A method for evaluating the positioning accuracy of a single low-orbit satellite using a hybrid pseudorange and Doppler measurement

Abstract

A method for evaluating the positioning accuracy of a single low-orbit satellite using a hybrid measurement of pseudorange and Doppler. After setting the positioning time and sampling interval, the satellite measurement data and sampling points are determined, and the pseudorange theoretical measurement value and pseudorange observation value as well as the Doppler theoretical measurement value are calculated. By constructing a hybrid measurement observation equation based on pseudorange and Doppler, the user position and clock error are solved, and the final positioning result and positioning accuracy of each grid point in the coverage area of ​​the single low-orbit satellite are obtained through continuous iteration.

Description

Technical Field

[0001] The invention relates to a method for evaluating the positioning accuracy of a single low-orbit satellite by pseudo-range and Doppler hybrid measurement, and belongs to the field of low-orbit satellite navigation. Background Art

[0002] The application of satellite navigation systems is ubiquitous, bringing subversive impacts to the positioning and navigation methods in various fields of industrial production and military applications. Because of this, the vulnerability of satellite navigation systems and ways to compensate for it have also received more and more attention. On the other hand, in recent years, low-orbit satellites have ushered in a booming development. Low-orbit satellites are different from medium- and high-orbit navigation satellites. They have a low orbit altitude and the coverage is much lower than that of medium- and high-orbit satellites at the same number. At the same time, they move fast and have short transit times. This not only makes it possible to navigate based on low-orbit satellites, but also makes navigation and positioning based on a few low-orbit satellites more difficult than traditional GNSS positioning. Summary of the invention

[0003] The technical problem solved by the present invention is: in view of the high difficulty in navigation and positioning of a few low-orbit satellites in the current prior art, a method for evaluating the positioning accuracy of a single low-orbit satellite through pseudorange and Doppler hybrid measurement is proposed.

[0004] The present invention solves the above technical problems by the following technical solutions:

[0005] A method for evaluating the positioning accuracy of a single low-orbit satellite using a pseudorange and Doppler hybrid measurement, the steps are as follows:

[0006] (1) At the set positioning time T k Within the sampling interval Δt, determine the satellite measurement data ρ k 、f k , k = 1, ..., n, and determine the number of sampling points Calculate the theoretical pseudorange measurement value ρ0 and the pseudorange observation value ρ at each sampling point k ;

[0007] (2) Based on step (1), calculate the Doppler theoretical measurement value f0 and the Doppler observation value f k ;

[0008] (3) Construct hybrid measurement observation equation based on pseudorange and Doppler;

[0009] (4) Calculate the user position and clock error based on the pseudorange and Doppler measurement accuracy generated by the single random number of pseudorange and Doppler calculation;

[0010] (5) Based on the mission data, the Monte Carlo method is used to evaluate the positioning accuracy of each grid point in the coverage area of ​​a single low-orbit satellite that follows a Gaussian white noise distribution.

[0011] The specific calculation method of the theoretical pseudo-range measurement value ρ0 at a single sampling moment is:

[0012]

[0013] In the formula, (x s ,y s ,z s ) is the satellite position at that moment, (x, y, z) is the preset user's real position, c is the speed of light, δt u0 is the initial clock difference of the user receiver, k is the number of sampling points, The user receiver clock drift;

[0014] Pseudorange observation value ρ k The specific calculation method is:

[0015] ρ k =ρ0+σ ρ rand(1,n)

[0016] In the formula, σ ρ is a pseudo-range single random number.

[0017] The calculation method of the Doppler theoretical measurement value f0 at a single sampling moment is as follows:

[0018]

[0019] Where f0 is the signal frequency received by the user receiver; (x s ,y s ,z s ) is the satellite position at that moment; v = [v x , v y , v z ] is the speed of the satellite relative to the user at that moment, which is the satellite speed for static or low-dynamic users; f * is the frequency of the original transmitted signal;

[0020] f k =f0+σ f rand(1,n)

[0021] In the formula, σ f Single random number for Doppler measurement.

[0022] The observation equation at different sampling times 1, ...k, ...n is specifically:

[0023]

[0024] In the formula, is the pseudorange calculated value at the first sampling moment, (x s1 ,ys1 ,z s1 ) is the satellite position at the first sampling moment, is the calculated pseudorange value at the nth sampling moment, (x sn ,y sn ,z sn ) is the satellite position at the nth sampling moment, The last iteration result of the user receiver position. The first calculation is the actual position plus a 5km deviation. The last iteration result of the receiver clock error. The first calculation is the set initial clock error plus 10m. The last iteration result of the user receiver clock drift. The first calculation is the set value plus 1m / s.

