JP2003098245A - Satellite navigation positioning device and satellite positioning calculation method - Google Patents

Abstract

(57) [Summary] [PROBLEMS] To provide a satellite navigation positioning device and a satellite positioning calculation method having a miniaturized signal processing function without being affected by multipath and capable of determining an integer value bias in a short time. SOLUTION: An RDOP operation 205 evaluates the arrangement of satellites by RDOP when there are four or more satellites in a management table, and sets the RDOP to an invalid value if the number is four or less. Bias judgment 207
Was evaluated only on satellites with a fixed integer bias
If RDOP is 30 or less, branch to relative position operation 208,
Otherwise, the process branches to the matrix operation 210. The operation 210 calculates a Γ matrix by a predetermined formula.
The Ω matrix operation 211 calculates an Ω matrix of the number of arrays corresponding to the satellites described in the management table. N ・ σ _N operation 21
2 calculates the integer bias and the variance σ _N , respectively. N
In the accuracy judgment 213, when the variance σ _N is smaller than 0.25 and each integer value bias includes an integer value within the range of the variance, it is determined that the integer value bias is determined.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a GPS satellite operated by the United States and a GLON operated by the Russian Republic.
The present invention relates to a satellite positioning calculation method in which positioning satellite signals such as ASS satellites are simultaneously received by a reference station and a positioning station, and carrier phases of the received signals are compared to obtain a relative position of the positioning station with respect to the reference station. Particularly, in the phase difference between the carrier waves observed by the reference station and the positioning station, the integer value bias corresponding to an integer multiple of the carrier wave period is undetermined, and the integer value bias is quickly obtained.

[0002]

2. Description of the Related Art In recent years, GPS surveys have been conducted by GSI
As shown in A-1-No.228, it is widely used in the field of surveying. In the GPS survey using the carrier wave phase, GPS receivers are provided on the reference side and the positioning side, respectively. Both receivers simultaneously observe the carrier wave phase of the satellite signal with respect to the reference signal of the receiver by comparing the carrier wave of each of the plurality of satellites with the reference signal of the receiver. The measured value of the carrier wave phase outputs a value that is continuously accumulated with respect to time, and includes a value exceeding one cycle.

Further, the relative positions of the positioning side antenna with respect to the reference side antenna are obtained with an accuracy of several cm by comparing the phases obtained by the two with each other. US GPS satellites transmit L1 and L2 signals, and carrier wavelengths λ1 and λ2 are about 19 cm and about 24 cm, respectively. The carrier phase difference of the positioning station with respect to the observed reference station includes an uncertain portion called "integer value bias" that is an integral multiple of λ1 and λ2. Since the integer value bias does not change while both receivers continuously track the carrier wave of the satellite signal, the integer value bias is derived from the observation result of the continuous carrier wave phase.

However, this requires complicated processing, and various techniques have been developed. Normally, the reference antenna is fixed on the ground. If the antenna on the positioning side does not move, the integer bias can be obtained relatively easily, but it is very difficult if the antenna on the positioning side moves. The technology that obtains an integer bias while the positioning side is moving is called “OTF (On The Fly)”.

As a conventional technique for determining the OTF integer value bias, Patrick YC Hwang, "Kinematic GPS for Differ
ential Positioning: Resolving Integer Ambiguities
on the Fly ", Navigation, Vol.38, No.1, Spring 1991
A technique using the Kalman filter shown in FIG. According to this, the position of the antenna on the positioning side and the integer value bias are used as variables, and the carrier phase difference on the positioning side with respect to the reference side is input to configure a tracking filter that updates the variable each time observation is repeated. The response characteristic of this tracking filter is sequentially obtained from the property of the input carrier phase difference, and is excellent in that it is a response characteristic optimized according to the measurement environment in the steady state.

Another conventional technique for determining the OTF integer bias is Hasanuddin Z. Abidin, "On the Construc.
tion of the Ambiguity Searching Space for On-the-F
ly Ambiguity Resolution ", Navigation, Vol.40, No.
There is known a technique for evaluating and selecting candidates for an integer bias shown in 3, Fall 1993. According to this, first, the relative position between the reference side and the positioning side is measured using the C / A code or P (Y) code transmitted by the GPS satellite.
The accuracy of the relative position obtained using the code is several meters to several tens of centimeters. Then, it is assumed that only one correct combination is included in all the combinations of the integer biases that fall within the predicted range. At least four satellites are required to determine the relative position of the positioning side with respect to the reference side. If the number of observable satellites is redundant, the relative position on the positioning side with respect to the reference side, which is determined by the combination of integer value biases, should be evaluated consistently on all satellites without any contradiction. Exclude. Then, the same evaluation is repeated for each observation, and all inappropriate combinations are eliminated to arrive at a set of correct combinations. This technique is excellent in that the integer bias can be determined by the observation result in a short period if the evaluation of the combination of the integer biases is appropriate.

[0007]

However, in the technique using the conventional Kalman filter, it takes a long time to reach a steady state, and the response when the movement characteristic on the positioning side changes is poor. There is a problem that it lacks versatility because it requires a specialized filter according to.

Further, in the above-mentioned conventional technique for evaluating and selecting candidates for integer value bias, the number of candidates for combinations of integer value bias is very large, and the number of evaluation processes for the combination becomes enormous. In order to measure at short intervals and process this in real time, a processor with a high processing capacity is required in the arithmetic part, and there is a problem that power consumption is large. In particular, in a situation where there is fluctuation in carrier phase due to multipath, there is a problem that it is difficult to reach one correct combination.

The present invention solves the above-mentioned conventional problem. The integer value bias can be determined in a short observation period equivalent to the technique of evaluating and selecting candidates for the integer value bias. In addition to the characteristics that are not easily affected by the above, a satellite navigation positioning device that does not require a processor with high processing power in the calculation part and can determine the integer value bias in a short time even with a signal processing function that is downsized with low power consumption And a satellite positioning calculation method.

[0010]

In order to solve the above-mentioned problems, the satellite positioning calculation method of the present invention uses a carrier phase double phase difference including an unknown integer bias at each observation timing, a satellite position and a reference side. And the relational expression with the position of the positioning side,
Corresponding to the position on the positioning side by substituting the condition for determining the position on the positioning side by the least-squares method in the range of the relational expression obtained at each observation timing and substituting the obtained condition into the relational expression on the carrier phase. The conditional expression in which the variable is deleted is obtained, and for each of the observation timings, the double phase difference is satisfied under the condition that the deviations are satisfied, with respect to the conditional expression that is obtained for a plurality of observation timings including before. By obtaining the integer value bias of, all valid observation results can be used without waste, and the integer value bias can be determined in a short time, and the conventional integer value bias candidates can be evaluated and selected. To evaluate a large number of integer bias combinations, such as
This eliminates the need for a large-capacity storage device or a computing device having high computing power.

In the satellite positioning calculation method of the present invention, the condition for determining the position on the positioning side is determined by the method of least squares within the range of the relational expression obtained at each observation timing, and the satellite is determined by the condition for determining the position. In the observation timing that determines the condition for evaluating the accuracy that can be placed, and at the observation timing that is determined to be an arrangement that does not satisfy the condition, a conditional expression in which the variable corresponding to the position on the positioning side is deleted is obtained for the plurality of observation timings. By not adding to the combination of the conditional expressions that eliminates, there is a possibility that it may have a negative effect on establishing the integer value bias, by accurately eliminating the observation results of poor satellite placement, The accuracy of the integer value bias can be improved without delay.

In the satellite positioning calculation method of the present invention, when solving the simultaneous equations for obtaining the integer bias, the integer bias obtained at the previous observation timing is used as an initial value, and the iterative method is used to solve the simultaneous equations. By using the asymptotically calculated integer bias, and using the integer bias calculated here as the initial value in the next calculation of the integer bias, the amount of calculation is reduced and the integer value that is an unknown Even if the number of biases is large, the increase in the amount of calculation can be suppressed.

