Satellite navigation double difference positioning method considering pseudo-range deviation

Abstract

The application discloses a satellite navigation double-difference positioning method considering pseudo-range deviation, which calibrates pseudo-range deviation by using double-difference method of juxtaposed receivers, and then compensates and corrects the pseudo-range deviation term in the double-difference result by the calibration value. Compared with the traditional double-difference positioning algorithm, the application further corrects the error caused by satellite signal distortion and distortion in the double-difference system, so that the ordinary user can obtain better positioning precision service when using the pseudo-range double-difference positioning. Based on a large amount of measured data analysis, the improved double-difference positioning algorithm considering pseudo-range deviation can significantly improve the positioning precision in the east, north and sky directions compared with the traditional double-difference positioning algorithm.

Description

Technical Field

[0001] The present invention belongs to the field of navigation and positioning, and in particular relates to a satellite navigation double-difference positioning method taking pseudorange deviation into consideration. Background Art

[0002] The Global Navigation Satellite System (GNSS) has been widely used in countries around the world due to its powerful functions. GNSS positioning methods can be simply divided into two categories: direct positioning and relative positioning. Differential positioning in relative positioning has always been one of the research focuses. Differential positioning can be divided into three categories: single difference, double difference, and triple difference. Among them, single difference and double difference are the most widely used. For high-precision users, the existing differential system can eliminate error sources such as satellite clock error and receiver clock error, and can effectively reduce the influence of the ionosphere and troposphere on pseudorange measurements when the receiver is arranged with a zero / short baseline. However, the pseudorange bias in the residual error term of the differential system cannot be eliminated.

[0003] GNSS pseudorange bias is caused by distortion in the downlink navigation signals from individual satellites, closely related to the non-ideal characteristics of the navigation satellite payload and transmitter components. Specifically, receivers with different technical parameters produce a constant term with varying magnitude and sign in the pseudorange measurements of navigation signals. Subsequent research has shown that pseudorange bias exists even when receivers measure signals from healthy GNSS satellites, and that the distortion of navigation signals from individual satellites is inconsistent.

[0004] GPS was the first to discover pseudorange bias and provided recommendations for mitigating its effects in its Inter-GPS (Interface Directive) (ICD) document. Unfortunately, research on pseudorange bias in my country's Beidou satellite navigation system is less in-depth, and the ICD document does not yet provide applicable values ​​to mitigate it. Currently, the mainstream approach focuses on modifying receiver configuration parameters, specifically reducing the differences in parameters such as the correlation interval and front-end bandwidth between user and reference receivers to minimize pseudorange bias.

[0005] Pseudorange bias cannot be directly obtained by a single receiver. It requires two receivers arranged in a zero / short baseline to observe two satellites simultaneously. The pseudorange measurement values ​​are then double-differenced to obtain the bias. This method is called the juxtaposed receiver double-difference method. Therefore, the pseudorange bias is a relative value and will have an adverse effect on the positioning accuracy of the double-difference system. If the pseudorange bias between different satellites can be calibrated using the receiver pseudorange measurement values, and then the pseudorange bias is compensated and corrected during the double-difference calculation process, the positioning accuracy of the double-difference system can be improved. Summary of the Invention

[0006] Pseudorange bias, an error caused by distortion in downlink signals from navigation satellites, negatively impacts the positioning accuracy of differential systems, thereby degrading GNSS system performance. The present invention aims to provide a satellite navigation double-difference positioning method that accounts for pseudorange bias, thereby overcoming the problems of existing technologies.

