Empfangszeiten der zwei Signale beschreiben, wobei eines durch die Referenzstation gesendet wird und eines durch den Transponder gesendet wird, und die zum Bestimmen der Differenz $\mathrm{\Delta }{T}_{\mathrm{1,2}}^{Si}$

zwischen den Empfangszeitstempeln verwendet werden, erhalten werden. Die Abweichung $C_{\mathrm{1,3}}^{Si}$

stellt eine Differenz zwischen einer Differenz von Sendezeitstempeln, die einem Senden zweier Signale mit denselben Signalleistungspegeln zugeordnet sind, die durch die Referenzstation gesendet werden, und einer Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^{Si}$

von Empfangszeitstempeln, die einem Empfang der zwei Signale mit denselben Signalleistungspegeln zugeordnet sind, durch die Station Si dar. Die Differenz von Sendezeitstempeln stellt beispielsweise eine Differenz zwischen einem zweiten Sendezeitstempel der Referenzstation, der beschreibt, wann ein drittes Signal durch die Referenzstation gesendet wird, und einem ersten Sendezeitstempel der Referenzstation, der beschreibt, wann ein erstes Signal durch die Referenzstation gesendet wird, dar. Die Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^{Si}$

von Empfangszeitstempeln stellt beispielsweise eine Differenz zwischen einem dritten Empfangszeitstempel der Station Si, der beschreibt, wann das durch die Referenzstation gesendete dritte Signal durch die Station Si empfangen wird, und einem ersten Empfangszeitstempel der Station Si, der beschreibt, wann das durch die Referenzstation gesendete erste Signal durch die Station Si empfangen wird, dar. Das erste Signal und das dritte Signal weisen dieselben Signalleistungspegel auf. Der Wert E₃ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, dar, die einer Korrektur von Empfangszeitstempeln der Station Si für empfangene Signale mit einem ersten Signalleistungspegel zugeordnet ist. Der Wert E₄ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, dar, die einer Korrektur von Empfangszeitstempeln der Station Si für empfangene Signale mit einem zweiten Signalleistungspegel zugeordnet ist. Der Wert K stellt einen Versatz dar, der eine Zeitverzögerung zwischen einem Senden der zwei Signale beschreibt, wobei eines durch die Referenzstation gesendet wird und eines durch den Transponder gesendet wird. Die Signalleistungskorrektur kann Funktionalitäten und/oder Merkmale aufweisen, wie sie oben bezüglich Signalleistungskorrekturen beschrieben wurden.According to one embodiment, the first time of arrival difference and the second time of arrival difference are according to $$T\mathrm{D.}O{\mathrm{A.}}_i=\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}+\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{S.}i}}{\mathrm{\Delta }{T}_{1.3}^{\mathrm{S.}i}}\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}+{\mathrm{E.}}_3-{\mathrm{E.}}_{\mathrm{4th}}\right)\right)-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3+K$$

calculated. The index I, e.g. B. i∈ [1; N], where N≥2, represents a number of a station Si in which the receive time stamps that describe the reception times of the two signals, one being sent by the reference station and one being sent by the transponder , and those for determining the difference $\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}$

used between the received timestamps. The deviation ${\mathrm{C.}}_{1.3}^{\mathrm{S.}i}$

represents a difference between a difference in transmission time stamps associated with transmitting two signals with the same signal power levels transmitted by the reference station and a difference $\mathrm{\Delta }{T}_{1.3}^{\mathrm{S.}i}$

of reception time stamps, which are assigned to a reception of the two signals with the same signal power levels, by the station Si. The difference of transmission time stamps represents, for example, a difference between a second transmission time stamp of the reference station, which describes when a third signal is transmitted by the reference station, and a first transmission time stamp of the reference station, which describes when a first signal is sent by the reference station. The difference $\mathrm{\Delta }{T}_{1.3}^{\mathrm{S.}i}$

of reception time stamps represents a difference between a third reception time stamp of the station Si, which describes when the third signal sent by the reference station is received by the station Si, and a first reception time stamp of the station Si, which describes when the first signal sent by the reference station Signal received by the station Si. The first signal and the third signals have the same signal power levels. The value E ₃ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the station Si for received signals with a first signal power level. The value E ₄ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the station Si for received signals with a second signal power level. The value K represents an offset which describes a time delay between a transmission of the two signals, one being transmitted by the reference station and one being transmitted by the transponder. The signal power correction can have functionalities and / or features as described above with regard to signal power corrections.

berechnet, wobei der Index i, z. B. i∈[1;N], wobei N≥2, eine Nummer einer Station Si darstellt, bei der die Empfangszeitstempel, die die Empfangszeiten der zwei Signale beschreiben, wobei eines durch die Referenzstation gesendet wird und eines durch den Transponder gesendet wird, und die zum Bestimmen der Differenz $\mathrm{\Delta }{T}_{\mathrm{1,2}}^{Si}$

zwischen den Empfangszeitstempeln verwendet werden, erhalten werden. Die Abweichung $C_{\mathrm{1,3}}^{Si}$

stellt eine Differenz zwischen einer Differenz von Sendezeitstempeln, die einem Senden zweier Signale mit denselben Signalleistungspegeln zugeordnet sind, die durch die Referenzstation gesendet werden, und einer Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^{Si}$

von Empfangszeitstempeln, die einem Empfang der zwei Signale mit denselben Signalleistungspegeln zugeordnet sind, durch die Station Si dar. Die Differenz von Sendezeitstempeln stellt beispielsweise eine Differenz zwischen einem zweiten Sendezeitstempel der Referenzstation, der beschreibt, wann ein drittes Signal durch die Referenzstation gesendet wird, und einem ersten Sendezeitstempel der Referenzstation, der beschreibt, wann ein erstes Signal durch die Referenzstation gesendet wird, dar. Die Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^{Si}$

von Empfangszeitstempeln stellt beispielsweise eine Differenz zwischen einem dritten Empfangszeitstempel der Station Si, der beschreibt, wann das durch die Referenzschätzung gesendete dritte Signal durch die Station Si empfangen wird, und einem ersten Empfangszeitstempel der Station Si, der beschreibt, wann das durch die Referenzstation gesendete erste Signal durch die Station Si empfangen wird, dar. Das erste Signal und das dritte Signal weisen dieselben Signalleistungspegel auf. Der Wert E₁ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, dar, die einer Korrektur von Empfangszeitstempeln des Transponders für empfangene Signale mit einem ersten Signalleistungspegel zugeordnet ist. Der Wert E₂ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, dar, die einer Korrektur von Empfangszeitstempeln der Referenzstation für empfangene Signale mit einem zweiten Signalleistungspegel zugeordnet ist. Der Wert E₃ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, dar, die einer Korrektur von Empfangszeitstempeln der Station Si für empfangene Signale mit einem ersten Signalleistungspegel zugeordnet ist. Der Wert E₄ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, dar, die einer Korrektur von Empfangszeitstempeln der Station Si für empfangene Signale mit einem zweiten Signalleistungspegel zugeordnet ist. Der Wert $\mathrm{\Delta }{T}_{\mathrm{1,2}}^T$

stellt eine Differenz zwischen einem ersten Sendezeitstempel des Transponders, der beschreibt, wann ein zweites Signal durch den Transponder gesendet wird, und einem ersten Empfangszeitstempel des Transponders, der beschreibt, wann ein durch die Referenzstation gesendetes erstes Signal durch den Transponder empfangen wird. Die Abweichung $C_{\mathrm{1,3}}^{RT}$

stellt eine Differenz zwischen einer Differenz von Sendezeitstempeln, die einem Senden zweier Signale, die dieselben Signalleistungspegel aufweisen und durch die Referenzstation gesendet werden, zugeordnet sind, und einer Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^T$

von Empfangszeitstempeln, die einem Empfang der zwei Signale, die dieselben Signalleistungspegel aufweisen, durch den Transponder zugeordnet sind, dar. Die Differenz von Sendezeitstempeln stellt beispielsweise eine Differenz zwischen einem zweiten Sendezeitstempel der Referenzstation, der beschreibt, wann ein drittes Signal durch die Referenzstation gesendet wird, und einem ersten Sendezeitstempel der Referenzstation, der beschreibt, wann ein erstes Signal durch die Referenzstation gesendet wird, dar. Die Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^T$

von Empfangszeitstempeln stellt beispielsweise eine Differenz zwischen einem dritten Empfangszeitstempel des Transponders, der beschreibt, wann das durch die Referenzstation gesendete dritte Signal durch den Transponder empfangen wird, und einem ersten Empfangszeitstempel des Transponders, der beschreibt, wann das durch die Referenzstation gesendete erste Signal durch den Transponder empfangen wird, dar; das erste Signal und das dritte Signal weisen dieselben Signalleistungspegel auf. Der Wert $\mathrm{\Delta }{T}_{\mathrm{1,2}}^R$

stellt eine Differenz zwischen einem ersten Empfangszeitstempel der Referenzstation, der beschreibt, wann das durch den Transponder gesendete zweite Signal durch die Referenzstation empfangen wird, und einem ersten Sendezeitstempel der Referenzstation, der beschreibt, wann das erste Signal durch die Referenzstation gesendet wird, dar. Der Wert A stellt eine auf die Referenzstation bezogene Antennenverzögerungskorrektur dar, z.B. einen vorbestimmten Wert, und der Wert B stellt eine auf den Transponder bezogene Antennenverzögerungskorrektur dar, z.B. einen vorbestimmten Wert.The first time of arrival difference and the second time of arrival difference are calculated according to $$\begin{array}{c}T\mathrm{D.}O{\mathrm{A.}}_i=\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{S.}i}}{\mathrm{\Delta }{T}_{1.3}^{\mathrm{S.}i}}\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}+{\mathrm{E.}}_3-{\mathrm{E.}}_{\mathrm{4th}}\right)\right)+0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^T+\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\mathrm{\Delta }{T}_{1.3}^T}\cdot \left(\mathrm{\Delta }{T}_{1.2}^T+{\mathrm{E.}}_1\right)\right)\\ +\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}+0.5\cdot \mathrm{\Delta }{T}_{1.2}^{\mathrm{R.}}-\mathrm{A.}+\mathrm{B.}+0.5\cdot \left({\mathrm{E.}}_1-{\mathrm{E.}}_2\right)-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3\end{array}$$

calculated, where the index i, e.g. B. i∈ [1; N], where N≥2, represents a number of a station Si, in which the receive time stamps, which describe the reception times of the two signals, one being sent by the reference station and one being sent by the transponder, and those for determining the difference $\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}$

used between the received timestamps. The deviation ${\mathrm{C.}}_{1.3}^{\mathrm{S.}i}$

represents a difference between a difference in transmission time stamps associated with transmitting two signals with the same signal power levels transmitted by the reference station and a difference $\mathrm{\Delta }{T}_{1.3}^{\mathrm{S.}i}$

of reception time stamps, which are assigned to a reception of the two signals with the same signal power levels, by the station Si. The difference of transmission time stamps represents, for example, a difference between a second transmission time stamp of the reference station, which describes when a third signal is transmitted by the reference station, and a first transmission time stamp of the reference station, the describes when a first signal is sent by the reference station. The difference $\mathrm{\Delta }{T}_{1.3}^{\mathrm{S.}i}$

of reception time stamps represents a difference between a third reception time stamp of the station Si, which describes when the third signal sent by the reference estimation is received by the station Si, and a first reception time stamp of the station Si, which describes when the first signal sent by the reference station Signal is received by the station Si. The first signal and the third signal have the same signal power levels. The value E ₁ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the transponder for received signals with a first signal power level. The value E ₂ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the reference station for received signals with a second signal power level. The value E ₃ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the station Si for received signals with a first signal power level. The value E ₄ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the station Si for received signals with a second signal power level. The value $\mathrm{\Delta }{T}_{1.2}^T$

represents a difference between a first transmission time stamp of the transponder, which describes when a second signal is transmitted by the transponder, and a first reception time stamp of the transponder, which describes when a first signal transmitted by the reference station is received by the transponder. The deviation ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T}$

represents a difference between a difference in transmission time stamps associated with transmission of two signals having the same signal power levels and transmitted by the reference station and a difference $\mathrm{\Delta }{T}_{1.3}^T$

of reception time stamps associated with a reception of the two signals having the same signal power level by the transponder. The difference in transmission time stamps represents, for example, a difference between a second transmission time stamp of the reference station, which describes when a third signal is transmitted by the reference station , and a first transmission time stamp of the reference station, which describes when a first signal is transmitted by the reference station. The difference $\mathrm{\Delta }{T}_{1.3}^T$

of reception time stamps represents a difference between a third reception time stamp of the transponder, which describes when the third signal sent by the reference station is received by the transponder, and a first reception time stamp of the transponder, which describes when the first signal sent by the reference station is received by the Transponder is received; the first signal and the third signal have the same signal power levels. The value $\mathrm{\Delta }{T}_{1.2}^{\mathrm{R.}}$

represents a difference between a first reception time stamp of the reference station, which describes when the second signal transmitted by the transponder is received by the reference station, and a first transmission time stamp of the reference station, which describes when the first signal is transmitted by the reference station Value A represents an antenna delay correction related to the reference station, for example a predetermined value, and value B represents an antenna delay correction related to the transponder, for example a predetermined value.

According to one embodiment, the arrival time is based on a transmission time stamp and a reception time stamp of a first signal that is sent by the reference station and received by the transponder, and on the basis of a transmission time stamp and a reception time stamp of a second signal that is sent by the transponder and received by the receiving station is received. Thus, the first signal is sent from the reference station to the transponder, and the second signal is sent back from the transponder to the reference station, which is, for example, a two-way ranging (TWR). Thus, with knowledge of the transmission time stamp and the reception time stamp of the first signal and the second signal, the arrival time can be calculated very precisely. To improve the accuracy in calculating the arrival time, a clock offset correction and / or a signal power correction and / or an antenna delay correction can be used to correct the transmission time stamps and / or the reception time stamps of the first signal and the second signal.

berechnet. Der Wert $T_1^R$

stellt einen ersten Sendezeitstempel der Referenzstation dar, der beschreibt, wann ein erstes Signal von der Referenzstation gesendet wird. Der Wert $T_1^T$

stellt einen ersten Empfangszeitstempel des Transponders dar, der beschreibt, wann das von der Referenzstation gesendete erste Signal durch den Transponder empfangen wird. Der Wert $T_2^T$

stellt einen ersten Sendezeitstempel des Transponders dar, der beschreibt, wann ein zweites Signal von dem Transponder gesendet wird. Der Wert $T_2^R$

stellt einen ersten Empfangszeitstempel der Referenzstation dar, der beschreibt, wann das von dem Transponder gesendete zweite Signal durch die Referenzstation empfangen wird. Der Wert E₁ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert dar, der einem tatsächlichen Signalleistungspegel zugeordnet ist, die einer Korrektur des ersten Empfangszeitstempels $T_1^T$

des Transponders zugeordnet ist, auf der Basis eines ersten Signalleistungspegels des ersten Signals. Der Wert E₂ stellt eine Signalleistungskorrektur, z. B. einen vorbestimmten Wert dar, der einem tatsächlichen Signalleistungspegel zugeordnet ist, die einer Korrektur des ersten Empfangszeitstempels $T_2^R$

der Referenzstation zugeordnet ist, auf der Basis eines Signalleistungspegels des zweiten Signals. Der Wert A stellt eine auf die Referenzstation bezogene Antennenverzögerungskorrektur dar, ist z. B. ein vorbestimmter Wert, und der Wert B stellt eine auf den Transponder bezogene Antennenverzögerungskorrektur dar, ist z. B. ein vorbestimmter Wert. Die Signalleistungskorrektur kann Funktionalitäten und/oder Merkmale aufweisen, wie sie oben in Bezug auf Signalleistungskorrekturen beschrieben wurden. Die Antennenverzögerungskorrektur kann Funktionalitäten und/oder Merkmale aufweisen, wie sie oben in Bezug auf eine Antennenverzögerungskorrektur beschrieben wurden.According to one embodiment, the arrival time TOA is according to $$TO\mathrm{A.}=0.5\cdot \left(\left({\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="DE102019202009A1\_0214.png,DE102019202009A1\_0215.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^{\mathrm{R.}}-{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="DE102019202009A1\_0217.png,DE102019202009A1\_0218.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^{\mathrm{R.}}\right)-\left(T_2^T-T_1^T\right)-{\mathrm{E.}}_1-{\mathrm{E.}}_2\right)-\mathrm{A.}-\mathrm{B.}$$

calculated. The value $T_1^{\mathrm{R.}}$

represents a first transmission time stamp of the reference station, which describes when a first signal is transmitted from the reference station. The value $T_1^T$

represents a first reception time stamp of the transponder, which describes when the first signal sent by the reference station is received by the transponder. The value $T_2^T$

represents a first transmission time stamp of the transponder, which describes when a second signal is transmitted by the transponder. The value $T_2^{\mathrm{R.}}$

represents a first reception time stamp of the reference station, which describes when the second signal sent by the transponder is received by the reference station. The value E ₁ represents a signal power correction, e.g. B. represents a predetermined value which is assigned to an actual signal power level, which is a correction of the first reception time stamp $T_1^T$

of the transponder is assigned based on a first signal power level of the first signal. The value E ₂ represents a signal power correction, e.g. B. represents a predetermined value which is assigned to an actual signal power level, which is a correction of the first reception time stamp $T_2^{\mathrm{R.}}$

associated with the reference station based on a signal power level of the second signal. The value A represents an antenna delay correction related to the reference station; B. a predetermined value, and the value B represents an antenna delay correction related to the transponder, is e.g. B. a predetermined value. The signal power correction can have functionalities and / or features as described above with regard to signal power corrections. The antenna delay correction can have functionalities and / or features as described above in relation to an antenna delay correction.

According to one embodiment, the clock offset correction used to calculate the arrival time is based on a transmission time stamp and a reception time stamp related to a third signal transmitted by the reference station and received by the transponder. Optionally or additionally, transmission time stamps and reception time stamps, which are related to a first signal which is transmitted by the reference station and received by the transponder, can be used to determine the clock shift correction. The first signal and the third signal have the same signal power level, for example. The clock shift correction is thus based, for example, on a clock shift error which describes a difference in time of arrival between a difference in transmission time stamps of the first signal and the third signal and a difference in reception time stamps of the first signal and the third signal. According to one embodiment, the clock shift correction can be determined with the same two signals as are used to determine the first time of arrival difference and / or the second time of arrival difference, which leads to a very efficient clock shift correction, whereby a very precise synchronization can be achieved.