As described above, even an arithmetic unit having a low processing capacity can perform highly accurate positioning by a carrier phase in real time, and can determine an integer value bias in a short time.
It realizes an excellent positioning calculation method based on the carrier phase of a satellite signal, and is a satellite signal for a satellite navigation receiver that is inexpensive, compact, and has low power consumption, and has centimeter-level accuracy, and many positioning stations connected to the network. It is possible to realize a central device capable of processing the positioning calculation based on the carrier wave phase with low processing capacity.

[0014]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The invention according to claim 1 of the present invention is an antenna for receiving a satellite signal, a carrier phase measuring unit for measuring a carrier phase of the satellite signal received by the antenna, and a predetermined reference. A calculation unit that obtains the position of the moving body from the first carrier phase information measured at the point and the second carrier phase information measured by the carrier phase measurement unit, and the calculation unit performs the calculation at each predetermined timing. A plurality of relational expressions of the double phase difference between the first carrier phase information and the second carrier phase information, the position of the satellite at the predetermined timing, the position of the reference point, and the position of the moving body. Seeking
A conditional expression in which a variable corresponding to the position of the moving body is deleted from the plurality of relational expressions is obtained, and an integer value bias of the double phase difference is obtained such that the conditional expressions at a plurality of timings are satisfied with a small deviation from each other. Since the position of the moving body is determined by the above, the versatility is improved because there is no influence by the movement of the positioning position, and in comparison with the conventional method of evaluating and selecting the integer bias candidate, It does not require a large-capacity storage device or an arithmetic unit with high arithmetic capacity, assuming a combination of many integer-value biases,
It has the effect of being less susceptible to the effects of multipath.

According to the second aspect of the present invention, receivers are installed on the reference side and the positioning side respectively, the carrier wave phase of the satellite signal is measured at the same timing on both sides, and the positioning is performed on the reference side for a plurality of timings. In the satellite positioning calculation method that finds the relative position of the positioning side with respect to the position of the reference side by using the carrier phase observed simultaneously on both sides, the carrier double position including an unknown integer bias at each observation timing. Obtain the relational expression between the phase difference, the position of the satellite and the position of the reference side and the position of the positioning side, and in the range of the relational expression obtained at each observation timing, find the condition for determining the position of the positioning side by the least squares method, and obtain it. By substituting the above condition into the relational expression regarding the carrier wave phase, a conditional expression in which the variable corresponding to the position on the positioning side is deleted is obtained, and at each observation timing, a plurality of conditional expressions including before it are obtained. Regarding the conditional expression in which the variable obtained for the measurement timing is deleted, the integer value bias of the double phase difference is obtained under the condition that a small deviation is satisfied, and the same is obtained at a plurality of observation timings. Since the conditional expression is an independent expression and the integer value bias is calculated by the least squares method, all valid observation results are used without waste, and in addition to the integer value bias being determined in a short time, the positioning side Since the variable corresponding to the position is deleted, it is not affected by the movement of the positioning position, which makes it more versatile.In addition, compared to the conventional method of evaluating and selecting integer value bias candidates, the integer value is calculated by the least square method. Since the bias is calculated comprehensively by calculation, a large-capacity storage device and a calculation device with high calculation capability are required, assuming a combination of many integer-valued biases as candidates. Without, it has the effect of also less susceptible to the influence of the multi-path.

The invention described in claim 3 is the same as that of claim 2
With respect to the satellite positioning calculation method described in (3), the variance of the obtained integer value bias is evaluated, and the predetermined range determined by the variance of the integer value bias is centered on the obtained integer value bias, and a unique integer is included. On the condition that the integer value bias has been determined, a method has been added to determine whether the integer value bias has been determined, so the determined integer value bias can be determined quickly at an appropriate timing, and a more accurate relative position can be obtained more quickly. Has the effect of.

The invention described in claim 4 is the same as that of claim 2
Alternatively, in the satellite positioning calculation method according to claim 3, the condition for determining the position on the positioning side by the least-squares method is obtained within the range of the relational expression obtained at each observation timing, and the condition for determining the position is obtained. By defining the conditions to evaluate the accuracy of satellite placement by the observation timing of the placement that does not meet the above conditions, the conditional expression that eliminates the variable corresponding to the position of the positioning side, the variable obtained for multiple observation timing Since it is not added to the combination of the conditional expressions that have been deleted, it is possible to accurately exclude the observation result of the bad satellite arrangement, which may have a negative effect on establishing the integer bias, It has the effect that the accuracy of the bias can be increased without delay.

The invention described in claim 5 is the same as claim 2
To the satellite positioning calculation method according to any one of claims 1 to 5, wherein an Ω matrix conditional expression and a ζ vector conditional expression are defined as conditions for obtaining the integer bias.
A storage function is provided for holding each element of the defined Ω matrix conditional expression (22) and ζ vector conditional expression (23),
For each element of the Ω matrix condition and the ζ vector condition that holds the conditional expression in which the variable corresponding to the position on the positioning side is deleted for each observation timing and the found variable is deleted Since the integral value bias is obtained based on the cumulative addition and the cumulative addition of the Ω matrix condition and the ζ vector condition, there is an effect that the calculation at the time of updating the integral value bias at each observation timing can be reduced.

The invention according to claim 6 is the same as claim 2
In the satellite positioning calculation method according to any one of claims 1 to 5, the integer value bias obtained at the previous observation timing is used as an initial value instead of the calculation for solving the simultaneous equations when obtaining the integer value bias. , The iterative method is used to solve the simultaneous equations, and the integer value bias is calculated asymptotically. The newly calculated integer value bias is used as the initial value for the calculation of the next integer value bias. In addition, even if the number of integer value biases, which is an unknown number, is large, there is an effect that the increase in the amount of calculation is small.

The invention according to claim 7 provides the invention according to claim 6.
With respect to the satellite positioning calculation method according to, the initial value of the integer bias is based on the receiver installed on the reference side,
The position on the positioning side is obtained by the differential positioning using the code phase of the satellite signal, the approximate integer value bias is obtained from the obtained position, and the obtained approximate integer value bias is used as the initial value to obtain the final solution. Since the initial values are close to each other, the convergence of the integer value bias obtained by the iterative method can be accelerated, and an accurate integer value bias can be obtained quickly.

The invention described in claim 8 is the same as claim 2
To the satellite positioning calculation method according to any one of claims 1 to 7, for integer value biases obtained by calculation, integer values obtained at observation timings sampled at intervals within continuous observation timings. Bias is saved, the integer value bias obtained at each observation timing is compared with the saved integer value bias, and the accuracy of the integer value bias is evaluated by evaluating the variation amount thereof,
Even if the amount of calculation for determining the accuracy of the integer value bias is small, the integer value bias can be accurately determined.

The invention according to claim 9 has a function of simultaneously observing the carrier wave phase of a satellite signal received by the antenna for a plurality of satellites, and a carrier wave phase simultaneously observed for the same satellite on the reference side through a communication path. In a satellite navigation receiver having a function for receiving via the satellite signal and a positioning calculation function based on the carrier phase of the satellite signal, the positioning calculation function based on the carrier phase is the satellite positioning calculation according to any one of claims 2 to 8. Since the method is used, even a small and inexpensive satellite navigation receiver having a positioning calculation device with low calculation processing capability can perform positioning by the carrier phase of the satellite signal with a short positioning cycle and real-time processing. Has the effect of becoming.

Further, the invention according to claim 10 has a function of receiving the carrier wave phase of the satellite signal observed by the receiver on the positioning side via a communication network, and the satellite signal observed by the receiver on the reference side. Is separately provided, and a positioning calculation function based on the carrier phase of the satellite signal is provided, and the positioning calculation function uses the satellite positioning calculation method according to any one of claims 2 to 8. , A positioning arithmetic unit having a low processing capability can perform positioning arithmetic using the carrier wave phase of a satellite signal for a large number of positioning stations in a short time, and has an excellent performance that an integer value bias can be determined in a short observation time. It has the effect that the device can provide.