[0007] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0008] A satellite navigation double-difference positioning method taking into account pseudorange bias, comprising:

[0009] Place the user receiver and the reference receiver in zero baseline or short baseline state to ensure that the two receivers can receive navigation satellite signals in the same frequency band;

[0010] Among all navigation satellites searched in the selected frequency band, a geostationary orbit satellite or an inclined geosynchronous orbit satellite whose elevation angle is greater than the elevation angle threshold during observation is selected as a reference satellite;

[0011] For the pseudorange measurement expressions of the reference receiver and the user receiver for the reference satellite and a certain satellite, the pseudorange measurement values ​​of the user receiver are subtracted from the pseudorange measurement values ​​of the reference receiver, respectively, to obtain the single difference of the pseudorange measurements of the user receiver and the reference receiver for the reference satellite and a certain satellite at the same time and in the same frequency band;

[0012] The single difference value of the pseudorange measurement of the user receiver and the reference receiver for the reference satellite is used as the single difference reference value, and the single difference value of the pseudorange measurement is further differentiated to obtain the double difference measurement value of a certain satellite in the user receiver and the reference receiver relative to the reference satellite, which includes the pseudorange deviation;

[0013] In the case of short baseline, the pseudorange bias considering thermal noise can be obtained by subtracting the double difference of the geometric distance between the reference satellite and a certain satellite from the double difference measurement value;

[0014] In the double-difference positioning algorithm, the pseudorange bias is compensated. For the double-difference measurement value calculated for each satellite except the reference satellite, the corresponding pseudorange bias considering thermal noise is subtracted from it to obtain the corrected pseudorange double difference value.

[0015] The matrix equation is constructed using the corrected pseudorange double difference and the unit observation vector of the reference satellite at the reference receiver position to solve the baseline vector between the user receiver and the reference receiver after correcting the pseudorange bias.

[0016] The three-dimensional position of the user receiver can be obtained by adding the baseline vector to the three-dimensional coordinates of the reference receiver.

[0017] Furthermore, the elevation angle threshold is 30°; if there are multiple geostationary orbit satellites or inclined geosynchronous orbit satellites with elevation angles greater than the threshold, the one with the largest elevation angle is selected as the reference satellite.

[0018] Furthermore, the pseudorange measurement values ​​of the reference receiver B and the user receiver u for the reference satellite i and satellite j are expressed as follows:

[0019]

[0020]

[0021] in represents the pseudorange measurement value of receiver r to satellite i, represents the straight-line distance between receiver r and satellite i, δt r represents the clock error of the receiver r, δt (i) represents the clock error of satellite i, Indicates the ionospheric delay and tropospheric delay when the receiver r measures the pseudorange of satellite i, bias r represents the pseudorange deviation of receiver r, represents the thermal noise when receiver r measures the pseudorange of satellite i; r = B,u; B represents the reference receiver and u represents the user receiver.

[0022] Furthermore, the single difference of pseudo-range measurements of the user receiver and the reference receiver for the reference satellite i and a certain satellite j at the same time and in the same frequency band is expressed as follows:

[0023]

[0024]

[0025] in, δ uB =δ u -δ B ,

[0026] The difference between the tropospheric and ionospheric delays in the pseudorange measurements of the user receiver u and the reference receiver B for the same satellite when the user receiver u and the reference receiver B are arranged as a zero / short baseline can be considered to be approximately equal, so the above formula can be simplified to:

[0027]

[0028]

[0029] Straight-line distance difference under zero baseline Can also be considered as 0.

[0030] Furthermore, the double-difference measurement value of satellite j relative to reference satellite i, including pseudorange deviation, between user receiver u and reference receiver B is expressed as:

[0031]

[0032] in,

[0033] Furthermore, in the case of short baseline, the double difference measurement is used Subtract the double difference of the geometric distance between reference satellite i and satellite j The pseudorange deviation considering thermal noise can be obtained:

[0034]

[0035] Furthermore, for satellite j, its corrected pseudorange double difference is expressed as:

[0036]

[0037] Furthermore, all the corrected pseudorange double differences Substituting into the matrix equation (8), we can solve the baseline vector b between the user receiver u and the reference receiver B after correcting the pseudorange bias: ur_corr :

[0038]

[0039] in, represents the unit observation vector of reference satellite i at the reference receiver B, and the superscript T indicates transpose.