According to one embodiment, the arrival time is calculated using a clock offset correction in order to correct a difference between a first transmission time stamp of the transponder and a first reception time stamp of the transponder. The first transmission time stamp of the transponder describes, for example, when a second signal is sent by the transponder, and the first reception time stamp of the transponder describes, for example, when a first signal sent by the reference station is received by the transponder. According to one embodiment, a signal power correction which corrects the first reception time stamp received at the transponder is carried out in order to calculate the arrival time. Furthermore, a signal power correction, which corrects a first reception time stamp of the reference station, which describes when the second signal is received by the reference station, is carried out in order to calculate the time of arrival. Thus, the influence of a signal power level on the receive time stamp and an influence of a clock shift, which is caused by a difference between the clock of the reference station and a clock of the transponder, can be at least partially compensated for by the clock shift correction and / or the signal power correction. Thus it is possible to determine the arrival time very precisely.

berechnet.According to one embodiment, the arrival time TOA is according to $$TO\mathrm{A.}=0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{R.}}-\mathrm{\Delta }{T}_{1.2}^T-\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\mathrm{\Delta }{T}_{1.3}^T}\cdot \left(\mathrm{\Delta }{T}_{1.2}^T+{\mathrm{E.}}_1\right)-{\mathrm{E.}}_2-{\mathrm{E.}}_1\right)+Z$$

calculated.

stellt eine Differenz zwischen einer Differenz von Sendezeitstempeln, die einem Senden zweier Signale zugeordnet sind, die dieselben Signalleistungspegel aufweisen und durch die Referenzstation gesendet werden, und einer Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^T$

von Empfangszeitstempeln, die einem Empfang der zwei Signale, die dieselben Signalleistungspegel aufweisen, durch den Transponder zugeordnet sind, dar. Die Differenz von Sendezeitstempeln stellt beispielsweise eine Differenz zwischen einem zweiten Sendezeitstempel der Referenzstation, der beschreibt, wann ein drittes Signal durch die Referenzstation gesendet wird, und einem ersten Sendezeitstempel der Referenzstation, der beschreibt, wann ein erstes Signal durch die Referenzstation gesendet wird, dar. Die Differenz $\mathrm{\Delta }{T}_{\mathrm{1,3}}^T$

von Empfangszeitstempeln stellt eine Differenz zwischen einem dritten Empfangszeitstempel des Transponders, der beschreibt, wann das durch die Referenzstation gesendete dritte Signal durch den Transponder empfangen wird, und einem ersten Empfangszeitstempel des Transponders, der beschreibt, wann das durch die Referenzstation gesendete erste Signal durch den Transponder empfangen wird, dar. Das erste Signal und das dritte Signal weisen dieselben Signalleistungspegel auf. Der Wert $\mathrm{\Delta }{T}_{\mathrm{1,2}}^R$

stellt eine Differenz zwischen einem ersten Empfangszeitstempel der Referenzstation, der beschreibt, wann das durch den Transponder gesendete zweite Signal durch die Referenzstation empfangen wird, und einem ersten Sendezeitstempel der Referenzstation, der beschreibt, wann das erste Signal durch die Referenzstation gesendet wird, dar. Der Wert $\mathrm{\Delta }{T}_{\mathrm{1,2}}^T$

stellt eine Differenz zwischen einem ersten Sendezeitstempel des Transponders, der beschreibt, wann ein zweites Signal durch den Transponder gesendet wird, und einem ersten Empfangszeitstempel des Transponders, der beschreibt, wann ein durch die Referenzstation gesendetes erstes Signal durch den Transponder empfangen wird, dar. Der Wert E₁ stellt eine Signalleistungskorrektur dar, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, die einer Korrektur von Empfangszeitstempeln des Transponders für empfangene Signale mit einem ersten Signalleistungspegel zugeordnet ist. Der Wert E₂ stellt eine Signalleistungskorrektur dar, z. B. einen vorbestimmten Wert, der einem tatsächlichen Signalleistungspegel zugeordnet ist, die einer Korrektur von Empfangszeitstempeln der Referenzstation für empfangene Signale mit einem zweiten Signalleistungspegel zugeordnet ist, und der Wert Z stellt einen konstanten Versatz dar, z. B. eine Nulllinie für die Signalleistung und den Antennenversatz. Z kann auch gleich null betragen.The deviation ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T}$

represents a difference between a difference in transmission time stamps associated with transmission of two signals having the same signal power levels and transmitted by the reference station and a difference $\mathrm{\Delta }{T}_{1.3}^T$

of reception time stamps associated with a reception of the two signals having the same signal power level by the transponder. The difference in transmission time stamps represents, for example, a difference between a second transmission time stamp of the reference station, which describes when a third signal is transmitted by the reference station , and a first transmission time stamp of the reference station, which describes when a first signal is transmitted by the reference station. The difference $\mathrm{\Delta }{T}_{1.3}^T$

of reception time stamps represents a difference between a third reception time stamp of the transponder, which describes when the third signal sent by the reference station is received by the transponder, and a first reception time stamp of the transponder, which describes when the first signal sent by the reference station is received by the transponder is received. The first signal and the third signal have the same signal power levels. The value $\mathrm{\Delta }{T}_{1.2}^{\mathrm{R.}}$

represents a difference between a first reception time stamp of the reference station, which describes when the second signal transmitted by the transponder is received by the reference station, and a first transmission time stamp of the reference station, which describes when the first signal is transmitted by the reference station value $\mathrm{\Delta }{T}_{1.2}^T$

represents a difference between a first transmission time stamp of the transponder, which describes when a second signal is transmitted by the transponder, and a first reception time stamp of the transponder, which describes when a first signal transmitted by the reference station is received by the transponder Value E ₁ represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, a correction of reception time stamps of the transponder for received signals with a is assigned to the first signal power level. The value E ₂ represents a signal power correction, e.g. B. a predetermined value associated with an actual signal power level associated with a correction of receive time stamps of the reference station for received signals with a second signal power level, and the value Z represents a constant offset, e.g. B. a zero line for the signal power and the antenna offset. Z can also be zero.

According to one embodiment, the apparatus is configured to calculate the position of the transponder using distance information that describes a distance between the reference station and the transponder based on the arrival time. Furthermore, the apparatus is configured, for example, to use first distance difference information which describes a difference between a distance between the reference station and the first station and a distance between the transponder and the first station, which is based on the first arrival time difference. The apparatus can be used to use second distance difference information describing a difference between a distance between the reference station and the second station and a distance between the transponder and the second station based on the second time of arrival difference. Information about absolute or relative positions of the reference station, the first station and the second station can be used by the apparatus to calculate the position of the transponder. Thus, the apparatus can be configured to, on the basis of the information about the positions of the reference station, the first station and the second station, an overlap region or an overlap point of the distance information describing a distance between the reference station and the transponder, the first distance difference information and the determine second distance difference information. This overlap region or this overlap point can represent the position of the transponder, for example. Thus, using the arrival time, the first arrival time difference and the second arrival time difference can lead to a two-dimensional position of the transponder which is calculated by the apparatus.

According to one exemplary embodiment, the apparatus is configured to calculate the position of the transponder using an intersection of a first circle or a first sphere, a first hyperbola or a first hyperboloid and a second hyperbola or a second hyperboloid. The intersection of the first circle, the first hyperbola and the second hyperbola leads, for example, to a two-dimensional position of the transponder, and the intersection of the sphere, the first hyperboloid and the second hyperboloid leads, for example, to a three-dimensional position of the transponder. The sphere can also represent a spherical surface, the first hyperboloid can also represent a hyperboloid surface and the second hyperboloid can also represent a second hyperboloid surface. The first circle or the first ball is determined, for example, by information about a position of the reference station and the arrival time TOA, from which a distance that can be used as a radius can be derived. Thus, the position of the reference station represents, for example, a center of the first circle or the sphere, and the arrival time defines, for example, the radius of the first circle or the first sphere. The first hyperbola or the first hyperboloid is determined, for example, by information about a position of the reference station and the first station and the first arrival time difference, from which a difference in distance between points of the first hyperbola or the first hyperboloid from the reference station and the first station can be derived. The second hyperbola or the second hyperboloid can be determined by information on a position of the reference station and the second station and the second arrival time difference, of which a distance difference from points of the second Hyperbola or the second hyperboloid can be derived from the reference station and the second station.

According to one embodiment, the apparatus is configured to solve a system of three or more equations in order to calculate the position of the transponder. A first of the equations describes, for example, a first circle or a first sphere which is centered at a position of the reference station, a radius of the first circle or the first sphere being determined by the time of arrival. This is based on the basic idea that the arrival time can represent a distance between the reference station and the transponder. A second of the equations describes, for example, a first hyperbola or a first hyperboloid, the foci of which are located at a position of the reference station and at a position of the first station. An absolute difference of distances between points of the first hyperbola or the first hyperboloid from the foci is determined, for example, by the first difference in arrival time. This is based on the basic idea that the first arrival time difference can represent a distance difference between the distance of the reference station from the transponder and a distance between the second station and the transponder. A third of the equations describes, for example, a second hyperbola or a second hyperboloid, the foci of which are located at a position of the reference station and at a position of the second station. An absolute difference of distances between points of the second hyperbola or the second hyperboloid from the foci is determined, for example, by the second difference in arrival time. This is based, for example, on the basic idea that the second arrival time difference can represent a distance difference between a distance of the reference station from the transponder and a distance of the second station from the transponder. According to one embodiment, the apparatus is configured to use information about absolute or relative positions of the reference stations of the first station and the second station to solve the system of three or more equations in order to calculate the position of the transponder.

According to one embodiment, the apparatus is configured to determine the position of the transponder using a multiplication of the flight time by a propagation speed of a signal using a multiplication of the first arrival time difference with the propagation speed of the signal and using a multiplication of the second arrival time difference with the propagation time of the signal to calculate the basis of lateration. The speed of propagation of the signal represents, for example, the speed of light. This is based on the basic idea that time distances that are multiplied by the speed of propagation of the signal can represent distances in a two-dimensional and / or three-dimensional space, on the basis of which the position of the transponder is calculated by the apparatus can be, for example, using information on a position of the reference station, the first station and the second station.

According to one embodiment, the multiplication of the flight time by a propagation speed of the signal represents a distance between the reference station and the transponder. The multiplication of the first arrival time difference by the propagation speed of the signal represents, for example, a difference between a distance between the reference station and the first station and a distance between the transponder and the first station.

The multiplication of the second arrival time difference with the propagation speed of the signal represents, for example, a difference between a distance between the reference station and the second station and a distance between the transponder and the second station. Thus, for example, the multiplication of the flight time with the propagation speed of the signal can be achieved with the Distance between the reference station and the transponder can be compensated, the multiplication of the first arrival time difference with the speed of propagation of the signal can be compensated with the difference between the distance between the reference station and the first station and the distance between the transponder and the first station, and the multiplication the second arrival time difference with the propagation speed of the signal can be compared to the difference between the distance between the reference station and the second station and the distance between be balanced between the transponder and the second station. Thus, for example, a system of equations can be achieved which can be solved by the apparatus using information about absolute or relative positions of the reference station, the first station and the second station in order to calculate the position of the transponder.

und/oder $$\begin{array}{l}TO{A}_n\cdot c_0=\sqrt{{\left(x_{R_n}-x_T\right)}^2+{\left(y_{R_n}-y_T\right)}^2+{\left(z_{R_n}-z_T\right)}^2},\text{ und}\\ \begin{array}{ccc}& & TDO{A}_i\cdot c_0=\sqrt{{\left(x_T-x_{Si}\right)}^2+{\left(y_T-y_{Si}\right)}^2+{\left(z_T-z_{Si}\right)}^2}\end{array}\\ \begin{array}{cccc}& & & -\sqrt{{\left(x_{R_n}-x_{Si}\right)}^2+{\left(y_{R_n}-y_{Si}\right)}^2+{\left(z_{R_n}-z_{Si}\right)}^2}\end{array}\end{array}$$

zu berechnen.According to one embodiment, the apparatus is configured to determine the position of the transponder by solving a system of equations according to $$\begin{array}{l}TO\mathrm{A.}\cdot c_0=\sqrt{{\left(x_{\mathrm{R.}}-x_T\right)}^2+{\left(y_{\mathrm{R.}}-y_T\right)}^2},\text{and}\\ \begin{array}{ccc}& & {\text{TDOA}}_i\cdot c_0=\sqrt{{\left(x_T-x_{\mathrm{S.}i}\right)}^2+{\left(y_T-y_{\mathrm{S.}i}\right)}^2}-\sqrt{{\left(x_{\mathrm{R.}}-x_{\mathrm{S.}i}\right)}^2+{\left(y_{\mathrm{R.}}-y_{\mathrm{S.}i}\right)}^2}\end{array}\end{array}$$

and or $$\begin{array}{l}TO{\mathrm{A.}}_n\cdot c_0=\sqrt{{\left(x_{{\mathrm{R.}}_n}-x_T\right)}^2+{\left(y_{{\mathrm{R.}}_n}-y_T\right)}^2+{\left(z_{{\mathrm{R.}}_n}-z_T\right)}^2},\text{and}\\ \begin{array}{ccc}& & T\mathrm{D.}O{\mathrm{A.}}_i\cdot c_0=\sqrt{{\left(x_T-x_{\mathrm{S.}i}\right)}^2+{\left(y_T-y_{\mathrm{S.}i}\right)}^2+{\left(z_T-z_{\mathrm{S.}i}\right)}^2}\end{array}\\ \begin{array}{cccc}& & & -\sqrt{{\left(x_{{\mathrm{R.}}_n}-x_{\mathrm{S.}i}\right)}^2+{\left(y_{{\mathrm{R.}}_n}-y_{\mathrm{S.}i}\right)}^2+{\left(z_{{\mathrm{R.}}_n}-z_{\mathrm{S.}i}\right)}^2}\end{array}\end{array}$$

to calculate.

zwischen den Empfangszeitstempeln verwendet werden, erhalten werden. Der Index n, z. B. n∈[1;N], wobei N≥1 oder N≥2, stellt eine Nummer einer Referenzstation R dar. Falls mehr als eine TOA bestimmt wird, wird beispielsweise mehr als eine Referenzstation verwendet. Somit wird beispielsweise zwischen jeder Referenzstation und dem Transponder eine andere TOA bestimmt. The value TOA represents the arrival time. The value TDOA represents the arrival time difference, and the value c ₀ represents a propagation speed of a signal. The value x represents a first coordinate in a 3D space or in a 2D space, the value y represents a second coordinate in a 3D space or in a 2D space and the value z represents a third coordinate in a 3D space. The index R indicates a reference station, the index T indicates a transponder and the index Si indicates an i-th station. According to one embodiment, the index i, e.g. B. i∈ [1; N], where N≥2, a number of a station Si, in which the receive time stamps that describe the reception times of the two signals, one being sent by the reference station and one being sent by the transponder, and those for determining the difference $\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}i}$

used between the received timestamps. The index n, e.g. B. n∈ [1; N], where N≥1 or N≥2, represents a number of a reference station R. If more than one TOA is determined, more than one reference station is used, for example. Thus, for example, a different TOA is determined between each reference station and the transponder.

According to an exemplary embodiment, the apparatus is configured to provide first transmission time stamp information relating to a clock of the reference station, the reference station, which describes when the reference station transmits a first signal with a first signal power level, first reception time stamp information of the first station which describes, relating to a clock of the first Station, when the first station receives the first signal sent by the reference station, first reception time stamp information of the second station, which describes, with respect to a clock of the second station, when the second station receives the first signal sent by the reference station, and first reception time stamp information of the transponder, which describe, with respect to a clock of the transponder, when the transponder receives the first signal sent by the reference station. Additionally or alternatively, the apparatus is configured to send first transmission time stamp information relating to a clock of the transponder, the transponder, which describes when the transponder sends a second signal, e.g. B. the signal power level of the second signal can be the first signal power level or, alternatively, a second signal power level, second reception time stamp information of the first station, which describes, with respect to a clock of the first station, when the first station receives the second signal sent by the transponder, first reception time stamp information the second station, which describes, with respect to a clock of the second station, when the second station receives the second signal sent by the transponder, and first reception time stamp information of the reference station, which describes, with respect to a clock of the reference station, when the reference station receives the signal sent by the transponder receiving second signal. Additionally or alternatively, the apparatus is configured to send second transmission time stamp information relating to a clock of the reference station, the reference station, which describes when the reference station transmits a third signal with the first signal power level, third reception time stamp information of the first station, which describes, relating to a clock of the first station, when the first station receives the third signal sent by the reference station, third reception time stamp information of the second station, which describes, with respect to a clock of the second station, when the second station receives the third signal sent by the reference station, and second reception time stamp information of the transponder which describe how to receive with respect to a clock of the transponder when the transponder receives the third signal sent by the reference station.

According to one embodiment, the apparatus is configured to obtain a first signal power correction for correcting the first received time stamp information of the transponder and the second received time stamp information of the transponder based on the first signal power level of the first and third signals. Since the first signal and the third signal have the same signal power level and since the first reception time stamp information of the transponder and the second reception time stamp information of the transponder both correspond to a clock of the transponder, both the first reception time stamp information and the second reception time stamp information of the transponder can be corrected using the same first signal power correction. For example, the apparatus is configured to obtain a second signal power correction for correcting the first received time stamp information of the reference station based on a signal power level of the second signal. Further, for example, the apparatus is configured to obtain a third signal power correction for correcting the first received time stamp information of the first station and the third received time stamp information of the first station based on the first signal power level of the first and third signals. Since the first signal and the third signal have the same signal power level, and since the first reception time stamp information of the first station and the third reception time stamp information of the first station both correspond to a clock of the first station, the third signal power correction can correct the first reception time stamp information as well as the third reception time stamp information of the first station. The apparatus is configured, for example, to have a fourth Signal power correction for correcting the second reception time stamp information of the first station based on a signal power level of the second signal. According to one embodiment, the apparatus is configured to receive a fifth signal power correction for correcting the first received time stamp information of the second station and the third received time stamp information of the second station on the basis of the first signal power level of the first and third signals, while the apparatus can be configured to obtain a sixth signal power correction for correcting the second reception time stamp information of the second station based on the signal power level of the second signal. Furthermore, the apparatus can be configured to use the signal power corrections to correct respective time stamp information. The first receive time stamp information of the transponder, the second receive time stamp information of the transponder, the first receive time stamp information of the first station, the third receive time stamp information of the first station, the first receive time stamp information of the second station and the third receive time stamp information of the second station are also based on the first signal power level of the first and third Signal, the respective time stamp information can be corrected with different signal power corrections based on the station receiving the first and third signals. Thus, for example, the signal power correction depends on the station receiving a signal and depends on the signal power level of the received signal. For example, signal power corrections may be applied to any received timestamp information used by the apparatus or by a device that calculates the TOA, the first time difference of arrival, and / or a second time difference of arrival for the apparatus. Thus, the apparatus is configured to reduce an influence of various signal power levels from signals used to locate the transponder.

According to one embodiment, the first signal power correction is related to the transponder, the second signal power correction is related to the reference station, the third signal power correction and the fourth signal power correction are related to the first station and the fifth signal power correction and the sixth signal power correction are related to the second station. The signal power correction is, for example, a power correction curve or information describing a power correction curve, or a database comprising one, two or a plurality of time stamping power correction values, each time stamping power correction value being associated with a signal power level of a signal, e.g. a signal received by a station, for which the timestamp performance correction information is determined. The first signal power correction, the second signal power correction, the third signal power correction, the fourth signal power correction, the fifth signal power correction and the sixth signal power correction are based on a deviation between a first time interval and a second time interval. The first time interval describes, for example, a difference between sending two signals with different signal power levels, and the second time interval describes, for example, a difference between reception of the two signals with different signal power levels by the station, which is related to the respective signal power correction. The first time interval is described by a difference of transmission time stamps, which are related to a first clock, and the second time interval is described by a difference of reception time stamps, which are related to a second clock, which represents a clock of the station that is related to the respective Signal power correction is related. Thus the first time interval can be the same for all signal power corrections, and the second time interval can be different for each signal power correction. According to one embodiment, the second time interval for the first signal power correction describes a difference between a reception of the two signals, which have different signal power levels, by the transponder. The signal power corrections are obtained, for example, by the apparatus using a clock skew correction based on sending time stamp information and receiving time stamp information of at least two signals having the same signal power levels. Thus, for example, two of the at least three signals have the same signal power level and one of the three signals has a signal power level that differs from the signal power level of the two signals that have the same signal power level. Alternatively, the apparatus may be configured to determine the signal power corrections on the basis of sending time stamp information and receiving time stamp information associated with more signals, where at least two signals have the same signal power levels and at least two signals have different signal power levels, for example four signals with two signals, having a first signal power level, a signal having a second signal power level, and a signal having a third signal power level. For example, a determination based on three signals may have two signal power corrections since two signal power levels are analyzed, the signal power correction related to the signal power level of the two signals having the same signal power level being, for example, zero. Thus, for example, a determination based on four signals can have three signal power corrections or two signal power corrections, since either three signal power levels or two signal power levels are analyzed.

According to an embodiment, the apparatus is configured to receive a first antenna delay correction value for correcting transmission time stamps and reception time stamps related to the reference station. The apparatus is configured, for example, to apply a second antenna delay correction value for correcting e.g. B. all transmission timestamps and z. B. to get all reception time stamps related to the transponder. The apparatus is configured, for example, to provide a third antenna delay correction value for correcting e.g. B. all transmission timestamps and z. B. to get all reception timestamps related to the first station. The apparatus is configured, for example, to provide a fourth antenna delay correction value for correcting e.g. B. all transmission timestamps and z. B. all reception time stamps related to the second station, and the apparatus is configured, for example, the first antenna delay correction value, the second antenna delay correction value, the third antenna delay correction value and / or the fourth antenna delay correction value to obtain the arrival time, the first Time of arrival difference and the second time of arrival difference.

According to one embodiment, the clock offset correction is made using a time interpolation or a time extrapolation of a deviation between a first difference of transmission time stamps associated with sending two signals that have the same signal power level and a second difference of reception time stamps associated with receiving the two signals that have the same signal power levels are determined. For example, the two signals on which the first difference is based and the two signals on which the second difference is based are the same two signals. The first difference is related to a second clock and the second difference is related to a second clock, and the deviation between the first difference and the second difference is caused, for example, by a deviation between the first clock and the second clock. The apparatus is configured to use the clock offset correction to obtain the time of arrival, the first time of arrival difference, and the second time of arrival difference. If the first clock and the second clock were running simultaneously, i. H. were synchronized, the first difference would be equal to the second difference, since no clock shift or almost no clock shift occurs. For example, if the clock shift correction is determined using time interpolation, the clock shift correction is determined for a signal that is transmitted in time between the transmission of the two signals with the same signal power levels, and if the clock shift correction is determined using time extrapolation, the clock shift correction is determined for a signal whose transmission takes place in time after the transmission of the two signals with the same signal power levels. A very precise clock shift correction can be determined by means of the time interpolation or the time extrapolation, as a result of which a high degree of accuracy can be achieved when determining the position of the transponder.