Further, according to the invention of claim 11, positioning satellite signals are simultaneously received by the reference station and the positioning station, the carrier wave phases of the received signals are respectively recorded, and the recorded carrier wave phases are compared to perform positioning with respect to the reference station. In the satellite positioning calculation method for obtaining the relative position of the station, the relational expression between the double phase difference of the carrier including an unknown integer bias for each observation timing, the position of the satellite, and the positions of the reference side and the positioning side are obtained. In the range of the relational expression obtained at the observation timing, the condition for determining the position on the positioning side is obtained by the method of least squares, and the obtained condition is substituted into the relational expression regarding the carrier phase to correspond to the position on the positioning side. A conditional expression that eliminates variables is found, and the conditional expressions that are obtained for a large number of observation timings are batched under conditions that satisfy small deviations from each other. By obtaining the integer value bias of the double phase difference, many valid observation results can be used without waste, and even if the observation time is short, the integer value bias can be more reliably determined and the amount of calculation throughout is reduced. In addition, since it is not necessary to assume a combination of a large number of integer biases as candidates, there is an effect that a large-capacity storage device or an arithmetic device having a high arithmetic capacity becomes unnecessary.

FIG. 1 shows an embodiment of the present invention.
It will be described with reference to FIG.

(First Embodiment) FIG. 1 shows the configuration of a system for GPS measurement using the positioning calculation method based on the carrier wave phase of a satellite signal according to the present invention. In FIG. 1, the GPS surveying system includes a GPS satellite 101 that transmits L1 and L2 signals for measuring a position, and a reference-side GPS that measures the phases of L1 and L2 carrier waves whose antenna installation positions are known. Positioning side G for measuring the phases of the carrier waves of L1 and L2 used for measuring the relative position with respect to the receiver 102 and the reference side.
Positioning calculation device 104 that compares the phase of the carrier waves observed on the reference side and the positioning side with PS receiver 103 to obtain the relative position
A transmission modem 105 for transmitting the phase of the carrier wave observed by the reference-side GPS receiver 102 to the positioning side; and the positioning arithmetic unit 10 for receiving the phase of the carrier wave from the reference side via the communication path.
4 and a receiving modem 106 for outputting to the No. 4 terminal.

The hardware configuration of the GPS surveying system of this embodiment is the same as that of the conventional example, but the positioning calculation device 1
The positioning calculation method based on the carrier phase in 04 is different.

The operation of the GPS surveying system configured as described above will be described below. First, the radio waves transmitted by the plurality of GPS satellites 101 in FIG.
The signal is received by the antenna of the receiver 102. GPS satellite 101
The L1 signal transmitted by the L1 signal has a code rate of 1.023 Mbps, a signal unique to the satellite called C / A code, and 50 bps navigation data that are phase-modulated on a 1.57542 GHz carrier, and a code rate of 10.23 Mbps with P ( It is a code unique to the satellite called Y) code, and it transmits a signal obtained by phase-modulating orthogonal 1.57542 GHz carriers.

The reference-side GPS receiver 102 generates the same C / A code and L1 carrier as the satellite to be received, multiplies this by the received signal, and then time-integrates with the cycle of 1 ms of the C / A code as a unit. The result of this time integration is used to track the phase of the C / A code and the L1 carrier and receive navigation data. In addition, the same P (Y) code as the receiving satellite and the L2 carrier are generated, and the product of this and the received signal is filtered by a low-pass filter with a cut-off frequency of 50 Hz to output P2.
(Y) Track the phase of the code and L2 carrier. And 1 per second
The carrier phases of L1 and L2 and the phases of C / A and P (Y) code generated in the receiver are simultaneously observed for all satellites that can be used for positioning, and output to the transmission modem 105 at every cycle. . The transmission modem 105 sequentially sends the phase data of the carrier and the code observed on the reference side to the communication path. On the other hand, the reception modem 106 receives this phase data from the communication path and outputs it to the positioning calculation device 104.

The positioning side GPS receiver 103 is a reference side GP.
Similar to the S receiver 102, it receives radio waves transmitted by a plurality of GPS satellites 101 and receives carrier waves of L1 and L2 and C / A and P (Y).
The phase of the code is tracked, these phases are observed once per second in accordance with the reference GPS receiver 102, and output to the positioning calculation device 104 together with the received navigation data.

The positioning calculation device 104 compares these phases with the phases of the L1 and L2 carriers and the C / A and P (Y) codes received from the reception modem 106 and the positioning side GPS receiver 103, and compares them with each other. The position of the antenna on the positioning side with respect to the antenna of is determined.

Referring to the navigation data received from the satellite,
C / A or P output by the positioning and reference GPS receivers
The phase of the (Y) code makes it possible to know the time at which the satellite emitted radio waves. These are all based on a unique time called GPS time.

Satellites observed by the GPS receiver 103 on the positioning side
Time and reception indicated by the phase of C / A or P (Y) code of n
The difference in the time when the aircraft observed the phase from the satellite to the receiver
It matches the radio wave propagation time. Multiply this time difference by the speed of light
And the apparent distance between the satellite and the receiver^{n, u}becomes ρ. here
Where u is an identifier indicating the positioning side. However, this is not
As the knowledge, the time and GPS time of the GPS receiver on the positioning side
Time bias which is the difference between ^uContains B.

In the xyz Cartesian coordinate system with the center of the earth as the origin, the position vector of the GPS receiver 103 on the positioning side is ^u r
_k, the position vector of the satellite at the time of transmitting the signal received by the positioning side ^{n, u} When r _k, positioning side GPS observed and the observed time at the receiver 103 C / A or P (Y) code phase Apparent distance ⁿ multiplied by the speed of light c
^{, u} R is obtained by the following equation (1).

[0035]

[Equation 1] Here, the time bias ^u B of the positioning side receiver is common between the satellites. The satellite time error ⁿ ε includes the propagation delay of the ionosphere and the atmosphere.

Assuming that the reference-side GPS receiver and the positioning-side GPS receiver have little difference in influence due to propagation delays in the ionosphere and the atmosphere, C / A or P observed by the reference-side GPS receiver
Similarly, for the phase of the (Y) code, the relationship of the following expression (2) is established.

[0037]

[Equation 2] In this equation (2), the position vector ^s r of the GPS receiver on the reference side
_k is known, apparent distance ^{n, s} R is the observed value, satellite position vector ^{n, s} r when the signal received on the reference side is transmitted from the satellite
_{k is} also an observed value. If the observation error ^{n, s} ε is small and the time bias ^s B is known, the satellite time error ⁿ ε can be obtained. It is not possible to obtain ^s B with high precision, but ⁿ
The time bias ^s B is comprehensively determined including the temporal change by referring to the influence of the delay of the ionosphere and the atmospheric layer on ε and the error information of the navigation data, and the satellite time error ⁿ is determined by the time bias ^s B. Determine ε.

The error of the time bias ^s B affects the determination of the time bias ^u B of the positioning side receiver, but does not affect the accuracy of the position vector of the positioning side GPS receiver 103 ^u r _k . The delay time in the ionosphere can also be obtained by comparing the phase of the C / A or P (Y) code observed in L1 with the phase of the P (Y) code observed in L2.

Next, the observation error on the positioning side as well^{n, u}ε is
Suppose it is small. In the above formula (1), calculated by the above
Error of satellite timeⁿSubstituting ε, the apparent distance^{n, u}R is
Observed value, position of satellite when the signal received by the positioning side is transmitted
Storage vector^{n, u}r_kIs also an observed value, the unknowns are
Position vector of GPS receiver 103^ur_kAnd time bias^u
Only B is unknown and there are only four independent variables.
Therefore, there are 4 or more satellites that are common to the positioning side and the reference side.
Position vector by least squares method if possible^ur _kAnd time
bias^uYou can ask for B.

By correcting the error ⁿ ε of the satellite time as described above, if the satellite arrangement is not bad, even if the distance between the positioning side and the reference side is about 100 km, the positioning with respect to the reference side is performed by the above calculation. The side position can be measured with an accuracy of about 1 m. Differential positioning using such a code phase is DG
I call it PS.

Reference side GPS receiver 102 and positioning side GPS
At the receiver 103, the phase of the L1 or L2 carrier wave is simultaneously observed by comparing the carrier wave of the reference signal with that of the satellite signal. As the measured value of the carrier phase, a value accumulated continuously with respect to time is output, and a value exceeding one cycle is also used.