[0040] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, the satellite navigation double-difference positioning method taking into account pseudorange deviation is implemented.

[0041] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the satellite navigation double-difference positioning method taking into account pseudorange deviation is implemented.

[0042] Compared with the prior art, the present invention has the following technical features:

[0043] Compared to traditional double-difference positioning algorithms, the double-difference positioning method proposed in this paper, which accounts for pseudorange deviation, further corrects errors introduced by satellite signal distortion in double-difference systems, enabling users to achieve superior positioning accuracy when using pseudorange double-difference positioning. Analysis of extensive field data indicates that this improved double-difference positioning algorithm, which accounts for pseudorange deviation, significantly improves positioning accuracy in the east, north, and sky directions compared to traditional double-difference positioning algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a schematic diagram of the principle of the double-difference method with collocated receivers;

[0045] Figure 2 Statistical graph of pseudorange deviations of satellites C08, C11, C12, C13, and C23 on the 258th day (September 14) of the mid-year accumulation day in an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram of the double-difference positioning accuracy (east, north, and sky directions) during the period when the C08, C11, C12, C13, and C23 satellites are visible together on the 258th day of the mid-year accumulation day in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] This invention proposes a satellite navigation double-difference positioning method that takes pseudorange bias into account, compensating for pseudorange bias in the double-difference positioning algorithm. The overall method can be divided into two steps: ① calibrating pseudorange bias using the double-difference method with collocated receivers; ② using the calibration value to compensate for the pseudorange bias term in the double-difference result. The technical solution of this invention is as follows:

[0048] Step 1: Place the user receiver u and the reference receiver B in a zero baseline or short baseline state. Ensure that the two receivers can receive navigation satellite signals in the same frequency band.

[0049] Step 2: Select a geostationary orbit (GEO) satellite or an inclined geosynchronous orbit (IGSO) satellite with an elevation angle greater than the elevation angle threshold during observation from among all the M navigation satellites searched in the selected frequency band as a reference satellite i; let j be any satellite among the remaining M-1 satellites.

[0050] In this solution, the elevation angle threshold is 30°; if there are multiple GEO / IGSO satellites with elevation angles greater than the threshold, the one with the largest elevation angle is selected as the reference satellite.

[0051] set up represents the pseudorange measurement value of receiver r to reference satellite i, represents the straight-line distance (geometric distance) between the receiver r and the reference satellite i, δt r represents the clock error of the receiver r, δt (i)represents the clock error of reference satellite i, The bias represents the ionospheric delay and tropospheric delay of the receiver r when measuring the pseudorange of the reference satellite i. r represents the pseudorange deviation of receiver r, represents the thermal noise when receiver r measures the pseudorange of reference satellite i; r = B,u; B represents the reference receiver and u represents the user receiver.

[0052] The pseudorange measurements of satellites i and j by reference receiver B and user receiver u are expressed as follows:

[0053]

[0054]

[0055] Step 3: For the pseudo-range measurement expressions of reference receiver B and user receiver u for reference satellite i and satellite j, the pseudo-range measurement values ​​of user receiver u are used in the above formulas (1) and (2): Subtract the pseudorange measurement value of reference receiver B respectively The pseudo-range measurement single difference of user receiver u and reference receiver B for reference satellite i and satellite j at the same time and in the same frequency band can be obtained: and

[0056]

[0057]

[0058] in, δ uB =δ u -δ B , n=i,j.

[0059] The difference between the tropospheric and ionospheric delays in the pseudorange measurements of the user receiver u and the reference receiver B for the same satellite when the user receiver u and the reference receiver B are arranged as a zero / short baseline can be considered to be approximately equal, so the above formula can be simplified to:

[0060]

[0061]

[0062] Straight-line distance difference under zero baseline It can also be approximated to 0.