One embodiment according to this invention relates to a method for locating a transponder. The method includes obtaining, e.g. B. Calculate an arrival time, e.g. B. a transit time of a signal between a reference station and a transponder, one or more signals, on the basis of transmission time stamps and reception time stamps, the z. From the ref. And the transponder are received by the apparatus, two or more signals sent between a reference station and a transponder, e.g. B. using clock skew correction and / or antenna delay correction and / or signal power correction. The method includes obtaining, e.g. B. Calculate, e.g. B. using a clock shift correction and / or a signal power correction and / or an antenna delay correction, the antenna delay correction being used, for example, to calculate an offset K, a first arrival time difference based on a difference between reception time stamps obtained at a first station and reception times of two Describe signals, one being sent by the reference station and one being sent by the transponder, for example in a time-synchronized manner, so that, for example, a difference in transmission times is predetermined or can be calculated at the first station. The method further comprises obtaining, e.g. B. Calculate, e.g. B. using a clock offset correction and / or a signal power correction and / or an antenna delay correction, a second arrival time difference on the basis of a difference between reception time stamps obtained at a second station and describe reception times of two signals, one being sent by the reference station and one is transmitted by the transponder, for example in a time-synchronized manner, so that, for example, a difference in transmission times is predetermined or can be calculated, at the second station, for example the two signals on which the receive time stamps obtained at the second station are based, equal to the may be two signals on which the receive time stamps obtained at the first station are based, or differ from the two signals on which the receive time stamps obtained at the first station are based. The method includes calculating a position of the transponder on the basis of the arrival time and the at least two arrival time differences.

An exemplary embodiment according to this invention relates to a computer program which has a program code for carrying out, when it runs on a computer, a method.

Figure list

• 1 eine schematische Ansicht einer Apparatur zum Lokalisieren eines Transponders gemäß einem Ausführungsbeispiel der Erfindung zeigt;
• 2 eine schematische Ansicht einer Bestimmung einer Ankunftszeit zeigt, die durch eine Apparatur gemäß einem Ausführungsbeispiel der vorliegenden Erfindung erhalten wird;
• 3 eine schematische Ansicht einer Bestimmung einer Ankunftszeit zeigt, die durch eine Apparatur gemäß einem Ausführungsbeispiel der vorliegenden Erfindung unter Verwendung einer Uhrenverschiebungskorrektur und/oder einer Signalleistungskorrektur erhalten werden soll;
• 4 eine schematische Ansicht eines Verbindens einer Bestimmung einer Ankunftszeit und einer Bestimmung einer Ankunftszeitdifferenz zeigt, die durch eine Apparatur gemäß einem Ausführungsbeispiel der vorliegenden Erfindung erhalten werden sollen;
• 5 eine schematische Ansicht eines Verbindens einer Bestimmung einer Ankunftszeit und einer Bestimmung einer Ankunftszeitdifferenz zeigt, die durch eine Apparatur gemäß einem Ausführungsbeispiel der vorliegenden Erfindung unter Verwendung einer Uhrenverschiebungskorrektur und/oder einer Signalleistungskorrektur erhalten werden sollen;
• 6 eine schematische Ansicht einer Konstellation von Stationen für eine zweidimensionale Lokalisierung eines Transponders durch eine Apparatur gemäß einem Ausführungsbeispiel der vorliegenden Erfindung zeigt;
• 7 Ergebnisse eines Verbindens einer Ankunftszeit und zumindest zweier Ankunftszeitdifferenzen zum Lokalisieren eines Transponders zeigt, der durch eine Apparatur gemäß einem Ausführungsbeispiel der vorliegenden Erfindung bestimmt wird;
• 8 eine schematische Ansicht einer Bestimmung einer Uhrenverschiebungskorrektur und/oder einer Signalleistungskorrektur zeigt, die zum Korrigieren einer Ankunftszeit und/oder einer ersten Ankunftszeitdifferenz und/oder einer zweiten Ankunftszeitdifferenz verwendet werden, die durch eine Apparatur zum Lokalisieren eines Transponders gemäß einem Ausführungsbeispiel der vorliegenden Erfindung erhalten werden sollen;
• 9a ein schematisches Diagramm eines gemessenen Signalleistungspegels gegenüber einem realen Signalleistungspegel zeigt, der für eine Bestimmung einer Signalleistungskorrektur gemäß einem Ausführungsbeispiel der vorliegenden Erfindung verwendet wird; und
• 9b ein schematisches Diagramm einer Signalleistungspegelkorrekturkurve zeigt, die zum Korrigieren einer Ankunftszeit und/oder einer ersten Ankunftszeitdifferenz und/oder einer zweiten Ankunftszeitdifferenz verwendbar ist, die durch eine Apparatur zum Lokalisieren eines Transponders gemäß einem Ausführungsbeispiel der vorliegenden Erfindung erhalten werden sollen.

The drawings are not necessarily to scale; instead emphasis is placed generally on illustrating the principles of the invention. In the following description, various exemplary embodiments of the invention are described with reference to the following drawings, in which:

• 1 shows a schematic view of an apparatus for locating a transponder according to an embodiment of the invention;
• 2 Figure 13 shows a schematic view of a determination of a time of arrival obtained by an apparatus according to an embodiment of the present invention;
• 3 shows a schematic view of a determination of a time of arrival to be obtained by an apparatus according to an embodiment of the present invention using a clock offset correction and / or a signal power correction;
• 4th Figure 13 shows a schematic view of combining a determination of a time of arrival and a determination of a time of arrival difference to be obtained by an apparatus according to an embodiment of the present invention;
• 5 Fig. 13 shows a schematic view of combining a determination of a time of arrival and a determination of a time of arrival difference to be obtained by an apparatus according to an embodiment of the present invention using a clock offset correction and / or a signal power correction;
• 6th shows a schematic view of a constellation of stations for a two-dimensional localization of a transponder by an apparatus according to an embodiment of the present invention;
• 7th Shows results of combining a time of arrival and at least two time-of-arrival differences for locating a transponder determined by an apparatus according to an embodiment of the present invention;
• 8th shows a schematic view of a determination of a clock shift correction and / or a signal power correction, which are used for correcting a time of arrival and / or a first time of arrival difference and / or a second time of arrival difference, which are obtained by an apparatus for locating a transponder according to an embodiment of the present invention should;
• 9a shows a schematic diagram of a measured signal power level versus a real signal power level, which is used for a determination of a signal power correction according to an embodiment of the present invention; and
• 9b Fig. 3 shows a schematic diagram of a signal power level correction curve which can be used for correcting a time of arrival and / or a first time of arrival difference and / or a second time of arrival difference to be obtained by an apparatus for locating a transponder according to an embodiment of the present invention.

Detailed description of the exemplary embodiments

Identical or equivalent elements or elements which have identical or equivalent functionality are designated in the following description with the same or equivalent reference symbols, even if they appear in different figures.

In the following description, numerous details are set forth in order to provide a thorough explanation of embodiments of the present invention. However, it will be apparent to those skilled in the art that embodiments of the present invention can be practiced without these specific details. In other instances, well known structures and devices are shown in block diagram form, rather than in detail, in order to avoid obscuring embodiments of the present invention. In addition, features of the various exemplary embodiments described below can be combined with one another, unless otherwise specified in detail.

angegeben werden, wobei i das entsprechende Signal darstellt und x der Station entspricht, die den Zeitstempel bestimmt. Der Index x kann R (Referenzstation), T (Transponder und/oder S (Ankerstation) sein. Der Index i kann im Bereich von 1 bis n liegen, wobei n eine positive Ganzzahl ist, die zumindest 2 beträgt. Somit stellt der Zeitstempel $T_1^R$

beispielsweise einen Zeitstempel dar, der einem durch eine Referenzstation bestimmten ersten Signal entspricht. Eine Differenz zwischen zwei Zeitstempeln $T_M^X-T_N^X$

kann als $\mathrm{\Delta }{T}_{N,M}^X$

angegeben werden, wobei der Index N und der Index M Werte des Indizes i im Bereich von 1 bis n darstellen und die zwei Zeitstempel $T_M^X\text{ und }{T}_N^X$

Zeiten darstellen, die durch dieselbe Station bestimmt werden, siehe Index x. Ein von den Zeitstempeln eines Signals N und eines Signals M, beispielsweise Sendezeitstempel und Empfangszeitstempel beider Signale, erhaltener Uhrenverschiebungsfehler kann durch C_N,M angegeben werden. Zeitstempelleistungskorrekturinformationen können einen Zeitstempelfehler aufweisen, der auf den Signalleistungspegel zurückzuführen ist, der als E_i angegeben sein kann, wobei der Index i einem definierten Signalleistungspegel zugeordnet ist. Ferner können ein Antennenverzögerungs- und ein Signalleistungskorrekturversatz durch A, B und/oder C angegeben sein. Eine Ankunftszeitdifferenz zwischen einer Referenzstation und einem Transponder kann als K angegeben sein, und eine Lichtgeschwindigkeit kann als c₀ angegeben sein. Überdies kann eine Position der Referenzstation durch (x_R, y_R, z_R) dargestellt sein, eine Position einer Basisstation (d. h. einer Ankerstation, z. B. einer ersten Station und/oder einer zweiten Station) kann durch (x_S, y_S, z_S) dargestellt sein, und eine Position des Transponders kann durch (x_T, y_T, z_T) dargestellt sein. After this, the following notation can be used: A time stamp can be used as a $T_i^X$

where i represents the corresponding signal and x corresponds to the station that determines the time stamp. The index x can be R (reference station), T (transponder and / or S (anchor station). The index i can be in the range from 1 to n, where n is a positive integer that is at least 2. Thus, the time stamp represents $T_1^{\mathrm{R.}}$

for example a time stamp which corresponds to a first signal determined by a reference station. A difference between two timestamps $T_{\mathrm{M.}}^X-T_N^X$

can as $\mathrm{\Delta }{T}_{N,\mathrm{M.}}^X$

are specified, where the index N and the index M represent values of the index i in the range from 1 to n and the two time stamps $T_{\mathrm{M.}}^X\text{and}{T}_N^X$

Show times that are determined by the same station, see index x. A clock shift error obtained from the time stamps of a signal N and a signal M, for example, sending time stamp and receiving time stamp of both signals, can be indicated by C _{N, M.} Timestamp power correction information may include a timestamp error attributable to the signal power level, which may be specified as E _i , where the index i is associated with a defined signal power level. Furthermore, an antenna delay and a signal power correction offset can be indicated by A, B and / or C. A time difference of arrival between a reference station and a transponder can be given as K, and a speed of light can be given as c ₀ . Furthermore, a position of the reference station can be represented by (x _R , y _R , z _R ), a position of a base station (ie an anchor station, e.g. a first station and / or a second station) can be represented by (x _S , y _S , z _S ), and a position of the transponder may be represented by (x _T , y _T , z _T ).

1 shows an apparatus 100 for locating a transponder necessary for obtaining an arrival time TOA 110 , a first arrival time difference TDOA ₁ 120 and a second arrival time difference TDOA ₂ 130 configured. Furthermore, the apparatus 100 to calculate a position 140 of the transponder based on the arrival time 110 and the at least two arrival time differences 120 , 130 configured.

According to one embodiment, the apparatus is 100 configured to the arrival time 110 and the at least two arrival time differences 120 , 130 calculate yourself or the arrival time 110 and / or the at least two arrival time differences 120 , 130 to receive from an external device that does the calculation of the arrival time 110 and / or the at least two arrival time differences 120 , 130 undertakes.

According to one embodiment, the time of arrival is based 110 , e.g. B. a flight time of a signal sent between a reference station and a transponder, on sending time stamps and receiving time stamps of two or more signals that are sent between a reference station and a transponder. The apparatus 100 or an external device can be configured to use the TOA 110 using e.g. B. a clock shift correction and / or an antenna delay correction and / or a signal power correction. According to one embodiment, one of the two or more signals is transmitted by the reference station and received by the transponder, and another signal of the two or more signals is transmitted by the transponder and received by the reference station.

The TOA 110 is the same for the two or more signals. To get the TOA 110 the apparatus can determine it 100 or an external device an arrival time difference between a transmission time stamp, which describes when a first signal of the two or more signals is sent, and a last reception time stamp, which describes when a last signal of the two or more signals either by the reference station or by the transponder received, calculate and can subtract time differences between a reception of a signal and a transmission of the next signal, ie a processing time of the reference station and / or the transponder, in order to obtain the total TOA, which is divided by the number of the two or more signals can be to the TOA 110 for a signal to be determined.

According to one embodiment, the apparatus is 100 configured for this, e.g. B. from the reference station and the transponder to receive the transmission time stamps and the reception time stamps of the two or more signals that are sent between the reference station and the transponder, to the TOA 110 to calculate.

According to one embodiment, the TOA 110 according to a referring to 2 , 3 , 4th and or 5 described embodiment by the apparatus 100 or computed by an external device that uses the computed TOA 110 for the apparatus 100 provides.

According to one embodiment, the first time of arrival difference is based on TDOA ₁ 120 on a difference between reception time stamps that are received at a first station and describe reception times of two signals, one being sent by the reference station and one being sent by the transponder, at the first station. The apparatus 100 or an external device can be configured to use the TDOA ₁ 120 using e.g. B. a clock shift correction and / or a signal power correction and / or an antenna delay correction. The determination of the TDOA ₁ 120 is carried out, for example, in a time-synchronized manner, for example in such a way that a difference in transmission times is predetermined or can be calculated. The TDOA ₁ represents, for example, a difference between a TOA of a first signal transmitted by the reference station and received by the first station and a TOA of a second signal transmitted by the transponder and received by the first station.

According to one embodiment, the apparatus is 100 configured for this, e.g. B. from the first station to receive the time stamps of the two signals that are sent by the reference station and by the transponder in order to use the TDOA ₁ 120 to calculate. The apparatus 100 is, according to one embodiment, part of the first station, whereby the apparatus 100 is configured to calculate the TDOA ₁ itself.

According to one embodiment, the TDOA ₁ 120 according to a related to 4th and or 5 described embodiment by the apparatus 100 or calculated by an external device, which the calculated TDOA ₁ 120 for the apparatus 100 provides.

According to one embodiment, the second time of arrival difference is based on TDOA ₂ 130 on a difference between reception time stamps that are received at a second station and describe reception times of two signals, one being sent by the reference station and one being sent by the transponder, at the second station. The apparatus 100 or an external device can be configured to use the TDOA ₂ 130 using e.g. B. a clock shift correction and / or a signal power correction and / or an antenna delay correction. The determination of the TDOA ₂ 130 is carried out, for example, in a time-synchronized manner, for example in such a way that a difference in transmission times is predetermined or can be calculated. The TDOA ₂ 130 For example, represents a difference between a TOA of a first signal sent by the reference station and received by the second station and a TOA of a second signal sent by the transponder and received by the second station.

According to one embodiment is apparatus 100 configured for this, e.g. B. to receive from the second station the reception time stamps of the two signals that are sent by the reference station and by the transponder to the TDOA ₂ 130 to calculate. The apparatus 100 is, according to one embodiment, part of the second station, whereby the apparatus 100 is configured to use the TDOA ₂ 130 calculate yourself.

According to one embodiment, the TDOA ₂ 130 according to a with reference to 4th and or 5 described embodiment by the apparatus 100 or calculated by an external device, which the calculated TDOA ₂ 130 for the apparatus 100 provides.

According to one embodiment, the two signals on which the receive time stamps obtained at the second station are based can be the same as the two signals on which the receive time stamps obtained at the first station are based, or they can be different from the two signals on which the receive time stamps at the receive time stamps obtained from the first station.

According to one embodiment, the apparatus is 100 configured to do this, the position 140 of the transponder using distance information that describes a distance between the reference station and the transponder, which is based on the arrival time TOA 110 based, using first distance difference information that describes a difference between a distance between the reference station and the first station and a distance between the transponder and the first station, which is based on the first arrival time difference TDOA ₁ 120 is based, and using second distance difference information that describes a difference between a distance between the reference station and the second station and a distance between the transponder and the second station, which is based on the second arrival time difference TDOA ₂ 130 is based to calculate. According to one embodiment, the apparatus is 100 configured to receive information about absolute or relative positions of the reference station, the first station and the second station and to use this information to the position 140 of the transponder. According to one embodiment, the position information of the reference station, the first station and the second station can be predetermined and can be on the apparatus 100 can be stored, or alternatively the apparatus 100 be configured to receive this position information from an external device.

According to one embodiment, the apparatus is 100 configured to do this, the position 140 of the transponder using an intersection of a first circle or sphere, e.g. B. a spherical surface, a first hyperbola or a first hyperboloid, e.g. B. a first hyperboloid surface, and a second hyperbola or a second hyperboloid, e.g. B. a second hyperboloid surface to calculate. The position 140 of the transponder represents, for example, the point of intersection or an area around the point of intersection, the area around the point of intersection representing an uncertainty of the apparatus 100 and / or other processing units, stations and / or devices used to calculate the point of intersection. Alternatively, the position 140 of the transponder is an intersection of a plurality of intersection points passed through the apparatus 100 be determined, represent, or position 140 of the transponder can represent an area around the average.

According to one embodiment, the apparatus is 100 configured to have a two-dimensional position 140 of the transponder on the basis of an intersection of the first circle, the first hyperbola and the second hyperbola. According to one embodiment, the apparatus is 100 configured to have a three-dimensional position 140 of the transponder on the basis of the first sphere, the first hyperboloid and the second hyperboloid.

According to one embodiment, the first circle or the first sphere is passed through the apparatus 100 based on information about a position of the reference station and the arrival time TOA 110 is determined from which a distance that can be used as a radius can be derived. According to one embodiment, the first hyperbola or the first hyperboloid is made by the apparatus 100 based on information on a position of the reference station and the first station and the first arrival time difference TDOA ₁ 120 determined, from which a distance difference of points of the first hyperbola or the second hyperboloid from the reference station and the first station can be derived. According to an embodiment, the second hyperbola or the second hyperboloid is through the apparatus 100 based on information on a position of the reference station and the second station and the arrival time difference TDOA ₂ 130 determined, from which a distance difference of points of the second hyperbola or the second hyperboloid from the reference station and the second station can be derived.

According to one embodiment, the apparatus is 100 configured to use a system of equations, e.g. B. of three or more equations, to solve to the position 140 of the transponder. A first of the equations describes, for example, the first circle or the first sphere, which is centered at a position of the reference station. The apparatus 100 is configured, for example, to calculate a radius of the first circle or the first sphere using the arrival time TOA 110 to determine. A second of the equations describes, for example, the first hyperbola or the first hyperboloid, the foci of which are located at a position of the reference station and at a position of the first station. The apparatus 100 is configured, for example, to calculate an absolute difference of distances of points of the first hyperbola or the first hyperboloid from the foci using the first arrival time difference TDOA ₁ 120 to determine. A third of the equations describes, for example, the second hyperbola or the second hyperboloid, the foci of which are located at a position of the reference station and at a position of the second station. The apparatus 100 is configured, for example, to calculate an absolute difference of distances from points of the second hyperbola or the second hyperboloid due to the foci using the second arrival time difference TDOA ₂ 130 to determine.

According to one embodiment, the apparatus is 100 configured to do this, the position 140 of the transponder using a multiplication of the TOA 110 with a propagation speed of a signal, using a multiplication of the first arrival time difference TDOA ₁ 120 with the speed of propagation of the signal and using a multiplication of the second arrival time difference TDOA ₂ 130 with the propagation speed of the signal on the basis of lateration. The speed of propagation of the signal is represented, for example, by a speed of light c ₀ . The lateration is, for example, a method, the position of the transponder, whereby the transponder can be movable or stationary in space, using several bandwidths (i.e. distances) between the transponder and several spatially separated positions (i.e. stations such as the reference station, the first station and of the second station).