Regarding the phase of observing the carrier wave LX of the satellite n by the reference side GPS receiver 102, the position vector of the receiver is
^s r _{k is} the satellite position vector when the signal is transmitted, ^{n, s} r _k ,
Assuming that the distance between the satellite and the receiver is ^{n, s} ρ, the following equation (3) holds.

[Equation 3]

The position vector _k ^s r of the receiver is known, and the position vector ^{n, s} r _k of the satellite is the azimuth vector ^{n, s} h _k.
In addition, the time is calculated according to the phase of the C / A or P (Y) code observed on the reference side, and ^{n, s} ρ is obtained from these.
Then, assuming that the carrier phase of the observed satellite n is ^{n, s, X} φ and the integer value bias of the carrier is ^{n, s, X} N, the following expressions (4) and (5) are established.

[0044]

[Equation 4]

[Equation 5]

Here, since ^{n, s, and X} φ are observed values, equation (5)
The value on the right side can be obtained. Further, regarding the carrier wave LX, similarly, in the observation of the satellite n in the positioning side GPS receiver 103, the position vector of the receiver is ^u r _k , the position vector of the satellite when the signal is transmitted is ^{n, u} r _k , When the distance between the receivers is ^{n, u} ρ, the relationship of the following expression (6) is established.

[Equation 6]

The satellite position vector ^{n, u} r _k is the azimuth vector
It is calculated by the time according to the phase of C / A or P (Y) code observed on the positioning side together with ^{n, u} h _k , but _k ^u r is an unknown variable.
Then, assuming that the observed carrier wave phase of the satellite n is ^{n, u, X} φ and the integer value bias of the carrier wave is ^{n, u, X} N, the following expressions (7) and (8) hold.

[0047]

[Equation 7]

[Equation 8]

By subtracting the equation (5) from the equation (8),
Equation (9) holds, and the phase of carrier wave LX transmitted by satellite n
^{u, X} φ can be deleted.

[Equation 9]

Here, ^{n, u, X} φ− ^{n, s, X} φ is called a single phase difference. Further, by subtracting the relational expression (9) for the satellite 1 and the satellite n, the expression (10) is established, and the phases ^{u, X} φ, ^{s, X} φ of the carrier wave LX serving as the reference on the positioning side can be deleted.

[Equation 10] Here, ^{n, 1, X} φ is called double phase difference. _k ^u r and
^{n, 1, X} N are unknowns and the latter is an integer.

The operation up to this point is the same as the operation that has been conventionally performed, but the following is a description of the operation which is a feature of the present invention.

First, with respect to the equation (10), the double phase difference ^{n, 1, X}
Considering the measurement error ^{n, 1, u, x} ε of φ, the following equation (11)
Holds.

[Equation 11]

[0052] Here, ^{n, 1, X} N is not determined the values in one observation timing unknowns, a invariant for observation timing can vary by observing the timing there _k ^u It is different in character from r. Therefore, suppose ^{n, 1, X}
Suppose N is known. Number of satellites observed m
If there are five or more, four or more independent equations (11) can be obtained, while there are three unknowns of _k ^u r, which is redundant. Therefore, _k ^u r is determined from the conditional expression (12) based on the least square method that reduces the variance of the measurement errors ^{n, 1, u, x} ε.

[Equation 12]

Here, strictly speaking, the azimuth vector ^{n, u} h _k is _k ^u r
Is a function of ^{n, u} h _k, and DG using the above code phase
It is approximated by the azimuth vector of the satellite viewed from the position obtained by PS. This agrees with the fact that the wavefront of the carrier wave is approximated by a plane wave near the observation point, but since the position obtained by DGPS is close to the actual observation position, it is a very good approximation, and for the variation The orientation vector ^{n, u} h _k can be treated as a constant. By substituting the equation (11) into the equation (12) and rearranging, the relation of the following equation (13) is established.

[Equation 13]

Here, the G matrix and RDOP are given by the following equations (14) and (15).

[Equation 14]

[Equation 15] , The satellite constellation can be evaluated by RDOP,
^{When n, 1, X} N is obtained, the accuracy of _k ^u r can be estimated by the product of the approximate RDOP and the dispersion σ _{φ of the} double phase difference ^{n, 1, X} _φ and the wavelength ^X λ.

Further, the Γ matrix is expressed by the following equation (16).

[Equation 16] Is defined as _k ^u r is the following equation (17)

[Equation 17] Can be expressed as Then, when this condition is substituted into the equation (11), the relationship of the following equation (18) is established.

[Equation 18]

This expression has m-1 pieces, but since _k ^u r is deleted, only m-4 pieces of conditions are practically obtained. On the other hand, since there are m-1 unknown integer biases ^{n, 1, X} N ^, it is clear that they cannot be determined by one observation. When calculating for two frequencies L1 and L2, this formula becomes 2m-2 and becomes 2m-5.
Although the condition is obtained, the integer bias ^{n, 1, X} N is also 2m-2.

Next, when the satellite arrangement changes with the passage of time, the satellite signal is observed again. At this time, it is assumed that the position _k ^u r on the positioning side is also changing, but if tracking of the satellite signal carrier wave is continuously maintained, an integer bias
^{n, 1, X} N does not change. Therefore, m-
Four, 2m-5 conditional expressions will be obtained at two frequencies.
When the number of observations is repeated, the number of equation (18) increases, so
Integer biases ^{n, 1, X} N can be obtained by the least squares method. However, even if the number of observations is increased in a very short time, the satellite orientation does not change so much that sufficient accuracy cannot be obtained. It takes several minutes depending on the location and number of satellites. Set the observation timing identifier to a and start from 1.
The condition that the variance of the errors ^{n, 1, u, X, a} ε is the smallest when the observation is performed up to t is the relationship of the following expression (19).

[0058]

[Formula 19] It is to be noted that in the above equation (18), only the integer biases ^{n, 1, X} N and the wavelength ^X λ are invariant with respect to the observation timing a. By substituting the equation (18) into the equation (19), the following equation (20) is obtained.

[0059]

[Equation 20]

When the integer biases ^{p, 1, X} N are arranged, the following equation (21) is obtained.

[Equation 21]

Here, the Ω matrix and the ζ vector are defined by the following equations (22) and (23).

[Equation 22]

[Equation 23]

Then, the integer-valued biases ^{p, 1, X} N can be obtained by the lateral vector as in the following equation (24).

[Equation 24]

Also, the obtained integer value bias^{p, 1, X}N minutes
Dispersion σ_NIs the double phase difference^{n, 1, X}φ and variance σ _φBy outline below
In equation (25)

[Equation 25] It can be estimated, and if this is sufficiently smaller than 1, and four or more integer biases ^{p, 1 , X} N contain only one integer within the range of variance, the integer bias ^{p, 1, X} Judge that N is confirmed.

FIG. 2 is a flow chart for explaining the processing in the positioning arithmetic unit 104 of FIG. In FIG. 2, 201 is the start of processing, 202 is the initialization of state variables, and 203 is the reference side GPS receiver 102 and the positioning side GPS receiver 103 in FIG.
Phase input for inputting the code and carrier phase observed in 1., 204 is carrier phase pre-processing for processing when there is an abnormality in the carrier tracking state, 205 is RDOP calculation of equation (15) for evaluating satellite constellation , 206 is an arrangement determination that determines whether positioning can be performed if the integer value bias is confirmed, 207 is a bias determination that determines whether the integer value bias is confirmed, and 208 is an expression ( 17) Relative position calculation for calculating the relative position on the positioning side, 209 is a position output for outputting the relative position obtained by the relative position calculation 208, 210 is an inverse matrix Γ formula of the matrix G that can be arranged by the satellite whose phase is input 203 Γ matrix operation for obtaining (16), 211 for the matrix Ω equation for obtaining the integer bias, Ω matrix operation for obtaining (22), 212 for Ω mat Integer-biased by box (24) and N · sigma _N calculation for obtaining the variance sigma _N Equation (25), 213 N accuracy determination for evaluating the accuracy of the integer ambiguity obtained by the equation for determining the bias, 214 integer This is a relative position calculation for calculating the relative position on the positioning side when the precision of the numerical bias is not sufficient and an integer value cannot be determined.