[0025] is the Doppler calculation value at the first sampling moment, The Doppler calculation value at the nth sampling moment.

[0026] In step (4), the specific method for calculating the user position and clock difference is:

[0027] (4-1) At a preset user position, Taylor expansion is performed on the pseudorange observation equation and the Doppler observation equation;

[0028] (4-2) Calculate the change in user position and determine the user position and clock error.

[0029] In the step (4-1), the pseudorange observation equation and the Doppler observation equation after Taylor expansion are specifically:

[0030]

[0031]

[0032] In the formula, ρ k is the pseudorange observation value obtained in step 3, is the result of the last iteration of the pseudorange calculation value obtained in step 4, is the last iteration result of the user receiver position, (x sk ,y sk ,z sk ) is the position of the satellite at the sampling time.

[0033]

[0034]

[0035]

[0036]

[0037] In the formula, (v xk ,v yk ,v zk ) is the speed of the satellite at the sampling moment.

[0038] In the step (4-2), the method for calculating the user position change is:

[0039] ΔX=(H T H) -1 H T ·Δy

[0040] H=[G1,G2] T

[0041]

[0042]

[0043] Δy=HΔx+εΔy=[Δρ,Δf] T

[0044] Where G1 and G2 are pseudorange and Doppler measurement matrices, H is the combined measurement matrix, and ΔX is the state quantity to be solved, including the three-dimensional position change of the user receiver (Δx, Δy, Δz,) T , clock error δt u , Zhongpiao The state quantity to be solved is composed of , and Δy is the deviation between the observed value and the calculated value.

[0045] In step (4-2), the method for calculating the user position and the clock error and clock drift is:

[0046] P * =P0+ΔX

[0047]

[0048] Where P0 is the initial state, including the initial position, clock error and clock drift of the user receiver, and P* is the new state obtained after iterative calculation.

[0049] In the step (5), the cyclic positioning calculation as described in step (4) is performed for each grid point for a specified number of times, and the calculated user position mean is used as the final positioning result, and the positioning accuracy is evaluated based on the obtained positioning result.

[0050] The formula for calculating the mean user position is:

[0051]

[0052] Where 100 is the specified number of loop positioning.

[0053] The advantages of the present invention compared with the prior art are:

[0054] (1) The present invention provides a method for evaluating the positioning accuracy of a single low-orbit satellite using a hybrid pseudorange and Doppler measurement. In the case where only one low-orbit satellite is available, a positioning and accuracy evaluation method based on two types of measurement information, pseudorange and Doppler, is provided. This method can be used for positioning solutions for static and low-dynamic users, as well as for evaluating the available positioning accuracy in the area of ​​interest. This method provides a technical method for navigation and positioning with single coverage of low-orbit satellites.

[0055] (2) Based on the typical single coverage of low-orbit satellites, the present invention proposes a positioning method and an accuracy assessment method based on pseudorange and Doppler hybrid measurement, providing a technical approach for low-orbit satellites to be used for navigation and positioning. The use of hybrid measurement data improves the problem of geometric singular points when there is only single measurement data to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A flow chart of the method for evaluating the positioning accuracy of pseudorange and Doppler hybrid measurement provided by the invention; DETAILED DESCRIPTION

[0057] A method for evaluating the positioning accuracy of a single low-orbit satellite using a hybrid pseudorange and Doppler measurement is proposed. In the case where only one low-orbit satellite is available, a positioning and accuracy evaluation method based on two types of measurement information, pseudorange and Doppler, is given. This method can be used for positioning solutions for static and low-dynamic users, as well as for evaluating the available positioning accuracy in the area of ​​interest. This method provides a technical method for navigation and positioning with single coverage of low-orbit satellites, such as Figure 1 As shown, the specific positioning evaluation method steps are:

[0058] (1) At the set positioning time T k Within the sampling interval Δt, determine the satellite measurement data ρ k 、f k , k = 1, ..., n, and determine the number of sampling points Calculate the theoretical pseudorange measurement value ρ0 and the pseudorange observation value ρ k ;