Thus, the multiplication represents the TOA 110 with the propagation speed of the signal represents, for example, a distance between the reference station and the transponder, the multiplication of the first arrival time difference TDOA ₁ 120 with the propagation speed of the signal represents, for example, a difference between a distance between the reference station and the first station and a distance between the transponder and the first station, and the multiplication of the second arrival time difference TDOA ₂ 130 with the propagation speed of the signal represents, for example, a difference between a distance between the reference station and the second station and a distance between the transponder and the second station. According to one embodiment, the apparatus is configured to receive the information about the absolute or relative positions of the reference station to use the first station and the second station.

und/oder $$\begin{array}{l}TO{A}_n\cdot c_0=\sqrt{{\left(x_{R_n}-x_T\right)}^2+{\left(y_{R_n}-y_T\right)}^2+{\left(z_{R_n}-z_T\right)}^2},\text{ und}\\ TDO{A}_i\cdot c_0=\sqrt{{\left(x_T-x_{Si}\right)}^2+{\left(y_T-y_{Si}\right)}^2+{\left(z_T-z_{Si}\right)}^2}\\ -\sqrt{{\left(x_{R_n}-x_{Si}\right)}^2+{\left(y_{R_n}-y_{Si}\right)}^2+{\left(z_{R_n}-z_{Si}\right)}^2},\end{array}$$

löst,
wobei eine Position der Referenzstation, z. B. eine 2D-Position (x_R, y_R) oder eine 3D-Position (x_R, y_R, z_R) und eine Position einer Station, z. B. eine 2D-Position (x_Si, y_Si) oder eine 3D-Position (x_Si, y_Si, z_Si), durch die Apparatur 100 bekannt ist und die Position des Transponders, z. B. eine 2D-Position (x_T, y_T) oder eine 3D-Position (x_T, y_T, z_T) durch die Apparatur 100 berechnet wird.According to one embodiment, the apparatus is 100 configured to do this, the position 140 of the transponder by using a system of equations according to $$\begin{array}{l}TO\mathrm{A.}\cdot c_0=\sqrt{{\left(x_{\mathrm{R.}}-x_T\right)}^2+{\left(y_{\mathrm{R.}}-y_T\right)}^2},\text{and}\\ \begin{array}{ccc}& & {\text{TDOA}}_i\cdot c_0=\sqrt{{\left(x_T-x_{\mathrm{S.}i}\right)}^2+{\left(y_T-y_{\mathrm{S.}i}\right)}^2}\end{array}\\ \begin{array}{cccc}& & & -\sqrt{{\left(x_{\mathrm{R.}}-x_{\mathrm{S.}i}\right)}^2+{\left(y_{\mathrm{R.}}-y_{\mathrm{S.}i}\right)}^2}\end{array}\end{array}$$

and or $$\begin{array}{l}TO{\mathrm{A.}}_n\cdot c_0=\sqrt{{\left(x_{{\mathrm{R.}}_n}-x_T\right)}^2+{\left(y_{{\mathrm{R.}}_n}-y_T\right)}^2+{\left(z_{{\mathrm{R.}}_n}-z_T\right)}^2},\text{and}\\ T\mathrm{D.}O{\mathrm{A.}}_i\cdot c_0=\sqrt{{\left(x_T-x_{\mathrm{S.}i}\right)}^2+{\left(y_T-y_{\mathrm{S.}i}\right)}^2+{\left(z_T-z_{\mathrm{S.}i}\right)}^2}\\ -\sqrt{{\left(x_{{\mathrm{R.}}_n}-x_{\mathrm{S.}i}\right)}^2+{\left(y_{{\mathrm{R.}}_n}-y_{\mathrm{S.}i}\right)}^2+{\left(z_{{\mathrm{R.}}_n}-z_{\mathrm{S.}i}\right)}^2},\end{array}$$

solves,
wherein a position of the reference station, e.g. B. a 2D position (x _R , y _R ) or a 3D position (x _R , y _R , z _R ) and a position of a station, e.g. B. a 2D position (x _Si , y _Si ) or a 3D position (x _Si , y _Si , z _Si ), through the apparatus 100 is known and the position of the transponder, e.g. B. a 2D position (x _T , y _T ) or a 3D position (x _T , y _T , z _T ) through the apparatus 100 is calculated.

According to one embodiment, the apparatus is 100 configured to include at least two arrival time differences, e.g. B. the first arrival time difference TDOA ₁ 120 and the second arrival time difference TDOA ₂ 130 , using a separate station for each TDOA. Thus the apparatus knows 100 For example the 2D position (x _S1 , y _S1 ,) or the 3D position (x _S1 , y _S1 , z _S1 ) of the first station and the 2D position (x _S2 , y _S2 ) or the 3D position (x _S2 , y _S2 . Z _S2 ) of the second station. According to one embodiment, the index I, e.g. B. i∈ [1; N], where N≥2, a number of a station Si, at which the reception time stamps, the reception times of the two signals, one being sent by the reference station and one being sent by the transponder, are obtained become.

According to one embodiment, the apparatus is 100 configured to have more than one arrival time TOA 110 with a separate reference station being used for each TOA _N. Thus the apparatus knows 100 for example the 2D position (x _{R n} , y _{R n} ) or the 3D position (x _{R n} , y _{R n} , z _{R n} ) each reference station. According to one embodiment, the index n, e.g. B. n∈ [1; N], where N≥1 or N≥2, a number of a reference station R.

2 Fig. 13 shows a concept of two-way ranging TWR and a shift of time stamps caused by signal power, ie power or signal power level of a signal, and an error due to antenna delay. In other words, on the left is the 2 an effect of the performance on a determination of a time of arrival TOA by a station, by an external device or by an apparatus such as e.g. B. in 1 described, shown. In other words, on the right is the 2 an effect of an offset, ie the antenna delay, on a determination of the arrival time TOA by a station, by an external device or by an apparatus such as e.g. B. in 1 described, shown.

220₁ und eines Empfangszeitstempels $T_1^T$

230₁ eines ersten Signals 210, das durch die Referenzstation 200₁ gesendet und durch den Transponder 200₂ empfangen wird, und eines Sendezeitstempels $T_2^T$

220₂ und eines Empfangszeitstempels $T_2^R$

230₂ eines zweiten Signals 212, das durch den Transponder 200₂ gesendet und durch die Referenzstation 200₁ empfangen wird, berechnet. According to one embodiment, the arrival time is based on a transmission time stamp $T_1^{\mathrm{R.}}$

220 ₁ and a receipt time stamp $T_1^T$

230 ₁ of a first signal 210 that by the reference station 200 ₁ sent and by the transponder 200 ₂ is received, and a time stamp $T_2^T$

220 ₂ and a receipt time stamp $T_2^{\mathrm{R.}}$

230 ₂ a second signal 212 that through the transponder 200 ₂ sent and by the reference station 200 ₁ is received.

d. h. einem ersten Sendezeitstempel 220₁ der Referenzstation 200₁ , gesendet. Ein Zeitstempel $T_1^T,$

d. h. ein erster Empfangszeitstempel 230₁ des Transponders 200₂ der empfangenen Nachricht an dem Transponder 200₂ wird durch die Signalleistung beeinflusst, was Ursache des Zeitstempels durch E1 ist. Mit anderen Worten stellt E1 eine Signalleistungskorrektur 240₁ dar, die einem ersten Signalleistungspegel des ersten Signals 210 zugeordnet ist, um den ersten Empfangszeitstempel 230₁ des Transponders 200₂ zu korrigieren. Dasselbe gilt beispielsweise für eine Antwortnachricht, d. h. ein zweites Signal 212, jedoch diesmal an der Referenzstation 200₁ . Mit anderen Worten stellt E2 eine Signalleistungskorrektur 240₂ dar, die einem zweiten Signalleistungspegel des zweiten Signals 212 zugeordnet ist, um den ersten Empfangszeitstempel 230₂ der Referenzstation 200₁ zu korrigieren. Es ist wichtig zu beachten, dass die Sendezeitstempel $T_1^R$

220₁ und $T_2^T$

220₂ nicht durch die Signalleistung beeinflusst werden.According to one embodiment, the reference station is 200 ₁ the initiator. A first message 210 , ie a first signal, is given by the reference station 200 ₁ to a timestamp $T_{}^{}$${}_1^{\mathrm{R.}},$

ie a first transmission timestamp 220 ₁ the reference station 200 ₁ , sent. A timestamp $T_1^T,$

ie a first reception timestamp 230 ₁ of the transponder 200 ₂ of the received message on the transponder 200 ₂ is influenced by the signal power, which is the cause of the time stamp by E1. In other words, E1 represents a signal power correction 240 ₁ represents a first signal power level of the first signal 210 is assigned to the first receive timestamp 230 ₁ of the transponder 200 ₂ to correct. The same applies, for example, to a reply message, ie a second signal 212 , but this time at the reference station 200 ₁ . In other words, E2 represents a signal power correction 240 ₂ represents a second signal power level of the second signal 212 is assigned to the first receive timestamp 230 ₂ the reference station 200 ₁ to correct. It is important to note that the airtime stamp $T_1^{\mathrm{R.}}$

220 ₁ and $T_2^T$

220 ₂ are not influenced by the signal power.

Die Flugzeit, d. h. die Ankunftszeit TOA, zwischen der Referenzstation 200₁ und dem Transponder 200₂ mit den Korrekturen kann mit der folgenden Formel geschätzt werden: $$TOA=\mathrm{0,5}\cdot \left(\left(T_2^R-T_1^R\right)-\left(T_2^T-T_1^T\right)-E2-E1\right)-A-B.$$

On the other hand, the antenna delay (A, B) affects 250 ₁ , 250 ₂ , i.e. an antenna offset, actually all timestamps (those in 2 shown on the right). For example, it is assumed that a transmission delay is equal to the reception delay. Without the correction there would be a TWR equation $0.5\cdot \left(\left({\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="DE102019202009A1\_0214.png,DE102019202009A1\_0215.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^{\mathrm{R.}}-{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="DE102019202009A1\_0217.png,DE102019202009A1\_0218.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^{\mathrm{R.}}\right)-\left(T_2^T-T_1^T\right)\right).$

The flight time, ie the arrival time TOA, between the reference station 200 ₁ and the transponder 200 ₂ with the corrections can be estimated using the following formula: $$TO\mathrm{A.}=0.5\cdot \left(\left({\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="DE102019202009A1\_0214.png,DE102019202009A1\_0215.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^{\mathrm{R.}}-{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="DE102019202009A1\_0217.png,DE102019202009A1\_0218.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^{\mathrm{R.}}\right)-\left(T_2^T-T_1^T\right)-\mathrm{E.}2-\mathrm{E.}1\right)-\mathrm{A.}-\mathrm{B.}.$$

260₁ zu, und eine Zeitdifferenz $\Delta T_{\mathrm{1,2}}^T$

260₂ nimmt ab. Aufgrund der Antennenverzögerung nimmt die Zeitdifferenz $\Delta T_{\mathrm{1,2}}^R$

260₁ zu, und die Zeitdifferenz $\Delta T_{\mathrm{1,2}}^T$

260₂ nimmt ab. Eine Nulllinie für die Signalleistung und den Antennenversatz sind beide unbekannt, jedoch konstant, somit können beide Werte durch die Variable Z dargestellt werden.The values E1 and E2 can be obtained from a signal power correction curve or a database of signal power correction values corresponding to various signal power levels, as with reference to FIG 8th or 9b is described. One should take into account that the signal power is the transponder 200 ₂ and the reference station 200 ₁ influenced differently. Due to the signal power, there is a time difference $\Delta T_{1.2}^{\mathrm{R.}}$

260 ₁ to, and a time difference $\Delta T_{1.2}^T$

260 ₂ decreases. Due to the antenna delay, the time difference increases $\Delta T_{1.2}^{\mathrm{R.}}$

260 ₁ to, and the time difference $\Delta T_{1.2}^T$

260 ₂ decreases. A zero line for the signal power and the antenna offset are both unknown, but constant, so both values can be represented by the variable Z.

Although in 2 an effect of the signal power level of a signal (see left side of the 2 ) and an antenna delay (see right side of the 2 ) are shown separately, it is clear that both errors can coexist. Thus, for example, the first transmission time stamp 220 ₁ the reference station 200 ₁ and a first broadcast timestamp 220 ₂ of the transponder 200 ₂ can be corrected by an antenna delay correction, and the first reception time stamp 230 ₁ of the transponder 200 ₂ and the first receive timestamp 230 ₂ the reference station 200 ₁ can be corrected by the antenna delay correction and / or the signal power correction.

According to an exemplary embodiment, a clock offset correction can additionally or alternatively be used in order to provide transmission time stamps 220 ₁ and or 220 ₂ to correct and / or receive timestamp 230 ₁ and or 230 ₂ to correct.

zu erhalten, wobei die Zeitdifferenz $\Delta T_{\mathrm{1,3}}^R$

262₁ eine Differenz zwischen Sendezeitstempeln 220₁ und 220₃ , die dem ersten Signal 210 und dem dritten Signal 214 zugeordnet sind, darstellt, und wobei die Zeitdifferenz $\Delta T_{\mathrm{1,3}}^T$

262₂ eine Differenz zwischen Empfangszeitstempeln 230₁ und 230₃ , die dem ersten Signal 210 und dem dritten Signal 214 zugeordnet sind, darstellt. Man kann sehen, dass die Signalleistung E1 keine Auswirkung auf die Zeitstempeldifferenz $\Delta T_{\mathrm{1,3}}^T$

262₂ hat. Die abschließende Flugzeitgleichung mit der Uhrenverschiebungskorrektur und drei Nachrichten wird beispielsweise zu: $$TOA=TOA=\mathrm{0,5}\cdot \left(\Delta T_{\mathrm{1,2}}^R-\Delta T_{\mathrm{1,2}}^T-\frac{C_{\mathrm{1,3}}^{RT}}{\Delta T_{\mathrm{1,3}}^T}\cdot \left(\Delta T_{\mathrm{1,2}}^T+E_1\right)-E_2-E_1\right)+Z$$

According to an exemplary embodiment, a clock shift can be corrected using three messages. 3 shows how this principle can be adapted for the two-way distance determination in order to enable a clock shift-corrected arrival time TOA to be determined. This in 3 The method shown may have features and functionalities that are described in 2 are shown, where in 3 in addition to the two messages 210 , 212 a third message 214 , ie a final message, by the reference station 200 ₁ sent and by the transponder 200 ₂ Will be received. The last message 214 is used, for example, to correct a clock shift error ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T}=\Delta T_{1.3}^{\mathrm{R.}}-\Delta T_{1.3}^T$

to get the time difference $\Delta T_{1.3}^{\mathrm{R.}}$

262 ₁ a difference between airtime stamps 220 ₁ and 220 ₃ that the first signal 210 and the third signal 214 are assigned, represents, and where the time difference $\Delta T_{1.3}^T$

262 ₂ a difference between receive timestamps 230 ₁ and 230 ₃ that the first signal 210 and the third signal 214 are assigned represents. It can be seen that the signal power E1 has no effect on the time stamp difference $\Delta T_{1.3}^T$

262 ₂ Has. For example, the final time-of-flight equation with clock shift correction and three messages becomes: $$TO\mathrm{A.}=TO\mathrm{A.}=0.5\cdot \left(\Delta T_{1.2}^{\mathrm{R.}}-\Delta T_{1.2}^T-\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\Delta T_{1.3}^T}\cdot \left(\Delta T_{1.2}^T+{\mathrm{E.}}_1\right)-{\mathrm{E.}}_2-{\mathrm{E.}}_1\right)+Z$$

220₃ und einem Empfangszeitstempel $T_3^T$

230₃ , die auf ein drittes Signal 214 bezogen sind, das durch die Referenzstation 200₁ gesendet und durch den Transponder 200₂ empfangen wird, und auf Sendezeitstempeln $T_1^R$

220₁ und Empfangszeitstempeln $T_1^T$

230₁ , die auf ein erstes Signal 210 bezogen sind, das durch die Referenzstation 200₁ gesendet und durch den Transponder 200₂ empfangen wird.In other words, the clock shift correction is based, for example, on a transmission time stamp $T_3^{\mathrm{R.}}$

220 ₃ and a receipt timestamp $T_3^T$

230 ₃ responding to a third signal 214 are related, that by the reference station 200 ₁ sent and by the transponder 200 ₂ received, and on airtime stamps $T_1^{\mathrm{R.}}$

220 ₁ and receipt timestamps $T_1^T$

230 ₁ responding to a first signal 210 are related, that by the reference station 200 ₁ sent and by the transponder 200 ₂ Will be received.

260₂ zwischen einem ersten Sendezeitstempel $T_2^T$

220₂ des Transponders 200₂ , der beschreibt, wann das zweite Signal 212 durch den Transponder 200₂ gesendet wird, und einem ersten Empfangszeitstempel $T_1^T$

230₁ des Transponders 200₂ , der beschreibt, wann das erste Signal 210, das durch die Referenzstation 200₁ gesendet wird, durch den Transponder 200₂ empfangen wird, und/oder wobei eine Signalleistungskorrektur E₁ 240₁ durchgeführt wird, die den ersten Empfangszeitstempel $T_1^T$

230₁ , der an dem Transponder 200₂ erhalten wird, korrigiert.In other words, the clock shift correction is used, for example, to calculate the difference $\Delta T_{1.2}^T$

260 ₂ between a first broadcast timestamp $T_2^T$

220 ₂ of the transponder 200 ₂ that describes when the second signal 212 through the transponder 200 ₂ is sent, and a first receive timestamp $T_1^T$

230 ₁ of the transponder 200 ₂ that describes when the first signal 210 that by the reference station 200 ₁ is sent by the transponder 200 ₂ is received, and / or wherein a signal power correction E ₁ 240 ₁ which is the first receive timestamp $T_1^T$

230 ₁ on the transponder 200 ₂ is corrected.

With the corrected time measurements TOA and the propagation speed of the signal, it is possible to use lateration to determine a position of the transponder 200 ₂ (x _T , y _T , z _T ) in terms of anchors, e.g. B. the reference station 200 ₁ , to obtain: $$\begin{array}{cc}TO{\mathrm{A.}}_i\cdot c_0=\sqrt{{\left(x_{{\mathrm{R.}}_i}-x_T\right)}^2+{\left(y_{{\mathrm{R.}}_i}-y_T\right)}^2+{\left(z_{{\mathrm{R.}}_i}-z_T\right)}^2}& 1\le i\le N\end{array}$$

3 showed how clock shift and offset can affect time of arrival position estimate. In 4th and 5 we show how the TOA messages 210 , 212 can be used to combine TOA with TDOA and the clocks, e.g. B. a clock of a reference station 200 ₁ , a clock of a transponder 200 ₂ and clocks from different stations 202 to sync wirelessly. In 4th and in 5 is only one station N by way of example 202 _N. a plurality of stations 202 where the subscript N is a number in a range from 1 to n and where n is at least two. Time of Arrival Difference (TDOA), for example, requires the clocks of the various stations to be synchronous. Otherwise, an additional signal from another station at a known position can be used for clock synchronization [12]. For example, two-way ranging (TWR) based on TOA requires that both stations, e.g. B. the reference station 200 ₁ and the transponder 200 ₂ , a signal 210 , 212 output. Therefore, one station can be used as a reference station for clock synchronization. In 5 this principle is illustrated. In other words shows 5 TOA and TDOA with a clock shift correction. The effect of clock shift and antenna delay on TDOA is in 4th to see. The effect of a signal power level of a signal on TDOA is in 4th seen on the left, and the effect of an offset, ie antenna delay, on the TDOA is seen on the right.

Although in 4th an effect of the signal power level of a signal (see 4th left) and an antenna delay (see 4th right) are shown separately, it is clear that both errors can coexist. Thus, for example, the first receive time stamp 230 ₄ the station 202 _N. and a second receive timestamp 230 ₅ the station 202 _N. by the antenna delay correction C 250 and / or by the signal power correction E3 or E4 Getting corrected.

According to one embodiment, the antenna delay is C250 as in 4th is shown on the right, for example the same for all time stamps, sending time stamps and receiving time stamps of a station and differs, for example, between two different stations. Although the antenna delay C 250 only for the station 202 _N. It is clear that for each station, the reference station, the transponder and / or other stations, an antenna delay can be determined which can be used by the apparatus or an external device to correct the transmission and reception time stamps of the corresponding station. For example, the antenna delay for the reference station and the transponder are on the right in 2 to see.

According to one embodiment, the values represent E ₃ 240 ₃ and E ₄ 240 ₄ , in the 4th and 5 are shown represent signal power corrections, e.g. B. a predetermined value that is associated with an actual signal power level, a correction of station N received time stamps 202 _N. for received signals with a first signal power level and a second signal power level are assigned. Although the signal power corrections are exemplary for only one station 202 _N. It is clear that similar signal power corrections are made to receive time stamps of all stations 202 can be applied.

According to one embodiment, the value E represents ₁ 240 ₁ who is in 5 is shown represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the transponder for received signals with a first signal power level.

According to one embodiment, the value E represents ₂ 240 ₂ who is in 5 is shown represents a signal power correction, e.g. B. a predetermined value which is assigned to an actual signal power level, which is assigned to a correction of reception time stamps of the reference station for received signals with a second signal power level.

230₄ und $T_3^S$

230₆ , die Signalen 210,214 mit selben Signalleistungspegeln zugeordnet sind, können durch dieselbe Signalleistungskorrektur E3 240₃ korrigiert werden. Dasselbe gilt beispielsweise für die Zeitstempel $T_1^T$

230₁ und $T_3^T$

230₃ , die durch E1 240₁ korrigiert werden.According to one embodiment, the first signal 210 and the third signal 214 a first signal power level and the second signal 212 has a second signal power level. Although E1 240 ₁ and E3 240 ₃ are assigned the same signal power level, they may differ from one another, since the signal power correction may depend on the station receiving the signals. The same applies to E2, for example 240 ₂ and E4 240 ₄ . Receive timestamps determined by the same station as $T_1^{\mathrm{S.}}$

230 ₄ and $T_3^{\mathrm{S.}}$

230 ₆ , the signals 210 , 214 are assigned with the same signal power levels, by the same signal power correction E3 240 ₃ Getting corrected. The same applies to the timestamps, for example $T_1^T$

230 ₁ and $T_3^T$

230 ₃ by E1 240 ₁ Getting corrected.

