CN104301868A - High-precision indoor positioning method based on frame round-trip-time and time-of-arrival ranging technology - Google Patents

Abstract

The present invention provides a high-precision indoor positioning method based on frame round-trip and time-of-arrival ranging technology. By using the TOA differential measurement method, a system solution that meets the indoor high-precision positioning requirements of mobile terminal equipment is provided. Based on frame round-trip Measurement information, by embedding the time information of frame transmission, adopts differential measurement method for time information to reduce frame processing delay error, due to the use of high-precision indoor positioning method based on frame round-trip and arrival time ranging technology, in addition to achieving traditional indoor positioning In addition to the functions, the frame round-trip and arrival time ranging technology effectively solves the time synchronization problem, and the ranging uses the differential measurement method to eliminate the phase error and frequency error between the node clock and the standard clock.

Description

High-precision indoor positioning method based on frame round-trip and time-of-arrival ranging technology

technical field

The invention relates to the field of indoor positioning, in particular to a high-precision indoor positioning method.

Background technique

With the rapid development of information technology, people's demand for information is emerging in an endless stream, especially the demand for the perception of spatial location information is increasing. In the field of outdoor, the maturity of satellite technology promotes the comprehensive development of Global Positioning System (Global Positioning System, GPS) technology. Since GPS has the characteristics of all-weather, high precision, and automatic measurement, it is widely used in military affairs, transportation, surveying and mapping, and people's daily life. The primary condition for the application of GPS technology is a good air-to-air communication condition, which is beyond reach for indoor positioning and navigation. Therefore, other technical approaches must be sought for the special indoor environment.

At present, although indoor positioning such as ultrasonic technology, radio frequency identification technology, infrared technology, ultra-wideband technology, and Bluetooth technology can achieve high positioning accuracy, it requires a large number of sensors and additional hardware equipment support, which has great limitations in practical applications. sex. With the maturity of IEEE802.11 wireless technology and the popularization of WIFI all over the world, its coverage is getting wider and wider, and it has become the standard configuration of communication devices such as smartphones and tablet computers. Warehouses, hospitals, etc. all provide WIFI support, and WIFI-based indoor positioning technology emerges as the times require. Compared with the current positioning technology, WIFI positioning can rely on the existing network, does not require additional hardware devices, and has a low cost of use. However, due to the existence of interference factors such as multipath signals and small-scale fading, the positioning accuracy based on the indoor transmission model often becomes difficult to meet the requirements.

The location feature information fingerprint database in the traditional indoor positioning method is too large, the calculation complexity is high in the online positioning matching process, and the real-time performance is poor; and with the change of the indoor space environment, the position based on received signal strength (RSS) technology The characteristic information is also constantly changing, which will affect the matching accuracy to a certain extent; the existing positioning method based on time of arrival (TOA, Time Of Arrival) technology cannot handle the clock crystal oscillator error and the transmission delay on the node well. Indoor high-precision positioning that meets the needs cannot be achieved.

Contents of the invention

In order to overcome the deficiencies of the prior art, the present invention proposes a high-precision indoor positioning method based on frame round trip (RTT, Round Trip Time) and time of arrival (TOA, Time Of Arrival) ranging technology, by using the TOA differential measurement method , providing a system solution that meets the indoor high-precision positioning requirements of mobile terminal equipment.

This case is based on the frame round-trip measurement information, by embedding the time information of the frame transmission, and adopting the differential measurement method for the time information to reduce the frame processing delay error. The technical solution adopted by the present invention to solve its technical problems is:

(1) The combination of RTT and TOA methods completes the time measurement of the frame transmission process