[0059] Among them, the calculation method of the pseudorange theoretical measurement value ρ0 is specifically as follows:

[0060]

[0061] In the formula, (x s ,y s ,z s ) is the satellite position at that moment, (x, y, z) is the preset user's real position, c is the speed of light, δt u0is the initial clock difference of the user receiver, k is the number of sampling points, The user receiver clock drift;

[0062] Pseudorange observation value ρ k The specific calculation method is:

[0063] ρ k =ρ0+σ ρ rand(1,n)

[0064] In the formula, σ ρ is a pseudo-range single random number;

[0065] (2) Based on step (1), calculate the Doppler theoretical measurement value f0 and the Doppler observation value f k ;

[0066] The calculation method of the Doppler theoretical measurement value f0 is specifically as follows:

[0067]

[0068] Where f0 is the signal frequency received by the user receiver; (x s ,y s ,z s ) is the satellite position at that moment; v = [v x , v y , v z ] is the speed of the satellite relative to the user at that moment, which is the satellite speed for static or low-dynamic users; f * is the frequency of the original transmitted signal; f k =f0+σ f rand(1,n)

[0069] In the formula, σ f A single random number for Doppler measurement;

[0070] (3) Construct hybrid measurement observation equation based on pseudorange and Doppler;

[0071] The observation equation is specifically:

[0072]

[0073] In the formula, is the pseudorange calculated value at the first sampling moment, (x s1 ,y s1 ,z s1 ) is the satellite position at the first sampling moment, is the calculated pseudorange value at the nth sampling moment, (x sn ,y sn ,z sn) is the satellite position at the nth sampling moment, The last iteration result of the user receiver position. The first calculation is the actual position plus a 5km deviation. The last iteration result of the receiver clock error. The first calculation is the set initial clock error plus 10m. The last iteration result of the user receiver clock drift. The first calculation is the set value plus 1m / s.

[0074] is the Doppler calculation value at the first sampling moment, The Doppler calculation value at the nth sampling moment.

[0075] (4) Calculate the user position and clock error based on the pseudorange and Doppler measurement accuracy generated by the single random number of pseudorange and Doppler calculation;

[0076] Among them, the specific method for calculating the user position and clock difference is:

[0077] (4-1) At a preset user position, Taylor expansion is performed on the pseudorange observation equation and the Doppler observation equation;

[0078] The pseudorange observation equation and Doppler observation equation after Taylor expansion are as follows:

[0079]

[0080]

[0081] In the formula, ρ k is the pseudorange observation value, is the result of the last iteration of the pseudorange calculation value, is the last iteration result of the user receiver position, (x sk ,y sk ,z sk ) is the position of the satellite at the sampling time.

[0082]

[0083]

[0084]

[0085]

[0086] In the formula, (v xk ,v yk ,v zk ) is the speed of the satellite at the sampling moment.

[0087] (4-2) Calculate the change in user position and determine the user position and clock error;

[0088] The calculation method of the user position change is:

[0089] Δx=(H T H) -1 H T ·Δy

[0090] H=[G1,G2] T

[0091]

[0092]

[0093] Δy=HΔx+εΔy=[Δρ,Δf] T

[0094] Where G1 and G2 are pseudorange and Doppler measurement matrices, H is the combined measurement matrix, and ΔX is the state quantity to be solved, including the three-dimensional position change of the user receiver (Δx, Δy, Δz,) T , clock error δt u , Zhongpiao The state quantity to be solved is composed of , and Δy is the deviation between the observed value and the calculated value.

[0095] The calculation method of user position and clock error is:

[0096] P * =P0+Δx

[0097]

[0098] Where P0 is the initial state, including the initial position, clock error and clock drift of the user receiver, and P* is the new state obtained after iterative calculation.

[0099] (5) Based on the mission data, the positioning accuracy of each grid point in the coverage area of ​​a single low-orbit satellite that obeys the Gaussian white noise distribution is evaluated by the Monte Carlo method. The cyclic positioning calculation described in step (4) is performed for each grid point a specified number of times, and the calculated user position mean is used as the final positioning result. The positioning accuracy is evaluated based on the obtained positioning result.