To determine the TOA and TDOA, signals are sent between stations. A first TOA signal is used in this regard, for example 210 ₁ through the reference station 200 ₁ sent and by the transponder 200 ₂ received, and a second TOA signal 212 ₁ is through the transponder 200 ₂ sent and by the reference station 200 ₁ received to determine the TOA. According to one embodiment, a first TDOA signal 210 ₂ through the reference station 200 ₁ sent and for example by the station 202 _N. received, and a second TOA signal 212 ₂ is through the transponder 200 ₂ sent and for example by the station 202 _N. received to determine the TDOA. According to one embodiment, the first TOA signal 210 ₁ be the same as the first TDOA signal 210 ₂ , or it can differ from the first TDOA signal 210 ₂ distinguish. According to one embodiment, the second TOA signal 212 ₁ be the same as the second TDOA signal 212 ₂ , or it can be different from the second TDOA signal 212 ₂ distinguish.

230₅ und eins $T_2^S$

230₄ für jeden Anker, d. h. Station 202, unterscheidet sich in Abhängigkeit von der Position der Referenzstation 200₁ und des Transponders 200₂ bezüglich des Ankers. Im Gegensatz zu den zuvor dargestellten TWR-Anwendungen, siehe 2 und/oder 3, sind der Einfluss der Signalleistung und der Antennenverzögerung für TDOA-Anwendungen unterschiedlich, siehe 4 und/oder 5.The two-way distance determination is, for example, between the transponder 200 ₂ and the reference station 200 ₁ receive. The other stations 202 are passive and do not speak to them Reference station 200 ₁ and / or the transponder 200 ₂ on. The difference between timestamp two $T_2^{\mathrm{S.}}$

230 ₅ and one $T_2^{\mathrm{S.}}$

230 ₄ for each anchor, ie station 202 , differs depending on the position of the reference station 200 ₁ and the transponder 200 ₂ regarding the anchor. In contrast to the previously presented TWR applications, see 2 and or 3 , the influence of the signal power and the antenna delay are different for TDOA applications, see 4th and or 5 .

230₄ und $T_2^S$

230₅ , derselbe ist, siehe 4 links. Deshalb ist die TDOA-Gleichung beispielsweise unabhängig von der Antennenverzögerung. Andererseits erscheint gemäß einem Ausführungsbeispiel ein neuer Versatz K 310, siehe 5. Dieser Versatz 310 stellt beispielsweise eine Verzögerung zwischen dem Signal des Transponders 200₂ , d. h. dem zweiten Signal 212, und dem Signal der Referenzstation 200₁ , d. h. dem ersten Signal 210, dar. Falls beide Stationen, z. B. die Referenzstation 200₁ und der Transponder 200₂ , gleichzeitig senden würden, wäre dieser Versatz K 310 null. Somit kann die TDOA gemäß $TDOA=\Delta T_{\mathrm{1,2}}^S-E_4+E_3+K$

berechnet werden.For example, it is assumed that for the TDOA application the influence of the antenna delay on the time stamp $T_1^{\mathrm{S.}}$

230 ₄ and $T_2^{\mathrm{S.}}$

230 ₅ , is the same, see 4th Left. Therefore, the TDOA equation is independent of the antenna delay, for example. On the other hand, according to one exemplary embodiment, a new offset K appears 310 , please refer 5 . This offset 310 for example represents a delay between the signal of the transponder 200 ₂ , ie the second signal 212 , and the signal from the reference station 200 ₁ , ie the first signal 210 If both stations, e.g. B. the reference station 200 ₁ and the transponder 200 ₂ , would send at the same time, this offset would be K. 310 zero. Thus, the TDOA according to $T\mathrm{D.}O\mathrm{A.}=\Delta T_{1.2}^{\mathrm{S.}}-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3+K$

be calculated.

gemäß $C_{\mathrm{1,3}}^S=\Delta T_{\mathrm{1,3}}^R-\Delta T_{\mathrm{1,3}}^S$

zu erhalten, wobei $\Delta T_{\mathrm{1,3}}^S=T_3^S-T_3^S\text{ und }\Delta T_{\mathrm{1,3}}^R=T_3^R-T_1^R.$

Mit anderen Worten stellt die Abweichung $C_{\mathrm{1,3}}^S$

eine Differenz zwischen einer Differenz $\Delta T_{\mathrm{1,3}}^R$

262₂ von Empfangszeitstempeln, die einem Senden zweier Signale 210, 214 mit denselben Signalleistungspegeln zugeordnet sind, die durch die Referenzstation 200₁ gesendet werden, und einer Differenz $\Delta T_{\mathrm{1,3}}^S$

262₃ von Empfangszeitstempeln, die einem Empfang der zwei Signale 210, 214 mit denselben Signalleistungspegeln zugeordnet sind, durch die Station S_N 202_N dar. Die Differenz $\Delta T_{\mathrm{1,3}}^R$

262₂ stellt z. B. eine Differenz zwischen einem zweiten Sendezeitstempel $T_3^R$

220₃ der Referenzstation 200₁ , der beschreibt, wann ein drittes Signal 214 durch die Referenzstation 200₁ gesendet wird, und einem ersten Sendezeitstempel $T_1^R$

220₁ der Referenzstation 200₁ , der beschreibt, wann ein erstes Signal 210 durch die Referenzstation 200₁ gesendet wird, dar. Die Differenz $\Delta T_{\mathrm{1,3}}^S$

262₃ stellt z. B. eine Differenz zwischen einem dritten Empfangszeitstempel $T_3^S$

230₆ der Station S_N, der beschreibt, wann das durch die Referenzstation 200₁ gesendete dritte Signal 214 durch die Station S_N empfangen wird, und einem ersten Empfangszeitstempel $T_1^S$

230₄ der Station S_N, der beschreibt, wann das durch die Referenzstation 200₁ gesendete erste Signal 210 durch die Station S_N empfangen wird, dar. Das erste Signal 210 und das dritte Signal 214 weisen beispielsweise dieselben Signalleistungspegel auf. Mit einer linearen Interpolation des Uhrenverschiebungsfehlers $C_{\mathrm{1,3}}^S$

wird die TDOA-Gleichung zu $$TDOA=\Delta T_{\mathrm{1,2}}^S+\left(\frac{C_{\mathrm{1,3}}^S}{\Delta T_{\mathrm{1,3}}^S}\cdot \left(\Delta T_{\mathrm{1,2}}^S+E_3-E_4\right)\right)-E_4+E_3+K.$$

In the 5 third message shown 214 from the reference station 200 ₁ is used to correct a clock shift error ${\mathrm{C.}}_{1.3}^{\mathrm{S.}}$

according to ${\mathrm{C.}}_{1.3}^{\mathrm{S.}}=\Delta T_{1.3}^{\mathrm{R.}}-\Delta T_{1.3}^{\mathrm{S.}}$

to get, being $\Delta T_{1.3}^{\mathrm{S.}}={\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="DE102019202009A1\_0215.png,DE102019202009A1\_0217.png"\; state="\{\{state\}\}">T</figure-callout>}}_3^{\mathrm{S.}}-{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="DE102019202009A1\_0215.png,DE102019202009A1\_0217.png"\; state="\{\{state\}\}">T</figure-callout>}}_3^{\mathrm{S.}}\text{and}\Delta T_{1.3}^{\mathrm{R.}}={\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="DE102019202009A1\_0215.png,DE102019202009A1\_0217.png"\; state="\{\{state\}\}">T</figure-callout>}}_3^{\mathrm{R.}}-T_1^{\mathrm{R.}}.$

In other words represents the deviation ${\mathrm{C.}}_{1.3}^{\mathrm{S.}}$

a difference between a difference $\Delta T_{1.3}^{\mathrm{R.}}$

262 ₂ of receive time stamps that correspond to the sending of two signals 210 , 214 with the same signal power levels assigned by the reference station 200 ₁ be sent, and a difference $\Delta T_{1.3}^{\mathrm{S.}}$

262 ₃ of reception time stamps indicating a reception of the two signals 210 , 214 with the same signal power levels are assigned by the station S _N 202 _N. represents. The difference $\Delta T_{1.3}^{\mathrm{R.}}$

262 ₂ represents z. B. a difference between a second transmission time stamp $T_3^{\mathrm{R.}}$

220 ₃ the reference station 200 ₁ that describes when a third signal 214 through the reference station 200 ₁ is sent, and a first sending time stamp $T_1^{\mathrm{R.}}$

220 ₁ the reference station 200 ₁ that describes when a first signal 210 through the reference station 200 ₁ is sent. The difference $\Delta T_{1.3}^{\mathrm{S.}}$

262 ₃ represents z. B. a difference between a third receive timestamp $T_3^{\mathrm{S.}}$

230 ₆ the station S _N , which describes when the reference station 200 ₁ sent third signal 214 is received by the station S _N , and a first receive time stamp $T_1^{\mathrm{S.}}$

230 ₄ the station S _N , which describes when the reference station 200 ₁ sent first signal 210 is received by the station S _N. The first signal 210 and the third signal 214 for example, have the same signal power levels. With a linear interpolation of the clock shift error ${\mathrm{C.}}_{1.3}^{\mathrm{S.}}$

becomes the TDOA equation too $$T\mathrm{D.}O\mathrm{A.}=\Delta T_{1.2}^{\mathrm{S.}}+\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{S.}}}{\Delta T_{1.3}^{\mathrm{S.}}}\cdot \left(\Delta T_{1.2}^{\mathrm{S.}}+{\mathrm{E.}}_3-{\mathrm{E.}}_{\mathrm{4th}}\right)\right)-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3+K.$$

dazu verwendet, die Differenz $\Delta T_{\mathrm{1,2}}^S$

260₃ zwischen den Empfangszeitstempeln $T_1^S$

230₄ und $T_2^S$

230₅ , die an einer Station 202 erhalten werden, zu korrigieren, und die Signalleistungskorrekturen E₃ 240₃ und E₄ 240₄ , die die an der Station 202 erhaltenen Empfangszeitstempel $T_1^S$

230₄ und $T_2^S$

230₅ korrigieren, zu korrigieren.According to one embodiment, the clock shift correction $\frac{{\mathrm{C.}}_{1.3}^{\mathrm{S.}}}{\Delta T_{1.3}^{\mathrm{S.}}}$

used to make up the difference $\Delta T_{1.2}^{\mathrm{S.}}$

260 ₃ between the received timestamps $T_1^{\mathrm{S.}}$

230 ₄ and $T_2^{\mathrm{S.}}$

230 ₅ working at a station 202 are obtained, and the signal power corrections E ₃ 240 ₃ and E ₄ 240 ₄ who are the ones at the station 202 received timestamp received $T_1^{\mathrm{S.}}$

230 ₄ and $T_2^{\mathrm{S.}}$

230 ₅ correct, correct.

Gemäß einem Ausführungsbeispiel kann der Versatz K 310 unter Verwendung einer Uhrenverschiebungskorrektur, bei der ein Uhrenverschiebungsfehler $C_{\mathrm{1,3}}^{RT}$

korrigiert wird, berechnet werden. Die Abweichung $C_{\mathrm{1,3}}^{RT},$

die den Uhrenverschiebungsfehler darstellt, stellt beispielsweise eine Differenz zwischen der Differenz $\Delta T_{\mathrm{1,3}}^R$

262₁ von Sendezeitstempeln und einer Differenz $\Delta T_{\mathrm{1,3}}^T$

262₂ von Empfangszeitstempeln dar, die einem Empfang der zwei Signale 210, 214 mit denselben Signalleistungspegeln durch den Transponder 200₂ zugeordnet sind. Die Differenz $\Delta T_{\mathrm{1,3}}^T$

262₂ stellt z. B. eine Differenz zwischen einem dritten Empfangszeitstempel $T_3^T$

230₃ des Transponders 200₂ , der beschreibt, wann das durch die Referenzstation 200₁ gesendete dritte Signal 214 durch den Transponder 200₂ empfangen wird, und einem ersten Empfangszeitstempel $T_1^T$

230₁ des Transponders 200₂ , der beschreibt, wann das durch die Referenzstation 200₁ gesendete erste Signal 210 durch den Transponder 200₂ empfangen wird, dar. This equation still depends on the offset K. 310 from. However, this offset will 310 for example by the transit time of the signal, ie of the first signal 210 , from the reference station 200 ₁ to the transponder 200 ₂ and the computing time 260 ₂ of the transponder 200 ₂ before the signal, ie the second signal 212 , is emitted by the transponder. This offset 310 is calculated as follows, for example: $$K=TO\mathrm{A.}+\Delta T_{1.2}^T+\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\Delta T_{1.3}^T}\cdot \left(\Delta T_{1.2}^T+{\mathrm{E.}}_1\right)\right)+{\mathrm{E.}}_1+2\mathrm{B.}$$

According to one embodiment, the offset K 310 using clock shift correction in which a clock shift error ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T}$

corrected. The deviation ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T},$

representing the clock shift error, for example, represents a difference between the difference $\Delta T_{1.3}^{\mathrm{R.}}$

262 ₁ of airtime stamps and a difference $\Delta T_{1.3}^T$

262 ₂ of reception time stamps indicating a reception of the two signals 210 , 214 with the same signal power levels through the transponder 200 ₂ assigned. The difference $\Delta T_{1.3}^T$

262 ₂ represents z. B. a difference between a third receive timestamp $T_3^T$

230 ₃ of the transponder 200 ₂ that describes when this is done by the reference station 200 ₁ sent third signal 214 through the transponder 200 ₂ is received, and a first receive time stamp $T_1^T$

230 ₁ of the transponder 200 ₂ that describes when this is done by the reference station 200 ₁ sent first signal 210 through the transponder 200 ₂ is received.

A new TDOA equation without the offset K. 310 and with all correction values, for example: $$\begin{array}{c}T\mathrm{D.}O{\mathrm{A.}}_i=\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{S.}i}}{\Delta T_{1.3}^{\mathrm{S.}i}}\cdot \left(\Delta T_{1.2}^{\mathrm{S.}i}+{\mathrm{E.}}_3-{\mathrm{E.}}_{\mathrm{4th}}\right)\right)+0.5\cdot \left(\Delta T_{1.2}^T+\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\Delta T_{1.3}^T}\cdot \left(\Delta T_{1.2}^T+{\mathrm{E.}}_1\right)\right)\\ +\Delta T_{1.2}^{\mathrm{S.}i}+0.5+\Delta T_{1.2}^{\mathrm{R.}}-\mathrm{A.}+\mathrm{B.}+0.5\cdot \left({\mathrm{E.}}_1-{\mathrm{E.}}_2\right)-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3\end{array}$$

According to an embodiment, it is now possible to obtain a TOA equation with each measurement, and depending on the number of anchors, ie stations 202 to get different TDOA equations. This method enables a high update rate to be used with only four stations for localization in a two-dimensional space, two anchors, a reference station and a transponder. $$\begin{array}{c}TO{\mathrm{A.}}_1\cdot c_0=\sqrt{{\left(x_{{\mathrm{R.}}_1}-x_T\right)}^2+{\left(y_{{\mathrm{R.}}_1}-y_T\right)}^2}\text{and}\\ T\mathrm{D.}O{\mathrm{A.}}_i\cdot c_0=\sqrt{{\left(x_r-x_{\mathrm{S.}i}\right)}^2+{\left(y_T-y_{\mathrm{S.}i}\right)}^2}-\sqrt{{\left(x_{{\mathrm{R.}}_1}-x_{\mathrm{S.}i}\right)}^2+{\left(y_{{\mathrm{R.}}_1}-y_{\mathrm{S.}i}\right)}^2}\end{array}$$

According to one embodiment, the index i, e.g. B. i∈ [1; N], where N≥2, a number of a station 202 represents, in which the receive timestamp, which the reception times of the two signals 210 , 212 describe, with one 210 is sent by the reference station and one 212 sent by the transponder.

According to one exemplary embodiment, the TDOA equation is one, ie the reference station, due to the dependence on the noise of the reference station 200 ₁ , not symmetrical. The selected reference station 200 ₁ should be the one with the lowest noise, otherwise we recommend the reader to read our earlier publication on symmetric TDOA equations [17].

According to one embodiment, an apparatus is configured to obtain time of arrival differences TDOAs, e.g. B. to receive or to calculate, as according to an embodiment of the 4th and or 5 is described.

260₃ zwischen ersten Empfangszeitstempelinformationen $T_1^S$

230₄ einer Station 202 und zweiten Empfangszeitstempelinformationen $T_2^S$

230₅ der Station. Die ersten Empfangszeitstempelinformationen $T_1^S$

230₄ der Station beschreiben beispielsweise bezüglich einer Uhr der Station, wann die Station ein durch die Referenzstation 200₁ gesendetes erstes Signal 210 empfängt, und die zweiten Empfangszeitstempelinformationen $T_2^S$

230₅ der Station beschreiben beispielsweise bezüglich der Uhr der Station, wann die Station ein durch den Transponder 200₂ gesendetes zweites Signal 212 empfängt. According to one embodiment, the arrival time differences are based on a difference $\Delta T_{1.2}^{\mathrm{S.}}$

260 ₃ between first received timestamp information $T_1^{\mathrm{S.}}$

230 ₄ one station 202 and second received time stamp information $T_2^{\mathrm{S.}}$

230 ₅ the station. The first received timestamp information $T_1^{\mathrm{S.}}$

230 ₄ the station describe, for example, with respect to a clock of the station, when the station is on by the reference station 200 ₁ sent first signal 210 receives, and the second received time stamp information $T_2^{\mathrm{S.}}$

230 ₅ the station describe, for example, with regard to the station's clock, when the station is on through the transponder 200 ₂ second signal sent 212 receives.

The theoretical concepts can be based on real measurements with, for example, a measurement setup as shown in 6th is shown to be verified. A two-dimensional position estimation can be done with four stations such as a reference station 200 ₁ , a transponder 200 ₂ , a first station 202 ₁ and a second station 202 ₂ can be accomplished. Tests were carried out, for example, with Decawave EVB DW1000. Decawave provides different message types that are defined for a discovery phase, a distance determination phase and a final data transmission. A single message can vary between 190 µs and 3.4 ms depending on the update rate and the header length. In our position estimation algorithm, for example, the 190µs messages are used, which are also referred to as blink messages.

General settings for TWR and TDOA position estimation can be a channel 2 or a channel 5 of the stations, a center frequency below 960 MHz, in the range from 3.1 GHz to 10.6 GHz, e.g. B. 3993.6 MHz, or in the range of 22 GHz to 29 GHz, with a bandwidth of at least 480 MHz, e.g. B. 499.2 MHz, or at least 500 MHz. A pulse repetition frequency is 64 MHz or 16 MHz, for example, and a header length is 128 or 1024 and / or a data rate can be 6.81 Mbps or 110 Kbps.

6th and Table 1 show an exemplary constellation of the stations. Ground truth data were obtained using a laser distance measurement. It is assumed that the position of the transponder 200 ₂ with the identification (ID) two is unknown. The other stations are used to estimate the position of the transponder 200 ₂ used. The station acting as the reference station 200 ₁ identified may change during TWR positioning. In other words, the first stop can 202 ₁ and the second station 202 ₂ at some point in the measurements represent the reference station for TOA measurements. This is due to the fact that for a TWR trilateration the distances between the transponder and the other stations are obtained one after the other, for example. In contrast to TDOA, where the reference station remains the same, in this exemplary station with the id one 200 ₁ . This is why TDOA is much faster than TWR. Table 1: Position of the stations according to an embodiment Station ID X-axis [m] Y-axis [m] 1 0 0 2 0 1.5134 3 1.27 1.643 4th 1.1439 0.0385

7th shows the results for the TOA and TDOA position estimation. A mean value of the TOA and the TDOA differs, for example, for the x-axis in a range from 0.0001 m to 0.05 m, in a range from 0.0005 m to 0.005 m or in a range from 0.001 m to 0, 03 m, for example by 0.0023 m, and for the y-axis in a range from 0.00001 m to 0.05 m, in a range from 0.00005 m to 0.005 m or in a range from 0.0001 m up to 0.001 m, e.g. B. at 0.0006 m. The small difference indicates that the assumptions of offset and clock shift as set out herein are correct. If the offset is calculated as the difference and not the sum for TOA, otherwise the shift between the mean of TOA and TDOA for the x-axis would be in a range from 0.001 m to 1 m, in a range from 0.01 m to 0 , 5 m or in a range of 0.1 m to 0.2 m, e.g. B. 0.17 m, and for the y-axis in a range from 0.0001 m to 0.5 m, in a range from 0.001 m to 0.05 m or in a range from 0.01 m to 0, 04 m, e.g. B. 0.034 m. The deviation between the mean of the TOA and TDOA measurements with regard to the ground truth data, for example, can be traced back to an uncertainty of the antenna delay and the estimation of the ground truth data.