The mobile terminal, that is, MT (Mobile Terminal) sends a wireless signal to the AP (AccessPoint) within the effective range of its wireless signal, and selects at least three APs closest to the MT to participate in positioning through the handshake mechanism in the 802.11 wireless protocol. After the selection is completed, the MT sends an inquiry frame to each selected AP. After receiving the inquiry frame from the MT, the selected AP returns a response frame to the MT, and obtains the frame round-trip transmission time T _RTT . The MT and any one of the selected APs In the process of frame transmission, the MT sends an inquiry frame at time _t1 , the selected AP receives the inquiry frame at time _t2 , the selected AP sends a response frame at time _t3 , and the MT receives the response frame at time _t4 , t ₁ is the time when the frame header sent by the MT appears on the MT antenna port; t ₃ is the time when the frame header sent by the selected AP appears on the selected AP antenna port; t ₂ is the time when the transmission frame header begins to arrive The time of the selected AP receiving antenna port; _t4 is the time when the header of the transmission frame arrives at the MT receiving antenna port, where the records of _t1 and t4 are completed by the MT clock, and the records of _t2 and _t3 are completed by the selected AP’s clock to complete;

Conversely, if the selected AP first initiates the measurement and sends an inquiry frame, the roles of the MT and the selected AP can be interchanged during the entire transmission process;

(2) Use TOA differential measurement method to eliminate or reduce measurement error

As described in step (1), after the round-trip transmission ends, the selected AP transmits its recorded time points _t2 and _t3 to the MT, and the MT calculates the time data to obtain the frame round-trip transmission time T _RTT as follows:

T _RTT ＝(t ₄ -t ₁ )-(t ₃ -t ₂ ) (1)

T _RTT is the difference between the time difference between the MT and the selected AP, that is, the differential measurement. The distance D between the MT and the selected AP is the transmission speed multiplied by the one-way transmission time, that is, half of the round-trip transmission time of the frame, to obtain:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; RTT</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

where C is the speed of light;

(3) Repeat the method described in steps (1) and (2) to measure the distance between the MT and each selected AP, and use the distance between the coordinates of each selected AP and the MT as the radius to establish At least 3 circular equations with the selected AP as the center, their common intersection point is the coordinate of MT, then the MT coordinate can be solved to complete the positioning;

(4) In step (1), the MT sends out an inquiry frame at t ₁ =t' ₁ +ε _MT , and the selected AP receives the inquiry frame at t ₂ =t' ₂ +ε _AP , and then at t ₃ =t' ₃ +ε _AP 'returns the response frame, MT receives the response frame at t ₄ =t' ₄ +ε _MT ', where t ₁ , t ₂ , t ₃ , t ₄ are time measurement values, t' ₁ , t' ₂ , t' ₃ , t' ₄ are the corresponding standard time, ε _MT , ε _AP , ε _AP ', ε _MT ' are the errors between each corresponding measured value and the standard time, and the errors are further divided into The phase error and frequency error between the clocks of nodes MT and AP and the standard clock, where the phase error is the time delay of the clocks of nodes MT and AP according to the time synchronization signal calibration time, and the frequency error is the frequency drift of the node clock crystal oscillator between two time synchronizations In the process of step (1), the standard time for node MT and AP to complete time synchronization is t ₀ , let T _i be the time interval from t ₀ to the measurement moment, after time T _i passes between node MT and AP The standard time of the AP is t' _i =t ₀ +T _i , (i=1,2...4), and t' ₁ =t ₀ +T ₁ is the time recorded by the standard clock, and the time recorded by the node MT is:

t ₁ ＝t' ₁ +u+η(t ₁ -ut ₀ ) (3)

Where u is the phase error between the MT clock and the standard clock, η is the frequency drift coefficient of the clock’s own crystal oscillator, then η(t ₁ -ut ₀ ) is the crystal oscillator of the node from its own measurement time (t ₀ +u) to t ₁ The cumulative error of frequency drift, after simplification, is:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;u</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Then the time when the MT clock receives the response frame _t4 can be expressed as:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Subtract formula (4) from formula (5) to get:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; \&ap;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Where t' ₄ -t' ₁ =t ₀ +T ₄ -(t ₀ +T ₁ )=T ₄ -T ₁ ;

Accordingly, t ₄ -t ₁ in the formula (6) is the time difference of the measurement time, t' ₄ -t' ₁ is the time difference of the standard time, η(t' ₄ -t' ₁ ) is the error, and the error is equal to the standard time The time difference is multiplied by the clock's own crystal oscillator frequency drift coefficient η, η is on the order of 10 ^-5 , η(t' ₄ -t' ₁ ) is used as the error part, which can be ignored, and the time difference t ₄ -t ₁ of the measurement time of the same clock is equal to The corresponding time difference t' ₄ -t' ₁ of the standard time makes the frame round-trip time T _RTT in the formula (1) can be calculated by using the time difference of the standard time, thereby eliminating the error and improving the accuracy of the measurement results, so that the positioning Accuracy is improved.