[0063] Step 4: Take the single difference value of pseudo-range measurement between user receiver u and reference receiver B for reference satellite i (i.e. the result of formula (3)) as the single difference reference value The single difference value obtained in step 3 is further differentiated, that is, the difference between formula (4) and formula (3) is used to obtain the double difference measurement value of the user receiver u and the reference receiver B relative to the reference satellite i, which includes the pseudorange bias:

[0064]

[0065] in,

[0066] Step 5: Using double difference measurements in case of short baseline Subtract the double difference of the geometric distance between reference satellite i and satellite j The pseudorange deviation considering thermal noise can be obtained:

[0067]

[0068] Step 6: At the same time, use the same method to calculate the double difference measurement values ​​of the remaining satellites k (k∈M, k≠i,j) relative to the reference satellite i Geometric distance double difference Get the corresponding pseudorange deviation considering thermal noise

[0069] Step 7: Compensate for the pseudorange bias in the double-difference positioning algorithm; for the double-difference measurement values ​​calculated for each satellite except the reference satellite i, subtract the corresponding pseudorange bias considering thermal noise from it to obtain the corrected pseudorange double difference value.

[0070] Taking satellite j as an example, the difference between formula (5) and formula (6) is used to obtain the corrected pseudorange double difference corresponding to satellite j:

[0071]

[0072] Step 8: All corrected pseudorange double differences Substituting into the matrix equation (8), we can solve the baseline vector b between the user receiver u and the reference receiver B after correcting the pseudorange bias: ur_corr :

[0073]

[0074] in, represents the unit observation vector of reference satellite i at the reference receiver B, which is solved based on the receiver position and the satellite position. The superscript T indicates transpose.

[0075] Step 9: Add the baseline vector b to the x, y, z coordinates of the reference receiver B. ur_corr The three-dimensional position of the user receiver u can be obtained.

[0076] Example:

[0077] The pseudorange bias between the two different types of receivers was calibrated and corrected based on the measured data of the LEICA GR50 receiver at the WTZR base station and the JAVAD TRE_3 receiver at the WTZZ base station on September 14 (the 258th day of the year).

[0078] LEICA GR50 was selected as the reference receiver and JAVAD TRE_3 as the user receiver. The baseline distance between the two receivers was 3.6 meters, which met the prerequisite of zero / short baseline collocation.

[0079] The method consists of two steps: ① using the double-difference method of juxtaposed receivers to calibrate the pseudorange deviation between the two receivers; ② using the pseudorange deviation calibration value to compensate and correct the double-difference result.

[0080] The pseudorange measurements of satellites i and j by the reference receiver LEICA GR5 and the user receiver JAVAD TRE_3 are expressed as follows:

[0081]

[0082]

[0083] The parameters in the formula are consistent with those described in the summary of the invention and will not be repeated here.

[0084] During the observation process, BDS GEO satellite C05, visible throughout the day, was selected as a reference satellite. The pseudorange deviations of five BeiDou navigation system B1-band satellites, C08, C11, C12, C13, and C23, relative to C05 were calibrated. The calibration results were used as error corrections to compensate for the double-difference calculations of these five satellites.

[0085] Step 1: Set the user receiver JAVAD TRE_3 and the reference receiver LEICA GR50 to zero / short baseline mode. Ensure that both receivers can receive navigation satellite signals in the B1 band.

[0086] Step 2: Select a satellite that is at a high elevation angle and visible for a long time during observation as a reference satellite. In this embodiment, the C05 satellite that is visible all day on the 258th day of the year is specified as the reference satellite.