Table 2 below shows a standard deviation precision for the TOA and TDOA position estimation. For example, the y-axis scatter is almost the same for both measurement principles. On the other hand, according to one embodiment, the x-axis spread for TDOA is higher than for TOA. This effect is due, for example, to the asymmetry of the TDOA, which is in fact a combination of TOA and TDOA. Compensation for this effect is described in an earlier publication [17]. In combination with a filter it is possible to get extremely precise results. According to one embodiment, the position of the anchors affects the transponder localization, with a transponder that is more centered with respect to the anchor, it is possible to achieve better results [15]. Table 2: Accuracy: standard deviation according to an embodiment TOA TDOA X-axis [m] 0.0175 0.0479 Y-axis [m] 0.0249 0.0256

The accuracy depends, for example, on the correct position of the anchors and on the offset estimate.

6th and 7th show explicit applications of exemplary embodiments of an apparatus described herein. It is clear that 6th and 7th show only examples and that the apparatus is not limited thereto.

Herein is a procedure, see 1 to 9b , for a clock shift, signal power dependency and antenna delay correction for arrival time and arrival time difference based on measurements. It was shown how the wireless clock calibration for the arrival time difference can be provided by an additional station. The corrected time-of-arrival and time-of-arrival-difference measurements were combined to increase the number of equations for time-of-arrival position estimation.

220₁ (T1), $T_2^{TX}$

220₂ (T2) und $T_3^{TX}$

220₃ (T3), die beispielsweise Sendezeitstempelinformationen darstellen, und ein Empfänger 200₂ ist beispielsweise dazu konfiguriert, die drei Signale 210, 212 und 214 zu den Empfangszeitstempeln $T_1^{RX}$

230₁ (T1), $T_2^{RX}$

230₂ (T2) und $T_3^{RX}$

230₃ (T3), die Empfangszeitstempelinformationen darstellen können, zu empfangen. Der Sender 200₁ kann die Referenzstation oder optional eine beliebige andere Station darstellen, und der Empfänger 200₂ kann den Transponder, die erste Station, die zweite Station oder optional die Referenzstation darstellen. Gemäß einem Ausführungsbeispiel stellt der Empfänger 200₂ die zu kalibrierende Station dar, für die die Zeitstempelkorrektur und/oder die Signalleistungskorrektur bestimmt wird. 8th FIG. 13 shows a schematic view of a proposed approach to determining time stamp performance correction information and / or a clock shift correction that can be used by the apparatus of the invention or an external device for calculating TOA and / or TDOA. The proposed approach can represent an alternative clock shift correction. The transmitter station (TX) 200 ₁ sends three signals, for example P1 210 , P2 212 and P3 214 to airtime stamps $T_1^{TX}$

220 ₁ (T1), $T_2^{TX}$

220 ₂ (T2) and $T_3^{TX}$

220 ₃ (T3) representing, for example, airtime stamp information, and a recipient 200 ₂ is configured, for example, to send the three signals 210 , 212 and 214 to the receipt timestamps ${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="DE102019202009A1\_0217.png,DE102019202009A1\_0218.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^{\mathrm{R.}X}$

230 ₁ (T1), ${\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="DE102019202009A1\_0214.png,DE102019202009A1\_0215.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^{\mathrm{R.}X}$

230 ₂ (T2) and ${\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="DE102019202009A1\_0215.png,DE102019202009A1\_0217.png"\; state="\{\{state\}\}">T</figure-callout>}}_3^{\mathrm{R.}X}$

230 ₃ (T3) which can represent reception time stamp information. The transmitter 200 ₁ can represent the reference station or optionally any other station, and the receiver 200 ₂ can represent the transponder, the first station, the second station or optionally the reference station. According to one embodiment, the recipient 200 ₂ represents the station to be calibrated for which the time stamp correction and / or the signal power correction is determined.

Dasselbe gilt für $\Delta T_{\mathrm{1,3}}.$

Falls die Uhr 300₂ des Empfängers 200₂ (RX), d. h. der Referenzstation, schneller ist als die Uhr 300₁ der Senderstation TX 200₁ , dann gilt $\Delta T_{\mathrm{1,3}}^{RX}>\Delta T_{\mathrm{1,3}}^{TX},$

und der Uhrenverschiebungsfehler beträgt $C_{\mathrm{1,2}}=\Delta T_{\mathrm{1,2}}^{RX}-\Delta T_{\mathrm{1,2}}^{TX}$

170₁ und/oder $C_{\mathrm{1,3}}=\Delta T_{\mathrm{1,3}}^{RX}-\Delta T_{\mathrm{1,3}}^{TX}{170}_2.$

A clock 300 ₁ of the transmitter 200 ₁ and a clock 300 ₂ of a recipient 200 ₂ are out of sync, for example. The clock 300 ₁ of the transmitter 200 ₁ can be specified as the first clock, and the clock 300 ₂ Recipient 200 ₂ can be specified as a second clock. If the clocks 300 ₁ , 300 ₂ show no shift, then both clocks should 300 ₁ , 300 ₂ have the same frequency, and the difference between ΔT _1,2 = T2-T1 should be for the transmitter 200 ₁ and the recipient 200 ₂ be the same if the first signal 210 and the second signal 212 have the same signal power levels, otherwise $\Delta T_{1.2}^{\mathrm{R.}X}\ne \Delta T_{1.2}^{TX}.$

The same applies to $\Delta T_{1.3}.$

If the clock 300 ₂ Recipient 200 ₂ (RX), ie the reference station, is faster than the clock 300 ₁ the transmitter station TX 200 ₁ , then applies $\Delta T_{1.3}^{\mathrm{R.}X}>\Delta T_{1.3}^{TX},$

and the clock shift error is ${\mathrm{C.}}_{1.2}=\Delta T_{1.2}^{\mathrm{R.}X}-\Delta T_{1.2}^{TX}$

170 ₁ and or ${\mathrm{C.}}_{1.3}=\Delta T_{1.3}^{\mathrm{R.}X}-\Delta T_{1.3}^{TX}{170}_2.$

220₁ (T1), $T_2^{TX}$

220₂ (T2) und $T_3^{TX}$

220₃ (T3) von der Senderstation 200₁ (TX) zu erhalten und die Empfangszeitstempelinformationen $T_1^{RX}$

230₁ (T1), $T_2^{RX}$

230₂ (T2) und $T_3^{RX}$

230₃ (T3) von dem Empfänger 200₂ (RX) zu erhalten, um die Uhrenverschiebungskorrektur zu berechnen. According to one embodiment, the recipient can 200 ₂ (RX) and / or the transmitter station 200 ₁ (TX) a clock shift correction based on the clock shift error C _1,2 170 ₁ and / or the clock shift error C _1,2 170 ₂ determine. Alternatively, the apparatus described herein is configured, for example, to receive the airtime stamp information $T_1^{TX}$

220 ₁ (T1), $T_2^{TX}$

220 ₂ (T2) and $T_3^{TX}$

220 ₃ (T3) from the transmitter station 200 ₁ (TX) and the reception timestamp information $T_{}^{}$${}_1^{\mathrm{R.}X}$

230 ₁ (T1), ${\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="DE102019202009A1\_0214.png,DE102019202009A1\_0215.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^{\mathrm{R.}X}$

230 ₂ (T2) and ${\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="DE102019202009A1\_0215.png,DE102019202009A1\_0217.png"\; state="\{\{state\}\}">T</figure-callout>}}_3^{\mathrm{R.}X}$

230 ₃ (T3) from the recipient 200 ₂ (RX) to calculate the clock shift correction.

The general approaches use the phase locked loop integrator (PLL) to obtain a correction value. Usually a frequency difference between two clocks was represented by an integrator of PLL. After the warm-up time, the clocks reached, for example the clock 300 ₁ and / or the clock 300 ₂ , their final frequency. The clock shift error would now increase linearly. This correction method is less suitable because it is dependent on the signal power. Alternative methods such as symmetrical and asymmetrical double-sided two-way distance determination [5] do not receive the clock shift, but use three or more messages to average the error. According to an embodiment, the apparatus is configured to use TOA and / or TDOA, which are determined by a common method. For short measurement periods, the linear clock shift error could also be assumed during the oscillator warm-up, for example on the basis of the proposed solution according to an exemplary embodiment of the present invention.

220₁ , den zweiten Sendezeitstempel $T_2^{TX}$

220₂ und den Sendezeitstempel $T_3^{TX}$

220₃ aufweisen, und die Empfangszeitstempelinformationen zu erhalten, die den ersten Empfangszeitstempel $T_1^{RX}$

230₁ , den zweiten Empfangszeitstempel $T_2^{RX}$

230₂ und dritte Empfangszeitinformationen $T_3^{RX}$

230₃ aufweisen. Die Apparatur ist beispielsweise dazu konfiguriert, die Zeitstempelleistungskorrekturinformationen unter Verwendung einer Uhrenverschiebungskorrektur zu bestimmen, die auf Sendezeitstempelinformationen beruht, die den ersten Sendezeitstempel $T_1^{TX}$

220₁ und den dritten Sendezeitstempel $T_3^{TX}$

220₃ aufweisen, und die auf Empfangszeitstempelinformationen beruht, die den ersten Empfangszeitstempel $T_1^{RX}$

230₁ und den dritten Empfangszeitstempel $T_3^{RX}$

230₃ , zumindest zweier Signale, beispielsweise des ersten Signals 210 und des dritten Signals 230, die dieselben Signalleistungspegel aufweisen, aufweisen. Die ersten Sendezeitstempelinformationen $T_1^{TX}$

220₁ , die zweiten Sendezeitstempelinformationen $T_2^{TX}$

220₂ und die dritten Sendezeitstempelinformationen $T_3^{TX}$

220₃ sind der zweiten Uhr 300₂ zugeordnet, die dem ersten Sende-/Empfangsgerät 200₂ zugeordnet ist, und die ersten Empfangszeitstempelinformationen $T_1^{RX}$

230₁ , die zweiten Empfangszeitstempelinformationen $T_2^{RX}$

230₂ und die dritten Empfangszeitstempelinformationen $T_3^{RX}$

230₃ sind der zweiten Uhr 300₂ zugeordnet.According to an embodiment shown in 8th is an apparatus for determining time stamping power correction information, ie, signal power correction, on the basis of sending time stamping information and receiving time stamping information corresponding to the at least three signals 210 , 212 and 214 are assigned, configured to receive, for example, the transmission time stamp information that includes the first time stamp $T_1^{TX}$

220 ₁ , the second broadcast timestamp $T_2^{TX}$

220 ₂ and the sending time stamp $T_3^{TX}$

220 ₃ and obtain the reception timestamp information that includes the first reception timestamp $T_{}^{}$${}_1^{\mathrm{R.}X}$

230 ₁ , the second receive timestamp $T_{}^{}$${}_2^{\mathrm{R.}X}$

230 ₂ and third reception time information $T_{}^{}$${}_3^{\mathrm{R.}X}$

230 ₃ exhibit. For example, the apparatus is configured to determine the timestamp performance correction information using clock skew correction based on broadcast timestamp information that includes the first broadcast timestamp $T_1^{TX}$

220 ₁ and the third broadcast timestamp $T_3^{TX}$

220 ₃ and which is based on received timestamp information representing the first received timestamp $T_{}^{}$${}_1^{\mathrm{R.}X}$

230 ₁ and the third receive timestamp $T_{}^{}$${}_3^{\mathrm{R.}X}$

230 ₃ , at least two signals, for example the first signal 210 and the third signal 230 that have the same signal power levels. The first airtime stamp information $T_1^{TX}$

220 ₁ , the second airtime stamp information $T_2^{TX}$

220 ₂ and the third airtime stamp information $T_3^{TX}$

220 ₃ are the second o'clock 300 ₂ assigned to the first transceiver 200 ₂ is assigned, and the first received time stamp information $T_{}^{}$${}_1^{\mathrm{R.}X}$

230 ₁ , the second received timestamp information $T_{}^{}$${}_2^{\mathrm{R.}X}$

230 ₂ and the third received time stamp information $T_{}^{}$${}_3^{\mathrm{R.}X}$

230 ₃ are the second o'clock 300 ₂ assigned.

Thus, the sending time stamp information and the receiving time stamp information of the first signal 210 and the third signal 214 , which have the same signal power levels, are used, for example, to determine the clock skew correction, and the transmission time stamp information and the reception time stamp information of the first signal 210 and the second signal 212 that have different signal power levels are used, for example, to determine the time stamp line correction information, ie the signal power correction.

einer Abweichung C_1,3/170₁ zwischen einer ersten Differenz $\Delta T_{\mathrm{1,3}}^{TX}/{262}_1$

von Sendezeitstempeln $T_3^{TX},T_1^{TX},$

die einem Senden der zwei Signale 210, 214 mit denselben Signalleistungspegeln zugeordnet sind, und einer zweiten Differenz $\Delta T_{\mathrm{1,3}}^{RX}/{262}_2$

von Empfangszeitstempeln $T_3^{TX},T_1^{TX},$

die einem Empfang der zwei Signale 210, 214 mit denselben Signalleistungspegeln zugeordnet sind, zu korrigieren. Der Hauptgedanke besteht darin, dass der Uhrenverschiebungsfehler $C_{\mathrm{1,3}}=\Delta T_{\mathrm{1,3}}^{RX}-\Delta T_{\mathrm{1,3}}^{TX}{170}_1$

dazu verwendet werden kann, den Zeitstempel $T_2^{TX}$

220₂ mit einer einfachen linearen Interpolation zu korrigieren. If the first signal 210 and the third signal 214 have the same signal power levels and the second signal 212 has a different signal power level, for example, the apparatus is configured to determine the clock skew correction to timestamps related to the second signal using time interpolation $\frac{\Delta T_{1.2}^{TX}}{\Delta T_{1.3}^{TX}}$

a difference C _1.3 / 170 ₁ between a first difference $\Delta T_{1.3}^{TX}/{262}_1$

of airtime stamps $T_3^{TX},T_1^{TX},$

the one sending the two signals 210 , 214 associated with the same signal power levels, and a second difference $\Delta T_{1.3}^{\mathrm{R.}X}/{262}_2$

of receipt time stamps $T_3^{TX},T_1^{TX},$

the one receiving the two signals 210 , 214 with the same signal power levels assigned to correct. The main thought is that the clock shift error ${\mathrm{C.}}_{1.3}=\Delta T_{1.3}^{\mathrm{R.}X}-\Delta T_{1.3}^{TX}{170}_1$

can be used to provide the timestamp $T_2^{TX}$

220 ₂ correct with a simple linear interpolation.

einer Abweichung C_1,2/170₂ zwischen einer ersten Differenz $\Delta T_{\mathrm{1,2}}^{TX}/{260}_1$

von Sendezeitstempeln $T_2^{TX},T_1^{TX},$

die einem Senden der zwei Signale 210, 212 mit denselben Signalleistungspegeln zugeordnet sind, und einer zweiten Differenz $\Delta T_{\mathrm{1,2}}^{RX}/{262}_2$

von Empfangszeitstempeln $T_2^{RX},T_1^{RX},$

die einem Empfang der zwei Signale 210, 212 mit denselben Signalleistungspegeln zugeordnet sind, zu korrigieren.If the first signal 210 and the second signal 212 have the same signal power levels and the third signal 214 has a different signal power level, the apparatus is configured to determine the clock skew correction to timestamps based on the second signal 212 are related using time extrapolation $\frac{\Delta T_{1.3}^{TX}}{\Delta T_{1.2}^{TX}}$

a deviation C _1.2 / 170 ₂ between a first difference $\Delta T_{1.2}^{TX}/{260}_1$

of airtime stamps $T_2^{TX},T_1^{TX},$

the one sending the two signals 210 , 212 associated with the same signal power levels, and a second difference $\Delta T_{1.2}^{\mathrm{R.}X}/{262}_2$

of receipt time stamps $T_2^{\mathrm{R.}X},T_1^{\mathrm{R.}X},$

the one receiving the two signals 210 , 212 with the same signal power levels assigned to correct.

von Sendezeitstempeln $T_3^{TX},T_1^{TX}$

die einem Senden zweier Signale 210, 214 mit denselben Signalleistungspegeln zugeordnet sind, und einer zweiten Differenz $\Delta T_{\mathrm{1,3}}^{RX}/{262}_2$

von Empfangszeitstempeln, die einem Empfang der zwei Signale mit selben Signalleistungspegeln zugeordnet sind, gemäß $$CDC=-\frac{C_{\mathrm{1,3}}}{\Delta T_{\mathrm{1,3}}^{TX}}\cdot \Delta T_{\mathrm{1,2}}^{TX}$$

zu bestimmen, wobei $\Delta T_{\mathrm{1,2}}^{TX}$

einer Differenz 260₁ von Sendezeitstempeln eines Sendens der zwei Signale mit unterschiedlichen Signalleistungspegeln zugeordnet ist.According to one exemplary embodiment, the apparatus is configured, for example, to perform the clock drift correction CDC on the basis of a deviation C _1.3 / 170 ₁ between a first difference $\Delta T_{1.3}^{TX}/{262}_1$

of airtime stamps $T_3^{TX},T_1^{TX}$

sending two signals 210 , 214 associated with the same signal power levels, and a second difference $\Delta T_{1.3}^{\mathrm{R.}X}/{262}_2$

of reception time stamps associated with reception of the two signals with the same signal power levels according to FIG $$\mathrm{C.}\mathrm{D.}\mathrm{C.}=-\frac{{\mathrm{C.}}_{1.3}}{\Delta T_{1.3}^{TX}}\cdot \Delta T_{1.2}^{TX}$$

to determine where $\Delta T_{1.2}^{TX}$

a difference 260 ₁ of sending time stamps of sending the two signals with different signal power levels is assigned.

und den zweiten Sendezeitstempelinformationen $T_2^{TX}$

anzuwenden, um die Zeitstempelleistungskorrekturinformationen zu bestimmen. Bei dieser linearen Interpolation ist es möglich, eine Verschiebung des Zeitstempels 220₂ , die auf die Uhrenverschiebung zurückzuführen ist, zu schätzen. Alternativ oder zusätzlich dazu ist die Apparatur dazu konfiguriert, die Uhrenverschiebungskorrektur auf die Abweichung 260₂ zwischen den ersten Empfangszeitstempelinformationen $T_1^{RX}$

und den zweiten Empfangszeitstempelinformationen $T_2^{RX}$

anzuwenden, um die Zeitstempelleistungskorrekturinformationen zu bestimmen.According to one embodiment, the apparatus is configured to apply the clock shift correction to the deviation 260 ₁ between the first airtime stamp information $T_1^{TX}$

and the second airtime stamp information $T_2^{TX}$

to apply to determine the timestamp performance correction information. With this linear interpolation it is possible to shift the time stamp 220 ₂ which is due to the clock shift. Alternatively or in addition to this, the apparatus is configured to apply the clock shift correction to the deviation 260 ₂ between the first received timestamp information $T_{}^{}$${}_1^{\mathrm{R.}X}$

and the second received time stamp information $T_{}^{}$${}_2^{\mathrm{R.}X}$

to apply to determine the timestamp performance correction information.

und Empfangszeitstempelinformationen $T_3^{RX},T_1^{RX}$

zumindest zweier Signale 210, 214 mit denselben Signalleistungspegeln beruht. Das erste Zeitintervall 260₁ stellt beispielsweise eine optional Uhrenverschiebung-korrigierte Abweichung zwischen den ersten Sendezeitstempelinformationen $T_1^{TX}$

und den zweiten Sendezeitstempelinformationen $T_2^{TX}$

dar, und das zweite Zeitintervall 260₂ stellt beispielsweise eine optional Uhrenverschiebung-korrigierte Abweichung zwischen den ersten Empfangszeitstempelinformationen $T_1^{RX}$

und den zweiten Empfangszeitstempelinformationen $T_2^{RX}$

dar.Timestamp performance correction information based on a deviation between a first time interval 260 ₁ between sending two signals 210 , 212 with different Signal power levels and a second time interval 260 ₂ between receiving the two signals 210 , 212 with different signal power levels using clock skew correction based on airtime stamp information $T_3^{TX},T_1^{TX}$

and received time stamp information $T_{}^{}$${}_3^{\mathrm{R.}X},{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="DE102019202009A1\_0217.png,DE102019202009A1\_0218.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^{\mathrm{R.}X}$

at least two signals 210 , 214 with the same signal power levels. The first time interval 260 ₁ represents, for example, an optional clock shift-corrected discrepancy between the first transmission time stamp information $T_1^{TX}$

and the second airtime stamp information $T_2^{TX}$

and the second time interval 260 ₂ represents, for example, an optional clock shift-corrected discrepancy between the first received time stamp information $T_{}^{}$${}_1^{\mathrm{R.}X}$

and the second received time stamp information $T_{}^{}$${}_2^{\mathrm{R.}X}$

represent.

der durch die Uhrenverschiebung bewirkt wird, zumindest teilweise von der Abweichung C_1,2/170₂ zumindest teilweise zu beseitigen, um dadurch eine Uhrenverschiebung-korrigierte Version C'_1,2 der Abweichung C_1,2/170₂ zu erhalten. Ferner kann die Apparatur dazu konfiguriert sein, die Uhrenverschiebung-korrigierte Version C'_1,2 als Zeitstempelleistungskorrekturinformationen bereitzustellen oder die Zeitstempelleistungskorrekturinformationen aufgrund der Uhrenverschiebung-korrigierten Version C'_1,2 zu bestimmen.In one embodiment, the deviation is _1.2 C / 170 ₂ caused by a watch movement and by the different signal power levels. Thus the apparatus can be configured to contribute $\frac{{\mathrm{C.}}_{1.3}}{\Delta T_{1.3}^{TX}}\cdot \Delta T_{1.2}^{TX},$

which is caused by the clock shift to at least partially eliminate the deviation C _1,2 / 170 ₂ at least partially, in order to thereby obtain a clock shift-corrected version C ' _{1,2 of} the deviation C _1,2 / 170 ₂ . Furthermore, the apparatus can be configured to provide the clock shift corrected version C ' _1,2 as time stamping performance correction information or to determine the time stamping performance correction information based on the clock shift corrected version C' _1,2 .

die beispielsweise einem Leistungspegel zugeordnet ist, gemäß $C_{\mathrm{1,2}}^{\text{'}}=C_{\mathrm{1,2}}-\frac{C_{\mathrm{1,3}}}{\Delta T_{\mathrm{1,3}}^{TX}}\cdot \Delta T_{\mathrm{1,2}}^{TX}$

berechnet werden.According to one embodiment, the clock shift-corrected version ${\mathrm{C.}}_{1.2}^{\text{'}},$

which is assigned, for example, to a power level according to ${\mathrm{C.}}_{1.2}^{\text{'}}={\mathrm{C.}}_{1.2}-\frac{{\mathrm{C.}}_{1.3}}{\Delta T_{1.3}^{TX}}\cdot \Delta T_{1.2}^{TX}$

be calculated.