The beneficial effects of the present invention are due to the adoption of a high-precision indoor positioning method based on frame round-trip and time-of-arrival ranging technology, in addition to the traditional indoor positioning function, the frame round-trip (RTT) and time-of-arrival (TOA) ranging technology effectively solves the problem. The time synchronization problem is solved, and the distance measurement uses the differential measurement method to eliminate the phase error and frequency error between the node clock and the standard clock.

Description of drawings

Fig. 1 is a block diagram of frame round-trip time measurement for indoor positioning of the present invention, wherein the MT sends out an inquiry frame at _t1 , the AP receives the inquiry frame at _t2 , then returns a response frame at _t3 , and the MT receives it at _t4 Response frame, MLME is the MAC layer management entity.

Fig. 2 is a block diagram of a basic system model of indoor positioning. In the figure, AP ₁ , AP ₂ , AP ₃ , and AP ₄ are respectively access points, and MT _i (i=1,...n) are mobile terminals.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

(1) The combination of RTT and TOA methods completes the time measurement of the frame transmission process

The mobile terminal, that is, MT (Mobile Terminal) sends a wireless signal to the AP (AccessPoint) within the effective range of its wireless signal, and selects at least three APs closest to the MT to participate in positioning through the handshake mechanism in the 802.11 wireless protocol. After the selection is completed, the MT sends an inquiry frame to each selected AP. After receiving the inquiry frame from the MT, the selected AP returns a response frame to the MT, and obtains the frame round-trip transmission time T _RTT . The MT and any one of the selected APs In the process of frame transmission, the MT sends an inquiry frame at time _t1 , the selected AP receives the inquiry frame at time _t2 , the selected AP sends a response frame at time _t3 , and the MT receives the response frame at time _t4 , t ₁ is the time when the frame header sent by the MT appears on the MT antenna port; t ₃ is the time when the frame header sent by the selected AP appears on the selected AP antenna port; t ₂ is the time when the transmission frame header begins to arrive The time of the selected AP receiving antenna port; _t4 is the time when the header of the transmission frame arrives at the MT receiving antenna port, where the records of _t1 and t4 are completed by the MT clock, and the records of _t2 and _t3 are completed by the selected AP’s clock to complete;

Conversely, if the selected AP first initiates the measurement and sends an inquiry frame, the roles of the MT and the selected AP can be interchanged during the entire transmission process;

(2) Use TOA differential measurement method to eliminate or reduce measurement error

As described in step (1), after the round-trip transmission ends, the selected AP transmits its recorded time points _t2 and _t3 to the MT, and the MT calculates the time data to obtain the frame round-trip transmission time T _RTT as follows:

T _RTT ＝(t ₄ -t ₁ )-(t ₃ -t ₂ ) (1)

T _RTT is the difference between the time difference between the MT and the selected AP, that is, the differential measurement. The distance D between the MT and the selected AP is the transmission speed multiplied by the one-way transmission time, that is, half of the round-trip transmission time of the frame, to obtain:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; RTT</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

where C is the speed of light;

(3) Repeat the method described in steps (1) and (2) to measure the distance between the MT and each selected AP, and use the distance between the coordinates of each selected AP and the MT as the radius to establish At least 3 circular equations with the selected AP as the center, their common intersection point is the coordinate of MT, then the MT coordinate can be solved to complete the positioning;