[0100] The following is further described in conjunction with specific embodiments:

[0101] In the current embodiment, a navigation positioning accuracy evaluation method using pseudorange and Doppler measurement information is provided for the availability of a single low-orbit satellite, as follows:

[0102] (1) Obtain the broadcast ephemeris user algorithm of the low-orbit satellite in advance to calculate any observation time tk Satellite position (x sk ,y sk ,z sk )、speed(v xk ,v yk ,v zk ) is used as a known condition to design pseudorange and Doppler observation values. At the set positioning time T k Under the sampling interval Δt, the satellite measurement data ρ within the continuous available period is designed k 、f k , k=1,...,n, the number of sampling points is

[0103] The theoretical pseudorange measurement value is ρ0:

[0104]

[0105] In the formula, (x s ,y s ,z s ) is the satellite position, and (x, y, z) is the preset user position.

[0106] The measurement noise is processed as Gaussian white noise, and the pseudo-range observation value of a certain time is:

[0107] ρ k =ρ0+σ ρ rand(1,n)

[0108] The theoretical Doppler measurement is:

[0109]

[0110] Where f0 is the signal frequency received by the user receiver; (x s ,y s ,z s ) is the satellite position; v = [v x , v y , v z ] is the speed of the satellite relative to the user, which is the satellite speed for static or low-dynamic users; f * is the frequency of the original transmitted signal;

[0111] The Doppler observation value of a certain time is:

[0112] f k =f0+σ f rand(1,n)

[0113] (2) Construct the observation equation based on the hybrid measurement of pseudorange and Doppler:

[0114]

[0115] (3) Based on the pseudo-range and Doppler measurement accuracy generated by a single random number, the user position and clock error are solved. First, an iterative calculation is performed to calculate the changing Doppler Δf based on the initial Doppler value and pseudo-range value. k , pseudorange change value Δρ k , in order to obtain the next Doppler theoretical value and pseudorange theoretical value, the pseudorange observation equation and Doppler observation equation after Taylor expansion are specifically:

[0116]

[0117]

[0118] In the formula, ρ k is the pseudorange observation value obtained in step 3, is the result of the last iteration of the pseudorange calculation value obtained in step 4, is the last iteration result of the user receiver position, (x sk ,y sk ,z sk ) is the position of the satellite at the sampling time.

[0119]

[0120]

[0121]

[0122]

[0123] In the formula, (v xk ,v yk ,v zk ) is the speed of the satellite at the sampling moment.

[0124] The user position change is calculated through the linearized combined observation positioning equation, and the user position and clock error and drift are solved, specifically:

[0125] Δx=(H T H) -1 H T ·Δy

[0126] H=[G1,G2] T

[0127]

[0128]

[0129] Δy=HΔx+εΔy=[Δρ,Δf] T

[0130] P * =P0+Δx

[0131]

[0132] Where G1 and G2 are pseudorange and Doppler measurement matrices, H is the combined measurement matrix, and ΔX is the state quantity to be solved, including the three-dimensional position change of the user receiver (Δx, Δy, Δz,) T , clock error δt u , Zhongpiao The state quantity to be solved is composed of , and Δy is the deviation between the observed value and the calculated value.

[0133] P0 is the initial state, including the initial position, clock error and clock drift of the user receiver, and P* is the new state obtained after iterative calculation.

[0134] (5) The Monte Carlo method is used to evaluate the positioning accuracy of each grid point in the target area. The positioning equation in step (4) is used to perform 100 loop positioning calculations on each location point, and the average of the 100 positioning results is calculated as the final positioning result:

[0135]

[0136] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0137] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for evaluating the positioning accuracy of a single low-orbit satellite by using a hybrid pseudorange and Doppler measurement, characterized in that Here are the steps: (1) At the set positioning time T k Within the sampling interval Δt, determine the satellite measurement data ρ k 、f k , k = 1, ..., n, and determine the number of sampling points Calculate the theoretical pseudorange measurement value ρ0 and the pseudorange observation value ρ at each sampling point k ; (2) Based on step (1), calculate the Doppler theoretical measurement value f0 and the Doppler observation value f k ; (3) Construct hybrid measurement observation equation based on pseudorange and Doppler; (4) Calculate the user position and clock error based on the pseudorange and Doppler measurement accuracy generated by the single random number of pseudorange and Doppler calculation; (5) Based on the mission data, the Monte Carlo method is used to evaluate the positioning accuracy of each grid point in the coverage area of ​​a single low-orbit satellite that follows a Gaussian white noise distribution; The observation equation at different sampling times 1, ...k, ...n is specifically: In the formula, is the pseudorange calculated value at the first sampling moment, (x s1 ,y s1 ,z s1 ) is the satellite position at the first sampling moment, is the calculated pseudorange value at the nth sampling moment, (x sn ,y sn ,z sn ) is the satellite position at the nth sampling moment, The last iteration result of the user receiver position. The first calculation is the actual position plus a 5km deviation. The last iteration result of the receiver clock error. The first calculation is the set initial clock error plus 10m. The last iteration result of the user receiver clock drift. The first calculation is the set value plus 1m / s. is the user receiver clock drift; f * is the frequency of the original transmitted signal; is the Doppler calculation value at the first sampling moment, is the Doppler calculation value at the nth sampling moment; In step (4), the specific method for calculating the user position and clock difference is: (4-1) At a preset user position, Taylor expansion is performed on the pseudorange observation equation and the Doppler observation equation; (4-2) Calculate the change in user position and determine the user position and clock error.