Although the calculation / determination of the clock shift correction and / or the signal power correction in 8th is explained mainly in relation to the apparatus, it is to be understood that the calculations can also or alternatively be performed by an external device and that the results can be received by the apparatus.

It is known that the time stamp of the DW1000 is influenced by the signal power [3,2]. An increase in signal power results in smaller time stamps, and vice versa. In 8th we have shown how a signal power correction curve can be automatically obtained for each Decawave UWB transceiver or other transceiver or stations individually, without additional measuring instruments. 9a shows the correction curves for the measured versus the actual signal power, and 9b shows the actual signal versus the timestamp error.

9a shows an estimated line based on the estimated slope. The results are the same as those obtained with Decawave, the difference being that in our case no additional measuring instruments are required and that it can be obtained individually for each station. 9b illustrates the correction curve 110 regarding the signal power. In other words, show 10A and 10B final results of a performance correction proposed herein, where 10A shows a measured signal power versus a real signal power and where 10B Figure 10 shows a correction curve representing, for example, time stamping power correction information for different signal power levels.

According to one embodiment, the signals that are analyzed herein and that are, for example, sent by a transceiver and received by a transceiver are as in FIG 1 , 2 , 3 , 4th , 5 , 6th , 7th , 8th , 9a and or 9b is described, ultra-broadband signals covering extremely large frequency ranges with a bandwidth of e.g. B. use at least 500 MHz or at least 20% of an arithmetic mean of lower and upper limit frequencies of a frequency band used. According to one embodiment, the apparatus is configured to use a time-of-arrival and time-of-arrival difference for ultra-wideband localization within buildings. In other words, the apparatus is focused, for example, on a localization based on a high frequency (HF) present inside buildings.

This presents a new approach to wireless time-of-arrival clock synchronization for Decawave and other ultra-wideband transceivers. The proposed techniques allow measurements of a time of arrival and a difference of arrival time to be combined without losing the advantages of either approach. The precision and accuracy of the results provided by Decawave ultra wideband transceivers depends on three effects, signal power, clock offset, and antenna delay. It is shown how all three effects can be compensated for both measurement techniques TOA and TDOA.

In our case, for example, the synchronization signal is part of the localization without the need to know the time interval. So far, the measurements have been provided by the Decawave EVK1000 transceiver, for example, without additional synchronization hardware. This system is able to work in indoor environments due to its fading ability. With the methods proposed herein, the signal power correction curve can be obtained automatically, and the clock shift can be corrected for each measurement. This shows how these corrections should be applied for a TOA and TDOA localization.

Although some aspects have been described in the context of an apparatus, it goes without saying that these aspects also represent a description of the corresponding method, wherein a block or a device corresponds to a method step or a feature of a method step. Similarly, aspects that have been described in the context of a process step also represent a description of a corresponding block or item or feature of a corresponding apparatus.

The methods of the invention can be stored on a digital storage medium or can be carried out on a transmission medium such as a wireless transmission medium or a wired transmission medium such as e.g. B. transmitted to the Internet.

Depending on the specific implementation requirements, embodiments of the invention can be implemented in hardware or in software. The implementation can be carried out using a digital storage medium, for example a floppy disk, a DVD, a Blu-ray disc, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, on which electronic readable control signals are stored which interact (or can interact) with a programmable computer system in such a way that the respective method is carried out. Therefore, the digital storage medium can be computer readable.

Some exemplary embodiments according to the invention thus have a data carrier which has electronically readable control signals which are able to interact with a programmable computer system in such a way that one of the methods described herein is carried out.

In general, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being effective to carry out one of the methods when the computer program product runs on a computer. The program code can for example also be stored on a machine-readable carrier.

Other exemplary embodiments have the computer program for performing one of the methods described herein, the computer program being stored on a machine-readable carrier.

In other words, an exemplary embodiment of the method according to the invention is thus a computer program which has a program code for carrying out one of the methods described here when the computer program runs on a computer.

A further exemplary embodiment of the method according to the invention is thus a data carrier (or a digital storage medium or a computer-readable medium) on which the computer program for performing one of the methods described herein is recorded.

A further exemplary embodiment of the method according to the invention is thus a data stream or a sequence of signals which represents or represents the computer program for performing one of the methods described herein. The data stream or the sequence of signals can, for example, be configured to be transferred via a data communication connection, for example via the Internet.

Another exemplary embodiment has a processing device, for example a computer or a programmable logic component, which is configured or adapted to carry out one of the methods described herein.

Another exemplary embodiment has a computer on which the computer program for performing one of the methods described herein is installed.

In some exemplary embodiments, a programmable logic component (for example a field-programmable gate array) can be used to carry out some or all of the functionalities of the methods described herein. In some exemplary embodiments, a field-programmable gate array can interact with a microprocessor in order to carry out one of the methods described herein. In general, in some exemplary embodiments, the methods are performed by any hardware device.

The above-described embodiments are merely illustrative of the principles of the present invention. It is to be understood that modifications and variations of the arrangements and details described herein will be apparent to other skilled persons. It is therefore intended that the invention be limited only by the scope of protection of the following patent claims and not by the specific details presented herein with reference to the description and explanation of the exemplary embodiments.

Claims (30)

Apparatus (100) for locating a transponder (200 ₂ ), which is configured to: obtain an arrival time of one or more signals (210, 212, 214) on the basis of transmission time stamps (220 ₁ - 220 ₃ ) and reception time stamps (230 ₁ - 230 ₃ ) two or more signals (210, 212, 214) which are sent between a reference station (200 ₁ ) and a transponder (200 ₂ ); Obtaining a first arrival time difference based on a difference (260 ₃ ) between reception time stamps (230 ₄ , 230 ₅ ) obtained at a first station (202 ₁ ) and reception times (230 ₄ , 230 ₅ ) of two signals (210, 212) describe, one being sent by the reference station (200 ₁ ) and the other being sent by the transponder (200 ₂ ), at the first station (202 ₁ ); Obtaining a second arrival time difference based on a difference (260 ₃ ) between reception time stamps (230 ₄ , 230 ₅ ) received at a second station (202 ₂ ) and reception times (230 ₄ , 230 ₅ ) of two signals (210, 212) describe, one being sent by the reference station (200 ₁ ) and the other being sent by the transponder (200 ₂ ), at the second station (202 ₂ ); Calculating a position (140) of the transponder (200 ₂ ) on the basis of the arrival time and the at least two arrival time differences. The apparatus (100) according to Claim 1 , wherein the apparatus (100) is configured to obtain the first arrival time difference, wherein the first arrival time difference is based on a difference (260 ₃ ) between first reception time stamp information (230 ₄ ) of the first station (202 ₁ ) and second reception time stamp information (230 ₅ ) of the first station (202 ₁ ), and wherein the apparatus (100) is configured to obtain the second arrival time difference, wherein the second arrival time difference is based on a difference (260 ₃ ) between first received time stamp information (230 ₄ ) of the second station (202 ₂ ) and second received time stamp information (230 ₅ ) of the second station (202 ₂ ) is based; wherein the first reception time stamp information (230 ₄ ) of the first station (202 ₁ ) describes when the first station (202 ₁ ) receives a first signal (210) transmitted by the reference station (200 ₁ ), the second reception time stamp information (230 ₅ ) of the first station (202 ₁ ) describe when the first station (202 ₁ ) receives a second signal (212) sent by the transponder (200 ₂ ), the first reception time stamp information (230 ₄ ) describing the second station (202 ₂ ) when the second station (202 ₂ ) receives the first signal (210) sent by the reference station (200 ₁ ), and wherein the second reception time stamp information (230 ₅ ) of the second station (202 ₂ ) describes when the second station (202 ₂ ) the receives second signal (212) transmitted by the transponder (200 ₂ ). The apparatus (100) according to Claim 2 in which the first arrival time difference is calculated using a signal power correction (240 ₃ , 240 ₄ ) in order to obtain the first reception time stamp information (230 ₄ ) of the first station (202 ₁ ) and the second reception time stamp information (230 ₅ ) of the first station (202 ₁ ) to correct; and or in which the second arrival time difference is calculated using a signal power correction (240 ₃ , 240 ₄ ) in order to assign the first reception time stamp information (230 ₄ ) to the second station (202 ₂ ) and the second reception time stamp information (230 ₅ ) to the second station (202 ₂ ) correct. The apparatus (100) according to one of the Claims 1 to 3 , in which the first arrival time difference and / or the second arrival time difference is or are calculated using an offset (310) which describes a time delay between a transmission of the two signals (210, 212), one by the reference station (200 ₁ ) and one is sent by the transponder (200 ₂ ). The apparatus (100) according to Claim 4 , in which the offset (310) based on the arrival time, based on a first reception time stamp of the transponder (200 ₂ ), which describes when a first signal (210) transmitted by the reference station (200 ₁ ) through the transponder (200 ₂ ) is received, and on the basis of a first transmission time stamp (220 ₂ ) of the transponder (200 ₂ ), which describes when a second signal (212) is transmitted by the transponder (200 ₂ ), using a Clock shift correction and / or an antenna delay correction (250 ₁ , 250 ₂ ) and / or a signal power correction (240 ₁ ) is determined. The apparatus (100) according to Claim 5 , in which a clock shift correction used to determine the offset (310) is based on transmission time stamps (220 ₃ ) and reception time stamps (230 ₃ ) which are related to a third signal (214) transmitted by the reference station (200 ₁ ) and by the Transponder (200 ₂ ) is received. The apparatus (100) according to one of the Claims 4 to 6th , in which the offset (310) K according to $$K=TO\mathrm{A.}+\Delta T_{1.2}^{TX}+\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\Delta T_{1.3}^{TX}}\cdot \left(\Delta T_{1.2}^T+{\mathrm{E.}}_1\right)\right)+{\mathrm{E.}}_1+2\mathrm{B.}$$

is determined, wherein the value TOA represents the arrival time of the one or more signals (210, 212) transmitted between the reference station (200 ₁ ) and the transponder (200 ₂ ); in which $\Delta T_{1.2}^T$

(260 ₂ ) a difference between a first transmission time stamp (220 ₂ ) of the transponder (200 ₂ ), which describes when a second signal (212) is sent by the transponder (200 ₂ ), and a first reception time stamp (230 ₁ ) of the Transponder (200 ₂ ), which describes when a first signal (210) transmitted by the reference station (200 ₁ ) is received by the transponder (200 ₂ ); being the deviation ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T}$

(170 ₁ ) a difference between a difference (262 ₁ ) of transmission time stamps (220 ₁ , 220 ₃ ) which are assigned to a transmission of two signals (210, 214) with the same signal power levels, which are transmitted by the reference station (200 ₁ ), and a difference $\Delta T_{1.3}^T$

(2622) of reception time stamps (230 ₁ , 230 ₃ ) associated with reception of the two signals (210, 214) with the same signal power levels by the transponder (200 ₂ ); wherein the value E ₁ (240 ₁ ) represents a signal power correction which is assigned to a correction of reception time stamps (230 ₁ , 230 ₃ ) of the transponder (200 ₂ ) for received signals (210, 214) with a first signal power level; and wherein the value B (250 ₂ ) represents an antenna delay correction related to the transponder (200 ₂ ). The apparatus (100) according to one of the Claims 1 to 7th , in which the first arrival time difference and the second arrival time difference according to $$T\mathrm{D.}O{\mathrm{A.}}_i=\Delta T_{1.2}^{\mathrm{S.}i}-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3+K$$

can be determined, the index i representing a number of a station Si (202), in which the reception time stamps (230 ₄ , 230 ₅ ), which describe the reception times of the two signals (210, 212), one being determined by the reference station (2001) is sent and one is sent by the transponder (200 ₂ ), and those for determining the difference $\Delta T_{1.2}^{\mathrm{S.}i}$

(260 ₃ ) used between the receive time stamps (230 ₄ , 230 ₅ ) are obtained; wherein the value E ₃ (240 ₃ ) represents a signal power correction which is associated with a correction of reception time stamps (230 ₄ , 230 ₆ ) of the station Si (202) for received signals (210, 214) with a first signal power level; wherein the value E ₄ (240 ₄ ) represents a signal power correction which is assigned to a correction of reception time stamps (230 ₅ ) of the station Si (202) for received signals (212) with a second signal power level; and wherein the value K represents an offset (310) which describes a time delay between a transmission of the two signals (210, 212), one being transmitted by the reference station (2001) and one being transmitted by the transponder (200 ₂ ). The apparatus (100) according to one of the Claims 1 to 8th in which the first arrival time difference is calculated using a clock offset correction in order to correct the difference (260 ₃ ) between the received time stamps (230 ₄ , 230 ₅ ) obtained at the first station (202 ₁ ) and / or for signal power corrections (240 ₃ , 240 ₄ ), which correct the reception time stamps (230 ₄ , 230 ₅ ) received at the first station (202 ₁ ); and / or wherein the second arrival time difference is calculated using a clock offset correction in order to correct the difference (260 ₃ ) between the received time stamps (230 ₄ , 230 ₅ ) obtained at the second station (202 ₂ ) and / or in order to correct the signal power corrections which the correct the received time stamp (230 ₄ , 230 ₅ ) received at the second station (202 ₂ ). The apparatus (100) according to Claim 9 , in which the clock offset correction used to calculate the first arrival time difference is based on a transmission time stamp (220 ₃ ) and a reception time stamp (230 ₆ ) which are related to a third signal (214) transmitted by the reference station (200 ₁ ) and by the first station (202 ₁ ) is received, and / or in which the clock offset correction that is used to calculate the second arrival time difference is based on a transmission time stamp (220 ₃ ) and a reception time stamp (230 ₆ ) based on the third signal (214) which is transmitted by the reference station (200 ₁ ) and received by the second station (202 ₂ ). The apparatus (100) according to one of the Claims 1 to 10 , in which the first arrival time difference and the second arrival time difference according to $$T\mathrm{D.}O{\mathrm{A.}}_i=\Delta T_{1.2}^{\mathrm{S.}i}+\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{S.}i}}{\Delta T_{1.3}^{\mathrm{S.}i}}\cdot \left(\Delta T_{1.2}^{\mathrm{S.}i}+{\mathrm{E.}}_3-{\mathrm{E.}}_{\mathrm{4th}}\right)\right)-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3+K$$

are calculated, the index i representing a number of a station Si (202) in which the reception time stamps (230 ₄ , 230 ₅ ), which describe the reception times of the two signals (210, 212), one of which is provided by the reference station (200 ₁ ) is sent and one is sent by the transponder (200 ₂ ) and that is used to determine the difference $\Delta T_{1.2}^{\mathrm{S.}i}$

(260 ₃ ) used between the receive time stamps (230 ₄ , 230 ₅ ) are obtained; being the deviation ${\mathrm{C.}}_{1.3}^{\mathrm{S.}i}$

a difference between a difference (262 ₁ ) of transmission time stamps (220 ₁ , 220 ₃ ) associated with sending two signals (210, 214) with the same signal power levels sent by the reference station (200 ₁ ) and a difference $\Delta T_{1.3}^{\mathrm{S.}i}$

(262 ₃ ) of reception time stamps (230 ₄ , 2306) associated with reception of the two signals (210, 214) with the same signal power levels by the station Si (202); wherein the value E3 (240 ₃ ) represents a signal power correction which is associated with a correction of reception time stamps (230 ₄ , 230 ₆ ) of the station Si (202) for received signals (210, 214) with a first signal power level; wherein the value E ₄ (240 ₄ ) represents a signal power correction which is associated with a correction of reception time stamps of the station Si (202) for received signals with a second signal power level; and wherein the value K represents an offset (310) which describes a time delay between a transmission of the two signals, one being transmitted by the reference station (200 ₁ ) and one being transmitted by the transponder (200 ₂ ). The apparatus (100) according to one of the Claims 1 to 11 , in which the first arrival time difference and the second arrival time difference according to $$\begin{array}{l}T\mathrm{D.}O{\mathrm{A.}}_i=\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{S.}i}}{\Delta T_{1.3}^{\mathrm{S.}i}}\cdot \left(\Delta T_{1.2}^{\mathrm{S.}i}+{\mathrm{E.}}_3-{\mathrm{E.}}_{\mathrm{4th}}\right)\right)+0.5\cdot \left(\Delta T_{1.2}^T+\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\Delta T_{1.3}^T}\cdot \left(\Delta T_{1.2}^T+{\mathrm{E.}}_1\right)\right)\\ +\Delta T_{1.2}^{\mathrm{S.}i}+0.5\cdot \Delta T_{1.2}^{\mathrm{R.}}-\mathrm{A.}+\mathrm{B.}+0.5\cdot \left({\mathrm{E.}}_1-{\mathrm{E.}}_2\right)-{\mathrm{E.}}_{\mathrm{4th}}+{\mathrm{E.}}_3\end{array}$$

are calculated, the index i representing a number of a station Si (202) in which the reception time stamps (230 ₄ , 230 ₅ ), which describe the reception times of the two signals (210, 212), one of which is provided by the reference station (200 ₁ ) is sent and one is sent by the transponder (200 ₂ ) and that is used to determine the difference $\Delta T_{1.2}^{\mathrm{S.}i}$

used between the reception timestamps (230 ₄ , 230 ₅ ); being the deviation ${\mathrm{C.}}_{1.3}^{\mathrm{S.}i}$

a difference between a difference (262 ₁ ) of transmission time stamps (220 ₁ , 220 ₃ ) associated with sending two signals (210, 214) with the same signal power levels sent by the reference station (200 ₁ ) and a difference $\Delta T_{1.3}^{\mathrm{S.}i}$

(262 ₃ ) of reception time stamps (230 ₄ , 230 ₆ ) associated with reception of the two signals (210, 214) with the same signal power levels by the station Si (202); wherein the value E ₁ (240 ₁ ) represents a signal power correction which is assigned to a correction of reception time stamps (230 ₁ , 230 ₃ ) of the transponder (200 ₂ ) for received signals with a first signal power level; wherein the value E ₂ (240 ₂ ) represents a signal power correction which is assigned to a correction of reception time stamps (230 ₂ ) of the reference station (200 ₁ ) for received signals with a second signal power level; wherein the value E ₃ (240 ₃ ) represents a signal power correction which is associated with a correction of reception time stamps (230 ₄ , 230 ₆ ) of the station Si (202) for received signals (210, 214) with a first signal power level; wherein the value E ₄ (240 ₄ ) represents a signal power correction which is assigned to a correction of reception time stamps (230 ₅ ) of the station Si (202) for received signals (212) with a second signal power level; in which $\Delta T_{1.2}^T$

(260 ₂ ) a difference between a first transmission time stamp (220 ₂ ) of the transponder (200 ₂ ), which describes when a second signal (212) is sent by the transponder (200 ₂ ), and a first reception time stamp (230 ₁ ) of the Transponder (200 ₂ ), which describes when a first signal (210) transmitted by the reference station (200 ₁ ) is received by the transponder (200 ₂ ); being the deviation ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T}$