The positioning calculation method based on the carrier wave phase of the satellite signal in this embodiment will be described in more detail below with reference to the configuration of FIG. 1 and the flow chart of FIG. In the positioning calculation, a management table for managing satellites used for positioning is provided, and the management table is emptied in initialization 202, and the observation timing a is set to 0. When the observed code and carrier wave phase are input at the phase input 203, the satellites for which the observed values are obtained on both the reference side and the positioning side are recorded in the management table. At this time, if the elevation angle of the satellite into which the phase is input or the signal-to-noise ratio does not satisfy the predetermined conditions, it is eliminated. In addition, if it matches the satellite already held in the control table, it is considered continuous, and if it is the first satellite, it is considered as initial. Then, satellites whose phase cannot be input on either the reference side or the positioning side are excluded. Further, even when the phases are input from both the reference side and the positioning side, it is assumed that it is an initial stage when a carrier phase discontinuity called cycle slip is detected on either the reference side or the positioning side.

In the RDOP calculation 205, the equation (15) is evaluated when there are four or more satellites in the management table, and when the number is four or less, the RDOP is set to an invalid value. In the placement determination 206, RD
If OP is 30 or less, the process branches to the bias determination 207, and if OP exceeds 30, it branches to the phase input 203 and waits for the next input. The bias determination 207 is performed by using the integer bias ^{n, 1, X} N shown in the equation (4) among the satellites that are continuous in the management table.
When the RDOP evaluated only by the satellites for which is determined is 30 or less, the process branches to the relative position calculation 208, and otherwise the process branches to the Γ matrix calculation 210. In the Γ matrix operation 210, the Γ matrix is calculated by the equation (16).

Next, in the Ω matrix calculation 211, the Ω matrix having the array number corresponding to the satellites listed in the management table is calculated by the formula (22). And N · σ _N operation 2
In Equation 12, the integer value bias ^{n, 1, X} N is calculated by the equation (24).
And the variance σ _N is calculated by the equation (25). N
In the precision judgment 213, when the variance σ _N is smaller than 0.25 and each integer bias ^{p, 1, X} N includes an integer within the range of variance, the integer bias ^{p, 1, X} N is determined. To judge. If the integer biases ^{p, 1, X} N are established, replace them with the corresponding integer values. Further, in the N accuracy determination 213, it is determined whether or not positioning is possible only by the satellite for which the integer value bias ^p 1,1 ^{, X} N is fixed, and if possible, the relative position calculation 20
8; otherwise, it branches to relative position calculation 214. In relative position calculation 208, an integer value bias
^The relative position is calculated by equation (17) by the satellite for which ^{p, 1, X} N is fixed, and this result is used to calculate the integer value bias ^{p, 1, X} N for the undetermined integer value bias ^{p, 1, X} N. Ask for. However, the added integer bias is 20
The evaluation is continued without being used for position calculation for 2 seconds, and if it can be determined that there is no problem, it is decided. The relative position obtained by the relative position calculation 208 is the satellite position,
1c depending on conditions such as multipath, relative distance, ionosphere, etc.
An accuracy of about m to 20 cm can be obtained. Relative position calculation 214
Then, the obtained integer value bias ^{p, 1, X} N is not rounded to an integer but is directly substituted into the equation (17) to obtain the relative position.
As for the accuracy of the obtained position, if a few minutes have passed since the satellite arrangement became good, compared to DGPS positioning by code phase,
Usually, the accuracy is good and the influence of multipath is small.

Next, after outputting the relative position obtained by the relative position calculation 208 or the relative position calculation 214 to the outside of the positioning calculation device 104 in FIG. 1 by the position output 209, the phase input 203 waits for the next input, Similar processing is continued for a new phase input.

As described above, according to the embodiment of the present invention, the phase of the code and the carrier obtained at one observation timing is compared with the evaluation that emphasizes the temporally new observation result using the Kalman filter of the conventional example. Within the range of, the condition for determining the position on the positioning side is obtained by the least squares method each time of observation, and the conditional expression (18) for obtaining the integer value bias excluding the information on the position on the positioning side at this observation time is obtained, By using these conditional expressions obtained at multiple observation timings as independent expressions and obtaining integer value bias by the least squares method, all valid observation results can be used without waste, so integer values can be obtained in a short observation time. In addition to being able to confirm the bias,
Since the determination of the integer value bias is not influenced by the movement on the positioning side, an excellent effect is obtained in that the versatility is increased.

Further, according to the embodiment of the present invention, compared with the conventional method of evaluating and selecting integer bias candidates,
These conditional expressions obtained at the same time at multiple observation timings are used as independent expressions and the integer value bias is calculated comprehensively by the least squares method. Therefore, a large capacity assuming a combination of many integer value biases as candidates. It is possible to obtain an excellent effect in that, in addition to requiring no storage device and high computing capacity, there is little influence of carrier phase fluctuation due to multipath on establishment of the integer bias.

A positioning calculation method using the carrier wave phase of the satellite signal according to the present embodiment, in which the positioning satellite signal is simultaneously received by the reference station and the positioning station, and the carrier wave phase of the received signal is compared to obtain the relative position of the positioning station with respect to the reference station. Is the range of the phase of the code and carrier obtained at one observation timing, and finds the condition to determine the position on the positioning side by the least squares method at each observation, and further adjusts the position of the position on the positioning side at this observation time. The conditional expression (18) for obtaining the numerical bias is obtained,
These conditional expressions obtained at the same time at multiple observation timings are used as independent expressions to obtain the integer bias by the least squares method, so that the integer bias can be determined in a short observation time, and it is low with a small storage device. Even a positioning computing device having a computing capability can perform positioning in real time by the carrier phase during movement, which is very effective.

The GPS receiver incorporating the positioning calculation function and the reception modem function, which uses the positioning calculation method based on the carrier wave phase of the satellite signal according to the present embodiment, can determine an integer value bias in a short observation time and is small in scale. Since it is possible to provide positioning using the carrier wave phase in real time even with the above memory device and a positioning operation device having a low calculation capability, and it is possible to provide a GPS receiver that uses a positioning calculation method using the carrier wave phase of a satellite signal with low power consumption. The effect is great.

The phases of the code and the carrier wave sent from the reference side and the positioning side via the communication network are received,
The central device connected to the network that obtains the position on the positioning side by using the positioning calculation method based on the carrier wave phase of the satellite signal according to the present embodiment can determine an integer value bias in a short observation time, and also has a small storage device. Even if the computing power is low, the positioning calculation can be performed in parallel for a larger number of positioning stations, so that the effect is great.

(Second Embodiment) The configuration of a system for GPS surveying using the positioning calculation method based on the carrier wave phase of a satellite signal of the present invention is the same as in FIG. FIG. 3 is a flow chart for explaining the processing in the positioning calculation device 104 of FIG. The general processing is the same as that in FIG. 2, and the difference will be described below. That is, 215 in FIG.
The integer ambiguities N differently from the N · sigma _N operation 212
N vector operation 216 for obtaining
N vector storage that holds the integer value bias N (vector) obtained in step 3 up to N operation 215 at the next observation timing,
Reference numeral 7 is an N accuracy judgment for individually evaluating the accuracy of the obtained integer value bias N.

In the GPS surveying system configured as described above, the general operation is the same as that of the first embodiment, but the operation different from that of the first embodiment will be described below.
The positioning calculation method based on the carrier wave phase of the satellite signal in this embodiment will be described in detail with reference to the flowchart of FIG. In FIG. 3, in the N vector calculation 215, the Ω matrix calculation 2
Receives the Ω matrix calculated in 11, and receives an integer bias N
(Vector) is calculated. Here, we define the identifier t that identifies the observation timing, and add () to the matrix or vector.
It is decided to distinguish the timing with an appendix. Assuming that the current observation timing is t, N (t-1 stored in the N vector storage 216 of the previous observation timing in the integer biases ^{p, 1, X} N (t) corresponding to the Ω matrix. ) If there is a component that is not included in the integer-valued bias ^{p, 1, X} N (t-1) that is a component of the vector, the relative position on the positioning side is obtained by DGPS based on the code phase, and Initialize with the approximate ^{p, 1, X} N found by substituting this position for ^u r. In the first N vector operation processing, all ^{p, 1, X} N are initialized. When all the components of the N (t-1) vector are determined, the N (t) vector is obtained by the following equation (26).