(4) In step (1), the MT sends out an inquiry frame at t ₁ =t' ₁ +ε _MT , and the selected AP receives the inquiry frame at t ₂ =t' ₂ +ε _AP , and then at t ₃ =t' ₃ +ε _AP 'returns the response frame, MT receives the response frame at t ₄ =t' ₄ +ε _MT ', where t ₁ , t ₂ , t ₃ , t ₄ are time measurement values, t' ₁ , t' ₂ , t' ₃ , t' ₄ are the corresponding standard time, ε _MT , ε _AP , ε _AP ', ε _MT ' are the errors between each corresponding measured value and the standard time, and the errors are further divided into The phase error and frequency error between the clocks of nodes MT and AP and the standard clock, where the phase error is the time delay of the clocks of nodes MT and AP according to the time synchronization signal calibration time, and the frequency error is the frequency drift of the node clock crystal oscillator between two time synchronizations The cumulative error generated, in the process of step (1), the standard time for the node MT and AP to complete time synchronization is t ₀ , let T _i be the time interval from t ₀ to the measurement moment, after the time Ti elapses, the node MT and AP The standard time is t' _i =t ₀ +T _i , (i=1,2...4), and t' ₁ =t ₀ +T ₁ is the time recorded by the standard clock, and the time recorded by the node MT is:

t ₁ ＝t' ₁ +u+η(t ₁ -ut ₀ ) (3)

Where u is the phase error between the MT clock and the standard clock, η is the frequency drift coefficient of the clock’s own crystal oscillator, then η(t ₁ -ut ₀ ) is the crystal oscillator of the node from its own measurement time (t ₀ +u) to t ₁ The cumulative error of frequency drift, after simplification, is:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;u</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Then the time when the MT clock receives the response frame _t4 can be expressed as:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Subtract formula (4) from formula (5) to get:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; \&ap;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Where t' ₄ -t' ₁ =t ₀ +T ₄ -(t ₀ +T ₁ )=T ₄ -T ₁ ;

Accordingly, t ₄ -t ₁ in the formula (6) is the time difference of the measurement time, t' ₄ -t' ₁ is the time difference of the standard time, η(t' ₄ -t' ₁ ) is the error, and the error is equal to the standard time The time difference is multiplied by the clock's own crystal oscillator frequency drift coefficient η, η is on the order of 10 ^-5 , η(t' ₄ -t' ₁ ) is used as the error part, which can be ignored, and the time difference t ₄ -t ₁ of the measurement time of the same clock is equal to The corresponding time difference t' ₄ -t' ₁ of the standard time makes the frame round-trip time T _RTT in the formula (1) can be calculated by using the time difference of the standard time, thereby eliminating the error and improving the accuracy of the measurement results, so that the positioning Accuracy is improved.

In order to make the above-mentioned purpose, features and advantages of the present invention more obvious and easy to understand, the following takes WIFI indoor positioning as an example to further describe this case in detail. Apparently, the embodiments described here are only part of the embodiments described in the present invention in conjunction with WIFI signals. Based on the solutions described in the present invention, the embodiments obtained by persons of ordinary skill in the art without making creative efforts are all within the protection scope of the present invention.

First of all, when mobile terminals (such as mobile phones, tablet computers, notebooks, etc.) or MTs choose to locate, they should first be connected to the WIFI system in indoor areas (such as inside enterprises, airports, schools, warehouses, hospitals, etc.). The MT sends a WIFI inquiry frame signal to the AP (router and other wireless devices) within the effective range of its WIFI signal, and selects at least 3 APs closest to the MT to participate in the positioning process through the handshake mechanism in the 802.11 wireless protocol. The principle is: select according to the order in which the AP responds to the MT. After AP selection is completed, the MT sends an inquiry frame to each AP, and the AP returns a response frame to the MT after receiving the inquiry frame from the MT, and obtains the frame round-trip transmission time T _RTT . Take the frame transmission process between MT and any AP as an example, MT sends an inquiry frame at time _t1 , AP receives the inquiry frame at time _t2 , AP sends a response frame at time _t3 , and MT receives the response at time t4 Frame (all times are the time when the header of the frame begins to appear or arrives at the antenna ports of the MT and AP). Of special concern is that the recording of each time point is completed by the corresponding node's own clock, and the frame round-trip time measurement block diagram is shown in Figure 1.