(170 ₁ ) a difference between a difference (262 ₁ ) of transmission time stamps (220 ₁ , 220 ₃ ) which are assigned to a transmission of two signals (210, 214) with the same signal power levels, which are transmitted by the reference station (200 ₁ ), and a difference $\Delta T_{1.3}^T$

(262 ₂ ) of reception time stamps (230 ₁ , 230 ₃ ) associated with reception of the two signals (210, 214) with the same signal power levels by the transponder (200 ₂ ); in which $\Delta T_{1.2}^{\mathrm{R.}}$

(260 ₁ ) a difference between a first reception time stamp (230 ₂ ) of the reference station (200 ₁ ), which describes when the second signal (212) transmitted by the transponder (200 ₂ ) is received by the reference station (200 ₁ ), and a first transmission time stamp (220 ₁ ) of the reference station (200 ₁ ), which describes when the first signal (210) is transmitted by the reference station (200 ₁ ); wherein the value A (250 ₁ ) represents an antenna delay correction related to the reference station (200 ₁ ); and wherein the value B (250 ₂ ) represents an antenna delay correction related to the transponder (200 ₂ ). The apparatus (100) according to one of the Claims 1 to 12 , in which the arrival time on the basis of a transmission time stamp (220 ₁ ) and a reception time stamp (230 ₁ ) of a first signal (210) transmitted by the reference station (200 ₁ ) and received by the transponder (200 ₂ ), and a Transmission time stamp (220 ₂ ) and a reception time stamp (230 ₂ ) of a second signal (212) which is transmitted by the transponder (200 ₂ ) and received by the reference station (200 ₁ ) is calculated. The apparatus (100) according to one of the Claims 1 to 13th , where the arrival time TOA according to $$TO\mathrm{A.}=0.5\cdot \left(\left(T_2^{\mathrm{R.}}-T_1^{\mathrm{R.}}\right)-\left(T_2^T-T_1^T\right)-{\mathrm{E.}}_1-{\mathrm{E.}}_2\right)-\mathrm{A.}-\mathrm{B.}$$

is calculated, where $T_1^{\mathrm{R.}}$

(220 ₁ ) represents a first transmission time stamp (220 ₁ ) of the reference station (200 ₁ ), which describes when a first signal (210) is sent by the reference station (200 ₁ ), wherein $T_1^T$

(230 ₁ ) represents a first reception time stamp (230 ₁ ) of the transponder (200 ₂ ), which describes when the first signal (210) sent by the reference station (200 ₁ ) is received by the transponder (200 ₂ ), wherein $T_2^T$

(220 ₂ ) represents a first transmission time stamp (220 ₂ ) of the transponder (200 ₂ ), which describes when a second signal (212) is sent by the transponder (200 ₂ ), wherein $T_2^{\mathrm{R.}}$

(230 ₂ ) represents a first reception time stamp (230 ₂ ) of the reference station (200 ₁ ), which describes when the second signal (212) sent by the transponder (200 ₂ ) is received by the reference station (200 ₁ ), the value E ₁ (240 ₁ ) is a signal power correction that is a correction of the first received time stamp $T_1^T$

(230 ₁ ) of the transponder (200 ₂ ) is assigned, based on the first signal power level of the first signal (210); where the value E ₂ (240 ₂ ) is a signal power correction that corresponds to a correction of the first receive time stamp (230 ₂ ) $T_2^{\mathrm{R.}}$

associated with the reference station (200 ₁ ) based on a signal power level of the second signal (212); wherein the value A (250 ₁ ) represents an antenna delay correction related to the reference station (200 ₁ ); and wherein the value B (250 ₂ ) represents an antenna delay correction related to the transponder (200 ₂ ). The apparatus (100) according to one of the Claims 1 to 14th in which the clock offset correction used to calculate the time of arrival is based on a transmission time stamp (220 ₃ ) and a reception time stamp (230 ₃ ) related to a third signal (214) sent by the reference station (200 ₁ ) and is received by the transponder (200 ₂ ). The apparatus (100) according to one of the Claims 1 to 15th in which the time of arrival is calculated using a clock offset correction in order to determine the difference between a first transmission time stamp (220 ₂ ) of the transponder (200 ₂ ) which describes when a second signal (212) is transmitted by the transponder (200 ₂ ), and to correct a first reception time stamp (230 ₁ ) of the transponder (200 ₂ ), which describes when a first signal (210) sent by the reference station (200 ₁ ) is received by the transponder (200 ₂ ), and / or at a signal power correction (240 ₁ ), which corrects the first reception time stamp (230 ₁ ) received on the transponder (200 ₂ ), is carried out. The apparatus (100) according to one of the Claims 1 to 16 , where the arrival time TOA according to $$TO\mathrm{A.}=0.5\cdot \left(\Delta T_{1.2}^{\mathrm{R.}}-\Delta T_{1.2}^T-\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\Delta T_{1.3}^T}\cdot \left(\Delta T_{1.2}^T+{\mathrm{E.}}_1\right)-{\mathrm{E.}}_2-{\mathrm{E.}}_1\right)+Z$$

is calculated, the deviation ${\mathrm{C.}}_{1.3}^{\mathrm{R.}T}$

(170 ₁ ) a difference between a difference (262 ₁ ) of transmission time stamps (220 ₁ , 220 ₃ ) which are assigned to a transmission of two signals (210, 214) with the same signal power levels, which are transmitted by the reference station (200 ₁ ), and a difference $\Delta T_{1.3}^T$

(262 ₂ ) of reception time stamps (230 ₁ , 230 ₃ ) associated with reception of the two signals (210, 214) with the same signal power levels by the transponder (200 ₂ ); in which $\Delta T_{1.2}^{\mathrm{R.}}$

(260 ₁ ) a difference between a first reception time stamp (230 ₂ ) of the reference station (200 ₁ ), which describes when the second signal (212) sent by the transponder (200 ₂ ) was transmitted by the Reference station (200 ₁ ) is received, and a first transmission time stamp (220 ₁ ) of the reference station (200 ₁ ), which describes when the first signal (210) is transmitted by the reference station (200 ₁ ); in which $\Delta T_{1.2}^T$

(260 ₂ ) a difference between a first transmission time stamp (220 ₂ ) of the transponder (200 ₂ ), which describes when a second signal (212) is sent by the transponder (200 ₂ ), and a first reception time stamp (230 ₁ ) of the Transponder (200 ₂ ), which describes when a first signal (210) transmitted by the reference station (200 ₁ ) is received by the transponder (200 ₂ ); wherein the value E ₁ (240 ₁ ) represents a signal power correction which is assigned to a correction of reception time stamps (230 ₁ , 230 ₃ ) of the transponder (200 ₂ ) for received signals (230 ₁ , 230 ₃ ) with a first signal power level; wherein the value E ₂ (240 ₂ ) represents a signal power correction which is associated with a correction of reception time stamps (230 ₂ ) of the reference station (200 ₁ ) for received signals (212) with a second signal power level; and where Z represents a constant offset. The apparatus (100) according to one of the Claims 1 to 17th wherein the apparatus (100) is configured to determine the position (140) of the transponder (200 ₂ ) using distance information that is a distance between the reference station (200 ₁ ) and the transponder (200 ₂ ) based on the arrival time , describe; using first distance difference information which is a difference between a distance between the reference station (200 ₁ ) and the first station (202 ₁ ) and a distance between the transponder (200 ₂ ) and the first station (202 ₁ ) on the first Arrival time difference based, describe; using second distance difference information which is a difference between a distance between the reference station (200 ₁ ) and the second station (202 ₂ ) and a distance between the transponder (200 ₂ ) and the second station (202 ₂ ) on the second Arrival time difference based, describe; and using information on positions of the reference station (200 ₁ ), the first station (202 ₁ ) and the second station (202 ₂ ). The apparatus (100) according to one of the Claims 1 to 18th , wherein the apparatus (100) is configured to calculate the position (140) of the transponder (200 ₂ ) using an intersection of the following: a first circle or a first sphere, which is determined by information about a position of the reference station ( 200 ₁ ) and the arrival time TOA is determined; a first hyperbola or a first hyperboloid which is determined by information on a position of the reference station (200 ₁ ) and the first station (202 ₁ ) and the first arrival time difference; and a second hyperbola or a second hyperboloid which is determined by information about a position of the reference station (200 ₁ ) and the second station (202 ₂ ) and the second arrival time difference. The apparatus (100) according to one of the Claims 1 to 19th , wherein the apparatus (100) is configured to solve a system of equations in order to calculate the position (140) of the transponder (200 ₂ ), wherein a first of the equations describes a first circle or a first sphere, the or the is centered at a position of the reference station (200 ₁ ), a radius of the first circle or the first sphere being determined by the time of arrival; a second of the equations describing a first hyperbola or a first hyperboloid, foci of which are located at a position of the reference station (200 ₁ ) and at a position of the first station (202 ₁ ), with an absolute difference of distances from points of the first Hyperbola or the first hyperboloid of the foci is determined by the first arrival time difference; a third of the equations describing a second hyperbola or a second hyperboloid, foci of which are located at a position of the reference station (200 ₁ ) and at a position of the second station (202 ₂ ), an absolute difference of distances from points of the second Hyperbola or the second hyperboloid is determined by the foci by the second arrival time difference. The apparatus (100) according to one of the Claims 1 to 20th , wherein the apparatus (100) is configured to determine the position (140) of the transponder (200 ₂ ) using a multiplication of the time of arrival with a propagation speed of a signal, using a multiplication of the first arrival time difference with the propagation speed of the signal and using a Multiplication of the to calculate the second time-of-arrival difference with the propagation speed of the signal on the basis of lateration. The apparatus (100) according to Claim 21 in which the multiplication of the arrival time by a propagation speed of the signal represents a distance between the reference station (200 ₁ ) and the transponder (200 ₂ ); in which the multiplication of the first arrival time difference with the propagation speed of the signal yields a difference between a distance between the reference station (200 ₁ ) and the first station (202 ₁ ) and a distance between the transponder (200 ₂ ) and the first station (202 ₁ ) represents; and in which the multiplication of the second arrival time difference by the propagation speed of the signal is a difference between a distance between the reference station (200 ₁ ) and the second station (202 ₂ ) and a distance between the transponder (200 ₂ ) and the second station (202 ₂ ) represents; and using information about positions of the reference station (200 ₁ ), the first station (202 ₁ ) and the second station (202 ₂ ). The apparatus (100) according to one of the Claims 1 to 22nd , wherein the apparatus (100) is configured to determine the position (140) of the transponder (200 ₂ ) by solving a system of equations according to $$\begin{array}{l}TO\mathrm{A.}\cdot c_0=\sqrt{{\left(x_{\mathrm{R.}}-x_T\right)}^2+{\left(y_{\mathrm{R.}}-y_T\right)}^2},\text{and}\\ T\mathrm{D.}O{\mathrm{A.}}_i\cdot c_0=\sqrt{{\left(x_T-x_{\mathrm{S.}i}\right)}^2+{\left(y_T-y_{\mathrm{S.}i}\right)}^2}-\sqrt{{\left(x_{\mathrm{R.}}-x_{\mathrm{S.}i}\right)}^2+{\left(y_{\mathrm{R.}}-y_{\mathrm{S.}i}\right)}^2}\end{array}$$

and or $$\begin{array}{l}TO{\mathrm{A.}}_n\cdot c_0=\sqrt{{\left(x_{{\mathrm{R.}}_n}-x_T\right)}^2+{\left(y_{{\mathrm{R.}}_n}-y_T\right)}^2+{\left(z_{{\mathrm{R.}}_n}-z_T\right)}^2},\text{and}\\ T\mathrm{D.}O{\mathrm{A.}}_i\cdot c_0=\sqrt{{\left(x_T-x_{\mathrm{S.}i}\right)}^2+{\left(y_T-y_{\mathrm{S.}i}\right)}^2+{\left(z_T-z_{\mathrm{S.}i}\right)}^2}\\ -\sqrt{{\left(x_{{\mathrm{R.}}_n}-x_{\mathrm{S.}i}\right)}^2+{\left(y_{{\mathrm{R.}}_n}-y_{\mathrm{S.}i}\right)}^2+{\left(z_{{\mathrm{R.}}_n}-z_{\mathrm{S.}i}\right)}^2}\end{array}$$

to calculate, where the value TOA represents the arrival time; where the value TDOA represents the time of arrival difference; where the value c _{0 represents} a propagation speed of a signal; where x represents a first coordinate in 3D space, where y represents a second coordinate in 3D space, and where z represents a third coordinate in 3D space; wherein the index R indicates a reference station (200 ₁ ); wherein the index T indicates a transponder (200 ₂ ); the index Si indicating an i-th station (202); and wherein the index n represents a number of a reference station (200 ₁ ) R. The apparatus (100) according to one of the Claims 1 to 23 , wherein the apparatus (100) is configured to receive first airtime stamp information (220 ₁ ) of the Reference station (200 ₁ ), which describes when the reference station (200 ₁ ) sends a first signal (210) with a first signal power level, first reception time stamp information (230 ₄ ) of the first station (202 ₁ ), which describes when the first station ( 202 ₁ ) receives the first signal (210) sent by the reference station (200 ₁ ), first reception time stamp information (230 ₄ ) of the second station (202 ₂ ), which describes when the second station (202 ₂ ) receives the signal from the reference station (200 ₁ ) receives transmitted first signal (210), and first reception time stamp information (230 ₁ ) of the transponder (200 ₂ ), which describes when the transponder (200 ₂ ) receives the first signal (210) transmitted by the reference station (200 ₁ ), to obtain; and wherein the apparatus (100) is configured to first send time stamp information (220 ₂ ) of the transponder (200 ₂ ), which describes when the transponder (200 ₂ ) sends a second signal (212), second reception time stamp information (230 ₅ ) of the first Station (202 ₁ ), which describes when the first station (202 ₁ ) receives the second signal (212) sent by the transponder (200 ₂ ), first receive time stamp information (230 ₄ ) of the second station (202 ₂ ), which describes when the second station (202 ₂ ) receives the second signal (212) sent by the transponder (200 ₂ ), and first receive time stamp information (230 ₂ ) of the reference station (200 ₁ ), which describes when the reference station (200 ₁ ) through receiving the second signal (212) transmitted to the transponder (200 ₂ ); and / or wherein the apparatus (100) is configured to provide second transmission time stamp information (220 ₃ ) of the reference station (200 ₁ ), which describes when the reference station (200 ₁ ) sends a third signal (214) with the first signal power level, third reception time stamp information (230 ₆ ) of the first station (202 ₁ ), which describe when the first station (202 ₁ ) receives the third signal (214) sent by the reference station (200 ₁ ), third reception time stamp information (230 ₆ ) of the second station (202 ₂ ), which describe when the second station (202 ₂ ) receives the third signal (214) sent by the reference station (200 ₁ ), and second reception time stamp information (230 ₃ ) of the transponder (200 ₂ ) which describes when the transponder (200 ₂ ) receives the third signal (214) sent by the reference station (200 ₁ ). The apparatus (100) according to Claim 24 , wherein the apparatus (100) is configured to perform a first signal power correction (240 ₁ ) for correcting the first received time stamp information (230 ₁ ) of the transponder (200 ₂ ) and the second received time stamp information (230 ₃ ) of the transponder (200 ₂ ) on the basis of obtain the first signal power level of the first and third signals (214); wherein the apparatus (100) is configured to receive a second signal power correction (240 ₂ ) for correcting the first reception time stamp information (230 ₂ ) of the reference station (200 ₁ ) based on a signal power level of the second signal (212); wherein the apparatus (100) is configured to apply a third signal power correction (240 ₃ ) for correcting the first reception time stamp information (230 ₄ ) of the first station (202 ₁ ) and the third reception time stamp information (230 ₆ ) of the first station (202 ₁ ) on the Obtain a basis of the first signal power level of the first and third signals (214); wherein the apparatus (100) is configured to receive a fourth signal power correction (240 ₄ ) for correcting the second reception time stamp information (230 ₅ ) of the first station (202 ₁ ) based on the signal power level of the second signal (212); wherein the apparatus (100) is configured to perform a fifth signal power correction (240 ₃ ) for correcting the first reception time stamp information (230 ₄ ) of the second station (202 ₂ ) and the third reception time stamp information (230 ₆ ) of the second station (202 ₂ ) on the Obtain a basis of the first signal power level of the first and third signals (214); wherein the apparatus (100) is configured to receive a sixth signal power correction (240 ₄ ) for correcting the second received time stamp information (230 ₃ ) of the second station (202 ₂ ) based on the signal power level of the second signal (212); and wherein the apparatus (100) is configured to use the signal power corrections (240) to correct respective timestamp information. The apparatus (100) according to Claim 24 or Claim 25 , in which the first signal power correction (240 ₁ ) is related to the transponder (200 ₂ ), the second signal power correction (240 ₂ ) is related to the reference station (200 ₁ ), the third signal power correction (240 ₃ ) and the fourth signal power correction (240 ₄ ) are related to the first station (202 ₁ ) and the fifth signal power correction (240 ₅ ) and the sixth signal power correction (240 ₆ ) are related to the second station (202 ₂ ); and in which the first signal power correction (240 ₁ ), the second signal power correction (240 ₂ ), the third signal power correction (240 ₃ ), the fourth signal power correction (240 ₄ ), the fifth signal power correction (240 ₅ ) and the sixth signal power correction (240 ₆ ) are based on a discrepancy between the following: a first time interval (260 ₁ ) between a transmission of two signals (210, 212) with different signal power levels, the first time interval (260 ₁ ) being determined by a difference in transmission time stamps (220 ₁ , 220) based on a first clock (300 ₁ ) is related, and a second time interval (260 ₂ ) between a reception of the two signals (210, 212) with different signal power levels by the station (202), which is based on the respective signal power correction (240 ₁ -240 ₆ ), the second time interval (260 ₂ ) being described by a difference in reception time stamps (230 ₁ , 230 ₁ ) which refer to a second clock (300 ₂ ), which is a clock of the station (202), which is related to the respective signal power correction (240 ₁ -240 ₆ ), and are obtained using a clock offset correction based on the transmission time stamp information (220 ₁ , 220 ₃ ) and received time stamp information (230 ₁ , 230 ₃ ) of at least two signals (210, 214) with the same signal power levels. The apparatus (100) according to one of the Claims 1 to 26th , wherein the apparatus (100) is configured to obtain a first antenna delay correction value (250 ₁ ) for correcting transmission time stamps (220 ₁ ) and reception time stamps (230 ₂ ) related to the reference station (200 ₁ ); wherein the apparatus (100) is configured to obtain a second antenna delay correction value (250 ₂ ) for correcting transmission time stamps (220 ₂ ) and reception time stamps (230 ₁ ) related to the transponder (200 ₂ ); wherein the apparatus (100) is configured to receive a third antenna delay correction value (250) for correcting transmission time stamps and reception time stamps (230 ₄ -230 ₆ ) related to the first station (202 ₁ ); wherein the apparatus (100) is configured to receive a fourth antenna delay correction value (250) for correcting transmission time stamps and reception time stamps (230 ₄ -230 ₆ ) related to the second station (202 ₂ ); and wherein the apparatus (100) is configured to use the first antenna delay correction value (250 ₁ ), the second antenna delay correction value (250 ₂ ), the third antenna delay correction value (250) and / or the fourth antenna delay correction value (250) to calculate the arrival time, the to obtain the first time of arrival difference and the second time of arrival difference. The apparatus (100) according to one of the Claims 1 to 27 , in which the clock offset correction is determined using a time interpolation or time extrapolation of a deviation (170 ₁ -170 ₂ ) between the following: a first difference (260 ₁ , 262 ₁ ) of transmission time stamps associated with a transmission of two signals with the same signal power levels, and a second difference (260 ₂ , 262 ₂ ) of receive time stamps associated with a reception of the two signals with the same signal power levels, the first difference (260 ₁ , 262 ₁ ) being related to a first clock (300 ₁ ) and the second difference (260 ₂ , 262 ₂ ) is related to a second clock (300 ₂ ); and wherein the apparatus (100) is configured to use the clock offset correction to obtain the time of arrival, the first time difference of arrival, and the second time of arrival difference. Method for locating a transponder, comprising the following steps: Obtaining an arrival time of one or more signals on the basis of transmission time stamps and reception time stamps of two or more signals transmitted between a reference station and a transponder; Obtaining a first arrival time difference based on a difference between reception time stamps obtained at a first station describing reception times of two signals, one being transmitted by the reference station and one being transmitted by the day, at the first station; Obtaining at the second station a second arrival time difference based on a difference between reception time stamps obtained at a second station describing reception times of two signals, one being transmitted by the reference station and one being transmitted by the day; and Calculating a position of the transponder on the basis of the arrival time and the at least two arrival time differences. Computer program with a program code for carrying out, when it runs on a computer, a method according to Claim 29 .

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