[0087] Step 3: Subtract the pseudorange measurement value of the reference receiver LEICA GR50 from the pseudorange measurement value of the user receiver JAVAD TRE_3 from the pseudorange measurement value of the reference receiver LEICA GR50 in the above formulas (1) and (2) to obtain the single difference of the pseudorange measurement between the user receiver JAVAD TRE_3 and the reference receiver LEICAGR50 in the B1 frequency band and the reference satellite i (C05) and other satellites at the same time:

[0088]

[0089]

[0090] When the receivers are arranged as short baselines, the tropospheric and ionospheric delays between the two receivers can be considered to be approximately equal, so the above formula can be simplified to:

[0091]

[0092]

[0093] Step 4: Take the single-difference pseudorange measurement values ​​of the user receiver and the reference receiver for reference satellite i (C05) (i.e., the calculation result of formula (2)) as the reference value, and further perform a differential operation on the single difference value obtained in step 3, that is, use formula (3) to subtract formula (2), and the double-difference measurement values ​​of satellites C08, C11, C12, C13, and C23 relative to the reference satellite C05 in the reference receiver LEICA GR50 and the user receiver JAVAD TRE_3, including pseudorange biases, can be obtained:

[0094]

[0095] Step 5: Subtract the double-difference geometric distance from the double-difference measurement value of each satellite on September 14 (the 258th day of the year) Get the pseudorange deviation values ​​of satellites C08, C11, C12, C13 and C23 relative to the reference star C05:

[0096]

[0097] Step 6: Compensate for the pseudorange deviation in the double-difference positioning algorithm by subtracting the pseudorange deviation from the calculated double-difference measurement value. That is, the difference between formula (5) and formula (6) is used to obtain the corrected double-difference value:

[0098]

[0099] Step 7: Use formula (7) to correct the double difference of pseudoranges between satellites C08, C11, C12, C13 and C23 and reference satellite C05 and insert them into matrix equation (8) to obtain the baseline vector b between the user receiver and the reference receiver after correcting the pseudorange bias. JL_corr :

[0100]

[0101] represents the unit observation vector of the position of satellite j at the reference receiver LEICA GR50.

[0102] Step 8: Add the baseline vector b to the x, y, z coordinates of the reference receiver LEICA GR50 JL_corr The three-dimensional position of the user receiver JAVAD TRE_3 can be obtained.

[0103] In this embodiment, two different receivers, the WTZR base station LEICA GR50 and the WTZZ base station JAVAD TRE_3, are used to measure the pseudorange data of the BeiDou navigation system B1 band C05, C08, C11, C12, C13 and C23 satellites on the 258th day of the year, and the improvement effect of the double-difference system positioning accuracy before and after the pseudorange bias correction is analyzed.

[0104] In this example, the pseudorange deviations of the C08, C11, C12, C13, and C23 satellites were calibrated and corrected using the C05 satellite as the reference satellite and the LEICA GR50 as the reference receiver. Comparing the positioning accuracy before and after pseudorange deviation correction, the double-difference positioning accuracy of the user receiver JAVAD TRE_3 using the C08, C11, C12, C13, and C23 satellites improved from 0.5657m, 1.0843m, and 1.1268m in the east, north, and sky directions, respectively, to a level close to zero. This significant improvement in positioning accuracy was achieved in all three directions.

[0105] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A satellite navigation double-difference positioning method taking into account pseudorange deviation, characterized in that: include: Place the user receiver and the reference receiver in zero baseline or short baseline state to ensure that the two receivers can receive navigation satellite signals in the same frequency band; Among all navigation satellites searched in the selected frequency band, a geostationary orbit satellite or an inclined geosynchronous orbit satellite whose elevation angle is greater than the elevation angle threshold during observation is selected as a reference satellite; For the pseudorange measurement expressions of the reference receiver and the user receiver for the reference satellite and a certain satellite, the pseudorange measurement values ​​of the user receiver for the reference satellite and a certain satellite are respectively subtracted from the pseudorange measurement values ​​of the reference receiver for the reference satellite and a certain satellite. This yields the single difference of the pseudorange measurements of the user receiver and the reference receiver for the reference satellite and a certain satellite at the same time and frequency band. The single difference value of the pseudorange measurement of the user receiver and the reference receiver for the reference satellite is used as the single difference reference value, and the single difference value of the pseudorange measurement is further differentiated to obtain the double difference measurement value of a certain satellite in the user receiver and the reference receiver relative to the reference satellite, which includes the pseudorange deviation; In the case of short baseline, the pseudorange bias considering thermal noise can be obtained by subtracting the double difference of the geometric distance between the reference satellite and a certain satellite from the double difference measurement value; In the double-difference positioning algorithm, the pseudorange bias is compensated. For the double-difference measurement value calculated for each satellite except the reference satellite, the corresponding pseudorange bias considering thermal noise is subtracted from it to obtain the corrected pseudorange double difference value. The matrix equation is constructed using the corrected pseudorange double difference and the unit observation vector of the reference satellite at the reference receiver position to solve the baseline vector between the user receiver and the reference receiver after correcting the pseudorange bias. The three-dimensional position of the user receiver can be obtained by adding the baseline vector to the three-dimensional coordinates of the reference receiver.