After the frame round-trip transmission is completed, the AP sends the recorded time points t2 and t3 to the MT, and the MT calculates the time data to obtain T _RTT

T _RTT ＝(t ₄ -t ₁ )-(t ₃ -t ₂ )

＝[(t' ₄ +ε _MT ')-(t' ₁ +ε _MT )]-[(t' ₃ +ε _AP ')-(t' ₂ +ε _AP )] (7)

＝[(t' ₄ -t' ₁ )-(t' ₁ -t' ₂ )]+[(ε _MT '-ε _MT )-(ε _AP '-ε _AP )]

In formula (7), [(t' ₄ -t' ₁ )-(t' ₃ -t' ₂ )] is the real transmission time of the frame, [(ε _MT '-ε _MT )-(ε _AP '-ε _AP )] is the transmission error of the frame, ε _MT and ε _MT ' are two errors measured by the MT clock, and their difference is η(t' ₄ -t' ₁ ), because (t' ₄ -t' ₁ ) The maximum is on the order of 10 ^-6 , and η is on the order of 10 ^-5 , so the result of this item is on the order of 10 ^-11 , which is too small to be ignored; similarly, ε _AP and ε _AP ' are two errors measured by the AP clock, and they The difference is η(t' ₃ -t' ₂ ), and the processing time of t' ₃ -t' ₂ AP clock from receiving the inquiry frame to sending out the response frame is less than t' ₄ -t' ₁ , η(t' ₃ -t' ₂ ) is also negligible because the order of magnitude is too small. Therefore, the influence of the second bracket part on the result is very small and negligible through differential measurement. Then the obtained T _RTT result is equal to the time consumed by the signal transmission between the two APs.

Since the coverage of WIFI is 100m, when the distance between MT and AP is 100m, the maximum standard time difference is on the order of 10 ^-6 , and the time on the order of 10 ^-11 corresponds to the distance of millimeter level, relative to the accuracy of indoor positioning of 1m, completely negligible.

In the actual measurement, at first it is necessary to make the MT and at least 3 APs involved in positioning carry out time synchronization according to the 802.11 protocol (the clock resolution of the existing positioning method is 1 μs, and the clock resolution according to the 802.11v protocol is 10 ns, the present invention sets the MT The clock resolution of each AP is 1 ns), and it takes time for the AP to adjust its clock time to the standard time after receiving the time synchronization signal. Therefore, in the simulation experiment, the clocks of the MT and each AP are set to be consistent with the standard clock Phase error u, take u as a discrete uniform distribution on [-5, -1] and can only be an integer, MT and AP’s own crystal oscillator frequency drift coefficient η is [-5×10 ^-5 ,5×10 ^-5 ] A uniform distribution of , where a negative value indicates that the crystal oscillator frequency is slower than the standard clock frequency, and a positive value indicates that the crystal oscillator frequency is faster than the standard clock frequency. Select an AP, and the position of each measurement point of the MT comes from the area of x∈[34,65], y∈[34,65] near the AP. The measurement experiment obtained the absolute difference between the measurement time of the traditional TOA method and the real frame transmission time. Error D ₁ , the mean value of the error is E[D ₁ ], the mean square error MSE ₁ ＝E[D ₁ ² ]; for the differential measurement method, the absolute error between T _RTT and the real frame transmission time is D ₂ , and the mean value of the error is E[ D ₂ ], mean square error MSE ₂ =E[D ₂ ² ]. Among them, E[·] represents the expectation of obtaining variables. And define P=MSE ₁ /MSE ₂ as the gain reference value.