[0076]

[Equation 26] However, the ζ vector is obtained by the equation (23), and D
It is assumed that the matrix is a matrix having 0 other than the diagonal components of the Ω matrix. The inverse matrix of the D matrix is expressed by the following equation (27).

[Equation 27] Can be expressed as Here, in order to improve the calculation accuracy,
The order of the arrays is rearranged so that the diagonal elements of the Ω matrix have as large values as possible. In the subsequent N vector storage 216, N (t) obtained at this observation timing is prepared in preparation for the N vector calculation 215 at the next observation timing.
Save the vector.

Next, in the N precision judgment 217, an integer value bias which is the N (t) vector obtained by the N vector calculation 215.
Each component of ^{p, 1, X} N, individually for all identifiers p, X,
Sample at 10 second intervals and hold for 49 seconds. Then, the four integer value biases sampled and stored for the same identifier are compared with the integer value bias obtained at this timing, and it is determined whether or not the same integer value is within the accuracy of 0.3 or less. . Then, a plurality of integer-valued biases satisfy this condition, and the arrangement determination 2 is performed by the combination of corresponding satellites.
When the condition of 06 is satisfied, the process branches to the relative position calculation 208 and it is determined that the corresponding integer value bias is fixed. In other cases, the process branches to the relative position calculation 214.

Normally, when the number of satellites is large and processing is performed at two frequencies, the integer value bias N can be determined in a short observation time. The number of integer-valued bias N is the number of satellites m-1 or 2
Double. However, in the first embodiment, in the calculation of the integer value bias N and the variance σ _N for evaluating the precision, it is necessary to perform the calculation of the inverse matrix twice by the formula (24) and the formula (25). Then, this calculation has a drawback that it increases sharply as the number of integer value bias N increases.

On the other hand, in the second embodiment of the present invention, the iterative method is used to find the integer value bias N, and the integer value bias N obtained at the previous observation timing is used as the initial value. In addition to being able to calculate the integer value bias N with high accuracy in the processing amount, the integer value bias N obtained at the sampled observation timing is saved, and the accuracy of the integer value bias N is evaluated by their fluctuations. Since the integer value bias N can be determined with a small processing amount, it is an excellent effect in that even a small-scale storage device and a positioning calculation device with low calculation capability can perform high-precision positioning by carrier phase in real time. Is obtained.

Further, according to the second embodiment of the present invention,
An excellent effect is obtained in that the amount of calculation for obtaining the integer value bias N can be significantly reduced as compared with the first embodiment.

The positioning calculation method by the carrier wave phase of the satellite signal according to the present embodiment, in which the positioning satellite signal is received by the reference station and the positioning station at the same time, and the carrier phase of the received signal is compared to obtain the relative position of the positioning station with respect to the reference station. Is an asymptotically-determined integer-value bias N using the iterative method to solve the simultaneous equations, with the integer-value bias N obtained at the previous observation timing as the initial value in the calculation of the integer-value bias N. It is possible to obtain an integer-valued bias N with sufficient accuracy regardless of the amount, and it is possible to perform positioning by the carrier phase in real time even with a small-scale storage device and a positioning calculation device with low calculation capability. The effect is great.

Further, in the positioning calculation method by the carrier wave phase of the satellite signal according to the present embodiment, for the obtained integer value bias N, the obtained integer value bias N is stored at the sampled observation timing, and is adjusted by the variation thereof. Numerical bias N
Since the accuracy of is evaluated, the determination of the integer value bias N can be reliably determined with a smaller processing amount and a small storage area for storing the integer value bias N, which is a great effect.

(Third Embodiment) FIG. 4 shows a third embodiment of the present invention.
2 is a configuration of a system that performs GPS surveying using the positioning calculation method based on the carrier wave phase of the satellite signal in the embodiment of FIG. In FIG. 4, the GPS according to the third embodiment of the present invention
The surveying system includes a GPS satellite 101 that transmits L1 and L2 signals for measuring the position, and a reference-side GPS receiver 102 that measures the phases of carrier waves of L1 and L2 whose antenna installation positions are known. A positioning-side GPS receiver 103 for measuring the phases of the L1 and L2 carriers used for measuring the relative position with respect to the reference side, and a recording device 1 for recording the code and the carrier phase observed by the reference-side GPS receiver 102.
07, the recording device 108 that records the phase of the code and the carrier wave observed by the positioning GPS receiver 103, and the recording of the phase recorded in the recording device 107 and the recording device 108 in the position measurement, and the post-processing It is composed of a positioning calculation device 109 for calculating the position at.

The operation of the GPS surveying system configured as described above will be described below. Third of the present invention
The GPS surveying system according to the embodiment is different from the first embodiment in that the phase observed on each of the reference side and the positioning side is recorded without providing a communication path, and the position is calculated by post-processing.

FIG. 5 is a flow chart for explaining the processing in the positioning arithmetic unit 109 of FIG. In FIG. 5, 201 is the start of processing, 202 is the initialization of state variables, 203 is the phase input for inputting the phases of the code and carrier waves recorded by the recording device 107 on the reference side and the recording device 108 on the positioning side in FIG.
Reference numeral 204 is a carrier phase pre-processing that performs processing when there is an abnormality in the tracking state of the carrier wave, 205 and 227 are RDOP operations of the equation (15) that evaluates the constellation of the satellite, and 206 and 228 are integer value biases. If so, an arrangement determination for determining whether positioning is possible, 210 and 229 are Γ matrix operations for obtaining an inverse matrix Γ equation (16) of a matrix G that allows satellites to be arranged, and 211 is a matrix Ω equation for obtaining an integer value bias ( 22) is an Ω matrix operation, 212 is Ω
N · σ _N operation for obtaining integer value bias N (Equation (24)) and its variance σ _N (Equation (25)) using a matrix, 2
13 is an N accuracy judgment for evaluating the accuracy of an integer bias obtained by an equation for obtaining a bias, 218 is an input end judgment for checking the end of phase recording, and 219 is a p end judgment for checking the end of scanning for an integer bias identifier p. , 22
0 is an integer that rounds the integer bias N to an integer when the precision of the integer bias is sufficient, 221 saves the integer bias N and its variance σ _N , saves N · σ _N , 222 indicates the next integer bias Update to change to the identifier of 223, 223 is a re-initialization for preparing to move to the process after the input is completed in the input end determination 218, 224 is a phase input for inputting a phase from the beginning again, and 225 is an end of phase recording. Input end determination to be checked, 226 is the end of processing, 230 is a relative position calculation for calculating the relative position on the positioning side by the integer value bias N stored in the N · σ _N storage 221, and 231 is a relative position calculated by the relative position calculation 230. Is a position output for outputting.

The positioning calculation method based on the carrier wave phase of the satellite signal according to this embodiment will be described in more detail with reference to the configuration of FIG. 4 and the flow chart of FIG. The calculation of the relative position and the calculation principle of the integer bias N are the same as in the first embodiment,
Only the difference will be described below.

In FIG. 5, the phase input 203 inputs the recorded phases in the order of observation. In this embodiment,
Unlike the first embodiment shown in FIG. 2, the relative position is not calculated in the first input. Further, the N · σ _N calculation 212 is performed after reaching the final input, and is not performed at each observation timing as in the first embodiment.

Also, in the first embodiment, an integer value bias
It is assumed that ^{p, 1, X} N is an identifier associated with the received satellite identifier n and the carrier frequency LX.
When a carrier phase discontinuity called a cycle slip was detected, it was initialized. On the other hand, in the present embodiment, the identifier p of a new integer value bias ^{p, 1, X} N is added to the satellite signal received again, and thereafter it is processed as another integer value bias. In addition, the integer-valued bias ^{p, 1, X} N corresponding to the period of less than 2 minutes of continuous reception on the reference side and the positioning side does not contribute to the position determination, and the load increases in the calculation of the integer-valued bias. However, since it becomes an obstacle in obtaining a solution, it is temporarily removed before the N · σ _N calculation 212.