2. The method for evaluating the positioning accuracy of a single low-orbit satellite by pseudorange and Doppler hybrid measurement according to claim 1, characterized in that: The specific calculation method of the theoretical pseudo-range measurement value ρ0 at a single sampling moment is: In the formula, (x s ,y s ,z s ) is the satellite position at that moment, (x, y, z) is the preset user's real position, c is the speed of light, δt u0 is the initial clock difference of the user receiver, k is the number of sampling points this time; Pseudorange observation value ρ k The specific calculation method is: r k =ρ0+σ ρ ·rand(1,n) In the formula, σ ρ is a pseudo-range single random number.

3. The method for evaluating the positioning accuracy of a single low-orbit satellite by pseudorange and Doppler hybrid measurement according to claim 1, characterized in that: The calculation method of the Doppler theoretical measurement value f0 at a single sampling moment is as follows: Where f0 is the signal frequency received by the user receiver; (x s ,y s ,z s ) is the satellite position at that moment; v = [v x , v y , v z ] is the speed of the satellite relative to the user at that moment, which is the satellite speed for static or low-dynamic users; f k =f0+σ f ·edge(1,n) In the formula, σ f Single random number for Doppler measurement.

4. The method for evaluating the positioning accuracy of a single low-orbit satellite by pseudorange and Doppler hybrid measurement according to claim 1, characterized in that: In step (4-1), the pseudorange observation equation and Doppler observation equation after Taylor expansion are specifically: In the formula, ρ k is the pseudorange observation value, is the result of the last iteration of the pseudorange calculation value, is the last iteration result of the user receiver position, (x sk ,y sk ,z sk ) is the position of the satellite at the sampling time; In the formula, (v xk ,v yk ,v zk ) is the speed of the satellite at the sampling moment.

5. The method for evaluating the positioning accuracy of a single low-orbit satellite by hybrid pseudorange and Doppler measurement according to claim 1, characterized in that: In step (4-2), the method for calculating the user position change is: ΔX=(H T H) -1 H T ·Δy H=[G1,G2] T Δy=HΔx+εΔy=[Δρ,Δf] T Where G1 and G2 are pseudorange and Doppler measurement matrices, H is the combined measurement matrix, and ΔX is the state quantity to be solved, including the three-dimensional position change of the user receiver (Δx, Δy, Δz,) T , clock error δt u , Zhongpiao The state quantity to be solved is composed of , and Δy is the deviation between the observed value and the calculated value.

6. The method for evaluating the positioning accuracy of a single low-orbit satellite by using a pseudorange and Doppler hybrid measurement according to claim 5, characterized in that: In step (4-2), the calculation method of user position and clock error and clock drift is: P * =P0+ΔX Where P0 is the initial state, including the initial position, clock error, and clock drift of the user receiver, and P * is the new state quantity obtained after iterative calculation.

7. The method for evaluating the positioning accuracy of a single low-orbit satellite by using a pseudorange and Doppler hybrid measurement according to claim 1, characterized in that: In the step (5), the cyclic positioning calculation of step (4) is performed for each grid point for a specified number of times, and the calculated user position mean is used as the final positioning result, and the positioning accuracy is evaluated based on the obtained positioning result.

8. The method for evaluating the positioning accuracy of a single low-orbit satellite by using a pseudorange and Doppler hybrid measurement according to claim 7, characterized in that: The formula for calculating the mean user position is: Where 100 is the specified number of loop positioning.

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