Experiment 1 mainly faces two measurement methods. In the case of T ₁ = 0 (T ₁ is the time from the completion of the last time synchronization to the time when the MT starts to send the inquiry frame), all MT measurement points in the vicinity of the AP have a relatively large impact on the time synchronization error the result of. Table 1 shows all the measurement results of this time:

Table 1 Comparison of error results between traditional measurement and differential measurement

E[D ₁ ](ns) E[D ₂ ](ns) MSE ₁ =E[D ₁ ² ] MSE ₂ ＝E[D ₂ ² ](×10 ^-6 ) P(×10 ⁹ ) 1.5294 0.0016 3.7474 4.2169 7.1945

Experimental results show that the TOA differential measurement method of the present invention greatly reduces measurement errors and improves measurement accuracy.

In Experiment 2, the parameters u and η of the MT and AP clocks remain unchanged. The difference between the results of all the measurement points in the x∈[34,65], y∈[34,65] area is mainly compared between the two measurement methods under different T ₁ conditions. For traditional TOA, its measured value:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

D ₁ =t ₂ -t ₁ -Δ (11)

Where Δ is the frame transmission time from the MT to the AP. According to formulas (10) and (11), it can be seen that the value of the absolute error D ₁ has a linear relationship with the value of T ₁ .

Table 2 Comparison of T for traditional measurement and differential measurement error results

According to Table 2, it can be found that the error and mean square error of the traditional TOA method change linearly with the increase of _T1 , while the error and mean square error of TOA differential measurement have nothing to do with the change of _T1 . Therefore, the differential measurement effectively suppresses the cumulative error caused by the frequency drift of the crystal oscillator.

The distance between MT and AP is the transmission speed multiplied by the one-way transmission time (half of the frame round-trip transmission time), that is Where C represents the speed of light, and the distance between the MT and several other selected APs can be measured using the same method as above. In this model, by selecting the coordinates of at least 3 APs and their distance from MT as the radius, at least 3 circle equations with AP as the center are established, and their common intersection points are the coordinates of MT, and the MT coordinates can be solved , complete the positioning, and the basic system model structure is shown in Figure 2.

Claims (1)

1. come and go the method for high accuracy indoor positioning with the ranging technology time of advent based on frame, it is characterized in that comprising the steps:

(1) RTT and TOA methods combining completes the time measurement of frame transmitting procedure

By mobile terminal, namely MT (Mobile Terminal) sends wireless signal to the AP (Access Point) in its wireless signal effective range, carry out at least 3 nearest AP of selected distance MT by the handshake mechanism in 802.11 wireless protocols and participate in location, after AP has selected, MT sends inquiry frame to each selected AP, selected AP returns acknowledgement frame to MT after receiving the inquiry frame of MT, obtains frame round-trip transmission time T _rTT, in MT and selected AP any one AP frame transmitting procedure in, MT is at t ₁moment sends inquiry frame, and selected AP is at t ₂moment receives inquiry frame, and selected AP is at t ₃moment sends acknowledgement frame, and MT is at t ₄moment receives acknowledgement frame, t ₁it is the time that frame heading that MT sends appears at MT antenna port; t ₃it is the time that frame heading that selected AP sends appears at selected AP antenna port; t ₂it is the time that transmission frame heading starts to arrive selected AP reception antenna port; t ₄that transmission frame heading starts to arrive the MT reception antenna port time, wherein t ₁come by MT clock with the record of t4, t ₂and t ₃record come by the clock selecting AP;

Otherwise if first initiated to measure by selected AP, send inquiry frame, the role of whole transmitting procedure MT and selected AP can exchange;

(2) adopt TOA differential measuring method to eliminate or reduce measure error

As described in step (1), after round-trip transmission terminates, the time point t that selected AP records it ₂and t ₃send MT to, by MT, frame round-trip transmission time T is calculated to time data _rTTas follows:

T _RTT＝(t ₄-t ₁)-(t ₃-t ₂) (1)

T _rTTfor the difference of the time difference on MT and selected AP, namely difference measurement, the distance D between MT and selected AP is that transmission speed is multiplied by the one-way transmission time, i.e. the half of frame round-trip transmission time, obtains:

$D=C\&CenterDot;\frac{T_{\mathrm{RTT}}}{2}---\left(2\right)$

Wherein C represents the light velocity;