In the Ω matrix calculation 211 of FIG. 5, each element of the Ω matrix of the equation (22) and the ζ vector of the equation (23) is used in accordance with the phase input and each element calculated by the input at the previous observation timing is used. , Additional cumulative addition.
In addition, for identifiers of integer value bias newly added due to signal interruption, etc., new vertical and horizontal vectors that do not include the corresponding integer value bias before the interruption so that the array elements of the matrix do not increase unnecessarily And hold.

When the end of input is detected by the input end determination 218, the process branches to the N · σ _N calculation 212. N · σ _N operation 212
Then, the integer value bias N and the variance σ _N are calculated by the equations (24) and (25) using the Ω matrix and the ζ vector obtained by the Ω matrix calculation 211. p End judgment 219 to N
Up to the σ _N storage 221, the integer value bias N is sequentially obtained for all the identifiers p, the variance σ _N is evaluated, the integer value bias N is rounded to an integer if possible, and the obtained result is stored.

[0091] Next, were stored at _N · σ N Save 221 _N · σ N
Phase input 224 in the relative position calculation 230
Then, the position on the positioning side is sequentially calculated again with the phase input from the beginning.

Since all of the recorded phases are used in the positioning calculation by the post-processing as described above, the integer value of the integer bias can be more surely fixed, and even when it cannot be fixed, the integer bias is highly accurately determined. I want it. Then, the relative position on the positioning side is calculated for all the observation timings with the integer value bias obtained by using all, so that the relative position on the positioning side can be obtained with high accuracy from the initial stage of the observation. In addition, since the calculation of the integer value bias is collectively performed, the amount of calculation in the whole is reduced.

As described above, according to the third embodiment of the present invention, the code and carrier obtained at one observation timing are compared with the evaluation that emphasizes the temporally new observation result using the Kalman filter of the conventional example. The condition for determining the position on the positioning side by the method of least squares in each phase range is calculated, and the condition for obtaining the integer bias excluding the information on the position on the positioning side at the time of observation is expressed by the formula (18). Asked in
These conditional expressions obtained in the same way at a large number of observation timings are treated as independent expressions, and the integer value bias is calculated. It has an excellent effect in that it can be used without waste, the integer value bias can be more reliably determined even when the observation time is short, and the amount of calculation throughout can be reduced.

Further, according to the third embodiment of the present invention, compared with the conventional method of evaluating and selecting the integer bias candidates, these conditional expressions similarly obtained at a plurality of observation timings are independent expressions. As, since the integer-value bias is calculated comprehensively by the least-squares method, it is not necessary to assume a combination of a large number of integer-value biases as candidates, and it is excellent in that it does not require a large-capacity storage device or high calculation capacity. There is an effect.

In the present embodiment, the positioning satellite signals are simultaneously received by the reference station and the positioning station, the carrier wave phases of the received signals are recorded, and the recorded carrier wave phases are compared to obtain the relative position of the positioning station with respect to the reference station. The positioning calculation method based on the carrier wave phase of the satellite signal concerned finds the condition for determining the position on the positioning side by the least squares method at each observation within the range of the code and the carrier wave phase obtained at one observation timing, and further at this observation time point. The conditional expression (18) for finding the integer value bias excluding the information of the position on the positioning side is calculated, and the conditional expression (18) similarly calculated at many observation timings is used as an independent expression to calculate the integer value bias. , Since a large number of observation timings are collectively calculated by the least squares method,
All valid observation results can be used without waste, and even if the observation time is short, the integer value bias can be determined more reliably, and the amount of calculation throughout can be reduced, so a small-scale storage device and low calculation capacity Even with this positioning calculation device, the positioning calculation by the carrier wave phase can be completed in a short time, so that the effect is great.

In the above description, the relative position and the integer bias are calculated by using one of the phases of the carrier waves, L1 or L2, but the present invention is not limited to this, and the sum is calculated by weighting L1 and L2 with integers. It is also possible to obtain the integer value bias in a short time and reduce the influence of the ionosphere by setting different integer value biases for both L1 and L2 and performing calculations. In addition, the delay due to the ionosphere is calculated from the phase difference between the L1 and L2 codes, the delay of the ionosphere obtained from a separately observed observation network, and high-precision orbit information are used to determine the difference between the positions on the reference side and the positioning side. It is also possible to reduce the error due to.

Further, in the above description, the time at which the phase was measured on the reference side coincides with the time at which the phase is measured, but the present invention is not limited to this, and the orbital element of the satellite or the carrier frequency of the observed satellite signal is used. It is also possible to predict and correct the phases of the code and the carrier observed when the time observed on the reference side is shifted to the time measured on the positioning side.

Further, in the first embodiment, the calculation of the formula (24) for obtaining the integer bias and the formula (25) for evaluating the bias is performed every observation timing, but the calculation is not limited to this. After the observation becomes possible, the period required for the calculation of the integer bias to be meaningful depends on the number of satellites and the arrangement, but it is possible to thin out the calculation to determine the integer bias by judging this in advance. . Further, depending on the distribution result of the integer value bias, it is possible to thin out the calculation for obtaining the integer value bias for several subsequent observation timings.

Further, in FIG. 1 of the first embodiment, the G on the positioning side is
Although the positioning calculation device and the reception modem are installed separately from the PS receiver, the present invention is not limited to this, and the positioning calculation device and the reception modem are GP.
It can also be built into the S receiver. Further, similarly to the reference side, a positioning modem can be installed in the GPS receiver on the positioning side to perform positioning calculation in a central device via a communication network or the like.

In the second embodiment, the Jacobi method described in “Matrix Calculation Software” (Maruzen) p174, edited by Oguni Riki, is used as the solution of simultaneous equations in the N vector calculation 215, and the number of iterations is only once. However, it is not limited to this, and the accuracy can be increased by making the number of iterations multiple times, and the amount of calculation increases and the complexity increases somewhat, but it is shown in the above-mentioned “Matrix Calculation Software” (Maruzen) p174, edited by Oguni Riki. The accuracy can be increased by using the Gauss-Seidel method described above.

[0102] In the third embodiment, it is assumed for calculating the integer ambiguity N and variance sigma _N in N · sigma _N operation 212 collectively for all phases recorded, not limited thereto, the integer ambiguity ^p It is also possible to divide and process by dividing at appropriate timing so that the number of ^{, 1, X} N does not increase too much.

Further, in the above description, it is assumed that the reference side position is known, but the case where the reference position changes is not mentioned. However, if the reference side accurate position is known at each observation timing, the reference side position moves. It doesn't matter.

In addition, the NA operated by the US so far
Although the example of receiving the signal of the VSTAR satellite and performing positioning calculation by the carrier wave phase has been described, the phase of the spread spectrum signal and the carrier wave phase of the satellite signal such as the GLONASS satellite operated by the Russian Republic are not limited to this. The same can be applied to a receiver that obtains a position by performing the same process.

[0104]

INDUSTRIAL APPLICABILITY As described above, according to the present invention, when the positioning satellite signal is simultaneously received by the reference station and the positioning station and the carrier phases of the received signals are compared to obtain the relative position of the positioning station with respect to the reference station, one observation is made. In order to find the condition to determine the position on the positioning side by the least squares method at each observation in the range of the code and carrier phase obtained at the timing, and to find the integer value bias excluding the information of the position on the positioning side at the time of this observation. In addition to determining the conditional expression of, and using these conditional expressions obtained in the same manner at multiple observation timings as independent expressions, the integer bias can be determined by the least squares method, and the integer bias can be determined in a short observation time. Even with a small-scale storage device and a positioning computing device with low computing power, it is possible to obtain the effect that positioning can be performed by the carrier wave phase in real time while moving.

Further, according to the present invention, in the calculation for obtaining the integer value bias N, the integer value bias N obtained at the previous observation timing is used as an initial value, and the iterative method is used to solve the simultaneous equations. It is possible to obtain an integer value bias N with sufficient accuracy despite the small amount of computation, and it is possible to perform positioning by carrier phase in real time even with a positioning computing device with low computing power. The effect is obtained.