2. The satellite navigation double-difference positioning method taking into account pseudorange deviation according to claim 1, characterized in that: The elevation angle threshold is 30°; if there are multiple geostationary orbit satellites or inclined geosynchronous orbit satellites with elevation angles greater than the threshold, the one with the largest elevation angle is selected as the reference satellite.

3. The satellite navigation double-difference positioning method taking into account pseudorange deviation according to claim 1, characterized in that: Reference receiver B and user receivers u For reference satellites i and satellite j The pseudorange measurement expression is as follows: (1) (2) in Indicates receiver r Satellite i The pseudorange measurement value of Indicates receiver r With satellite i The straight-line distance between Indicates receiver r The clock difference, Indicates satellite i The clock difference, Indicates receiver r Satellite i Ionospheric delay and tropospheric delay during pseudorange measurement, Indicates receiver r Satellite i The pseudorange deviation, Indicates receiver r Measurement satellite i Thermal noise during pseudo-range; ; B represents the reference receiver, u Represents a user receiver.

4. The satellite navigation double-difference positioning method taking into account pseudorange deviation according to claim 3, characterized in that: The user receiver and the reference receiver are targeting the reference satellite at the same time and in the same frequency band. i and a satellite j The single difference of pseudorange measurement is expressed as follows: in, = , = , = , = , = , = ; ; In the user receiver u With reference receiver B In the case of zero / short baseline arrangement, the user receiver u With reference receiver B The difference between the tropospheric and ionospheric delays in pseudorange measurements for the same satellite 、 can be considered to be approximately equal, so the above formula can be simplified to: (3) (4) Straight-line distance difference under zero baseline Also set to 0.

5. The satellite navigation double-difference positioning method taking into account pseudorange deviation according to claim 4, characterized in that: User Receiver u With reference receiver B Medium Satellite j Relative to the reference star i The double difference measurement value including pseudorange bias is expressed as: (5) in, = - , = - , = - .

6. The satellite navigation double-difference positioning method taking into account pseudorange deviation according to claim 4, characterized in that: In the case of short baseline, double difference measurement is used Subtract reference satellite i With satellite j Double difference of geometric distance between The pseudorange deviation considering thermal noise can be obtained: (6)。 7. The satellite navigation double-difference positioning method taking into account pseudorange deviation according to claim 6, characterized in that: For satellites j , and the corrected pseudorange double difference is expressed as: (7)。 8. The satellite navigation double-difference positioning method taking into account pseudorange deviation according to claim 7, characterized in that: All corrected pseudorange double differences 、 … Substituted into the matrix equation (8), the user receiver after correcting the pseudorange bias can be solved as u With reference receiver B The baseline vector between b ur_corr : (8) in, Indicates the reference satellite i At the reference receiver B The unit observation vector of the position, superscript T Indicates transpose.

9. A terminal device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, it implements the satellite navigation double-difference positioning method taking into account pseudorange deviation according to any one of claims 1-8.

10. A computer-readable storage medium storing a computer program; wherein: When the computer program is executed by a processor, the satellite navigation double-difference positioning method taking into account pseudorange deviation according to any one of claims 1 to 8 is implemented.

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