(3) step (1) and the method described in (2) is repeated, the distance between MT and each selected AP can be measured, the distance between the coordinate of each selected AP and MT is utilized to be radius, set up the equation of a circle that at least 3 is the center of circle with selected AP, their common intersection is exactly the coordinate of MT, MT coordinate can be solved, complete location;

(4) in step (1), MT is at t ₁=t ' ₁+ ε _mTmoment sends inquiry frame, and selected AP is at t ₂=t ' ₂+ ε _aPmoment receives inquiry frame, then at t ₃=t ' ₃+ ε _aP' returning acknowledgement frame, MT is at t ₄=t ' ₄+ ε _mT' receive acknowledgement frame, t here ₁, t ₂, t ₃, t ₄for time measured value, t ' ₁, t ' ₂, t ' ₃, t ' ₄for the standard time of correspondence, ε _mT, ε _aP, ε _aP', ε _mT' be the measured value of each correspondence and the error between the standard time, error is divided into again the clock of node M T and AP and the phase error of standard time clock and frequency error, wherein phase error is that the clock of node M T and AP is according to the time delay of time synchronizing signal alignment time, frequency error is the accumulated error that between twice time synchronized, the drift of nodal clock crystal oscillator frequency produces, in the process of step (1), node M T and synchronous standard time AP deadline are t ₀if, T _ifrom t ₀to the time interval of measuring the moment, elapsed time T _ithe standard time of posterior nodal point MT and AP is t ' _i=t ₀+ T _i, (i=1,2 ... 4), t ' is obtained ₁=t ₀+ T ₁by standard time clock is clocked quarter, quarter that node M T clocks is:

t ₁＝t' ₁+u+η(t ₁-u-t ₀) (3)

Wherein u is the phase error of MT clock and standard time clock, and η is clock self crystal oscillator frequency coefficient of deviation, then η (t ₁-u-t ₀) for node is from the Measuring Time (t of oneself ₀+ u) moment is to t ₁the cumulative errors of the crystal oscillator frequency drift in moment, after abbreviation:

$t_1=\frac{t_1^{\&prime;}+u-\mathrm{\&eta;}(t_0+u)}{1-\mathrm{\&eta;}}=\frac{t_0+T_1+u-{\mathrm{\&eta;t}}_0-\mathrm{\&eta;u}}{1-\mathrm{\&eta;}}=t_0+u+\frac{T_1}{1-\mathrm{\&eta;}}---\left(4\right)$

Then MT clock receives acknowledgement frame t ₄moment can be expressed as:

$t_4=t_0+u+\frac{T_4}{1-\mathrm{\&eta;}}---\left(5\right)$

Formula (5) deducts formula (4) and can obtain:

$t_4-t_1=\frac{T_4-T_1}{1-\mathrm{\&eta;}}=\frac{t_4^{\&prime;}-t_1^{\&prime;}}{1-\mathrm{\&eta;}}\&ap;(t_4^{\&prime;}-t_1^{\&prime;})(1+\mathrm{\&eta;})=(t_4^{\&prime;}-t_1^{\&prime;})+\mathrm{\&eta;}(t_4^{\&prime;}-t_1^{\&prime;})---\left(6\right)$

Wherein t ' ₄-t ' ₁=t ₀+ T ₄-(t ₀+ T ₁)=T ₄-T ₁;

Accordingly, t in formula (6) ₄-t ₁for the time difference of Measuring Time, t' ₄-t' ₁for the time difference of standard time, η (t' ₄-t' ₁) be error, the time difference that error equals the standard time is multiplied by clock self crystal oscillator frequency coefficient of deviation η, and η is 10 ^-5the order of magnitude, η (t' ₄-t' ₁) as error component, negligible, obtain the time difference t of the Measuring Time of same clock ₄-t ₁equal the time difference t' of the standard time of its correspondence ₄-t' ₁, make frame T two-way time in formula (1) _rTTcan calculate with the time difference of standard time, thus eliminate error, the precision of measurement result improves, thus positioning precision is improved.