Further, in the present invention, for the obtained integer value bias N, the obtained integer value bias N is stored at the sampled observation timing, and the integer value bias N is changed by the variation thereof.
By evaluating the accuracy of, the integer value bias N can be reliably determined with a small amount of processing and a small storage area for storing the integer value bias N.

[Brief description of drawings]

FIG. 1 is a configuration diagram of a system that performs GPS surveying using a positioning calculation method based on a carrier wave phase of a satellite signal according to a first embodiment of the present invention.

FIG. 2 is a flowchart illustrating processing of the positioning calculation device 104 according to the first embodiment of the present invention.

FIG. 3 is a flowchart illustrating processing of the positioning calculation device 104 according to the second embodiment of the present invention.

FIG. 4 is a configuration diagram of a system that performs GPS surveying using a positioning calculation method based on a carrier wave phase of a satellite signal according to a third embodiment of the present invention.

FIG. 5 is a flowchart illustrating processing of the positioning calculation device 109 according to the third embodiment of the present invention.

[Explanation of symbols]

102 Reference side GPS receiver 103 Positioning GPS receiver 104 Positioning calculation device 105 sending modem 106 receiving modem 107 recording device 108 recording device

Claims (11)

[Claims] 1. An antenna for receiving a satellite signal, a carrier phase measuring unit for measuring a carrier phase of the satellite signal received by the antenna, first carrier phase information measured at a predetermined reference point, and the carrier. Second measured by the phase measurement unit
And a calculation unit that obtains the position of the moving body from the carrier phase information, and the calculation unit has a double phase difference between the first carrier phase information and the second carrier phase information at every predetermined timing, The position of the satellite at the predetermined timing,
A plurality of relational expressions between the position of the reference point and the position of the moving body are obtained, and a conditional expression in which a variable corresponding to the position of the moving body is deleted from the plurality of relational expressions is obtained. A satellite navigation positioning device, characterized in that the position of the moving body is determined by obtaining an integer value bias of the double phase difference which is satisfied with a small deviation from each other. 2. An antenna for receiving a satellite signal and a receiver for simultaneously observing a carrier wave phase of the satellite signal received by the antenna for a plurality of satellites are provided as a reference side position whose position is known and a positioning side. Satellite positioning calculation that installs at different positions, observes carrier phase simultaneously on both the reference side and positioning side for multiple timings, and uses the observed carrier phase to determine the relative position of the positioning side with respect to the reference side. In the method, the relational expression between the double phase difference of the carrier including an unknown integer bias for each observation timing, the position of the satellite and the positions of the reference side and the positioning side is obtained, and the relational expression obtained at each observation timing The position of the positioning side is obtained by substituting the condition for finding the position of the positioning side by the method of least squares in the range The conditional expression in which the variable corresponding to is deleted is obtained, and for each observation timing, the conditional expression in which the variables are deleted obtained for a plurality of observation timings including before is doubled under the condition that the mutual deviation is small. A satellite positioning calculation method characterized by obtaining an integer value bias of a phase difference. 3. At a certain observation timing, regarding a plurality of observation timings including past observation timings,
A conditional expression that eliminates the position variable on the positioning side is obtained, and the integer value bias of the double phase difference is obtained under the condition that these conditional expressions are satisfied with a small deviation, and the variance of the integer value bias is evaluated to 3. A determination is made as to whether or not the integer bias has been established, provided that a unique integer is included in a predetermined range defined by the variance of the integer bias centering on the numeric bias. The satellite positioning calculation method described. 4. At a certain observation timing, a condition for determining the position on the positioning side is obtained by the least squares method within the range of the relational expression obtained at each observation timing, and the satellite can be arranged according to the condition for determining the position. For the observation timing of satellite arrangements that do not satisfy the above conditions, the condition that evaluates the accuracy is determined, and the conditional expression that deletes the variable corresponding to the position on the positioning side is deleted. The satellite positioning calculation method according to claim 2, wherein the combination is not added to the combination of the conditional expressions. 5. An Ω matrix conditional expression and a ζ vector conditional expression are defined as a condition for obtaining the integer bias, and a storage function for holding each element of the defined Ω matrix conditional expression and the ζ vector conditional expression is provided. A conditional expression that eliminates the variable corresponding to the position on the positioning side is provided for each observation timing, and the conditional expression that erases the variable corresponding to the position on the positioning side holds the Ω matrix condition and the ζ vector. The elements of the condition are cumulatively added, and the cumulatively added Ω matrix condition and the ζ
The satellite positioning calculation method according to any one of claims 2 to 4, wherein an integer bias is obtained according to a vector condition. 6. In the calculation for obtaining the integer bias, the integer bias obtained at the previous observation timing is used as an initial value, and the iterative method is used to solve the simultaneous equations to obtain the integer bias asymptotically. The satellite positioning calculation method according to any one of claims 2 to 5, wherein the obtained integer value bias is used as an initial value in a calculation for obtaining the next integer value bias. 7. In an operation for asymptotically obtaining an integer value bias by using an iterative method for solving the simultaneous equations, an initial value of the integer value bias is used as a reference for a satellite signal of a satellite signal. The position on the positioning side is obtained by differential positioning using the code phase, the approximate integer value bias is obtained from the obtained position on the positioning side, and the obtained approximate integer value bias is used as an initial value. 6. The satellite positioning calculation method described in 6. 8. An integer value bias obtained by calculation,
Within the continuous observation timing, the integer value bias obtained for the observation timing sampled at intervals is stored, and the integer value bias obtained at each observation timing is compared with the stored integer value bias. The satellite positioning calculation method according to any one of claims 2 to 7, characterized in that the accuracy of integer bias is evaluated by evaluating the fluctuation amounts thereof. 9. A function of simultaneously observing the carrier phase of a satellite signal received by the antenna for a plurality of satellites, a function of receiving simultaneously the carrier phase of the same satellite observed on the reference side through a communication path, and a satellite signal A positioning calculation function based on a carrier phase is provided, and the positioning calculation function finds a condition for determining the position on the positioning side by the least square method within the range of the relational expression obtained at each observation timing, and the found condition is the carrier phase. By deleting the variable corresponding to the position on the positioning side by substituting it into the relational expression regarding, the conditional expression in which the variable is deleted is obtained as an integer value bias of the double phase difference under the condition that a small deviation is satisfied. A satellite navigation receiver using the satellite positioning calculation method according to any one of claims 2 to 8. 10. An antenna for receiving a radio wave of a satellite signal and a receiver for simultaneously observing the carrier wave phase of the satellite signal received by the antenna for a plurality of satellites are separated from the reference side position whose position is known. The positioning of the satellite signal observed by the receiver on the positioning side and the function of receiving the carrier wave phase of the satellite signal observed by the receiver on the positioning side via the communication network. A function of separately inputting a carrier wave phase and a positioning calculation function based on a carrier wave phase of a satellite signal are provided, and the positioning calculation function is within the range of a relational expression obtained at individual observation timings.
Find the condition to determine the position on the positioning side by the least squares method,
The variable corresponding to the position on the positioning side is deleted by substituting the obtained condition into the relational expression relating to the carrier phase, and the conditional expression in which the variable is deleted is adjusted so that the double phase difference is satisfied under the condition that the deviations are small. A central apparatus using the satellite positioning calculation method according to any one of claims 2 to 8, wherein a numerical bias is obtained. 11. A positioning satellite signal is simultaneously received by a reference station and a positioning station, carrier phases of these received signals are respectively recorded, and the recorded carrier phases are compared to obtain a relative position of the positioning station with respect to the reference station. In the satellite positioning calculation method, the relational expression between the carrier dual phase difference including an unknown integer bias, the satellite position, and the positions on the reference side and the positioning side is obtained for each observation timing, and obtained at each observation timing. In the range of the relational expression, a condition for determining the position on the positioning side is obtained by the method of least squares, and the obtained condition is substituted into the relational expression regarding the carrier phase to eliminate the variable corresponding to the position on the positioning side. For the conditional expression obtained by obtaining an expression and deleting the variables obtained for a large number of observation timings, the double phase difference can be adjusted collectively under the condition that small deviations are satisfied. A satellite positioning calculation method characterized by obtaining a numerical bias.