A Beidou four-frequency combination positioning solution method under short baseline

Abstract

The present invention discloses a Beidou four-frequency combination positioning solution method under a short baseline. Aiming at the problem that the dual-frequency narrow lane ambiguity is sometimes difficult to fix, this paper proposes a four-frequency dual narrow lane combination model. By combining two independent and unrelated dual-frequency narrow lane observation equations, redundant observation quantities are added, thereby improving the efficiency and reliability of ambiguity resolution. First, the B1C and B2a frequencies and the other B1I and B3I frequencies are selected for dual-frequency narrow lane combination using combination coefficients of (1, 0, 0, 1) and (0, 1, 1, 0), and then the two dual-frequency narrow lane equations are combined. When there are n+1 satellites in an epoch, each dual-frequency narrow lane combination can list n pseudo-range observation equations and n carrier phase observation equations respectively, and there are only 2n+3 unknowns in total. All equations can be combined to solve a single epoch. Finally, the solution result is compared with the true value of the coordinates to perform accuracy assessment.

Description

Technical Field

[0001] The present invention belongs to the field of high-precision positioning, and in particular relates to a Beidou four-frequency combination positioning solution method under a short baseline. Background Art

[0002] At present, various satellite navigation systems are constantly being built and improved. my country's BeiDou-3 global satellite navigation system also announced the successful networking in June 2020 and provided multi-frequency data services. With the gradual increase in the types of signal spectrum in satellite data, multi-frequency combined observation is one of the hot directions for the development of navigation and positioning technology. Studies have shown that through the linear combination of multi-frequency data, combined observation values ​​with advantages such as long wavelength, weak ionospheric delay, and small observation noise can be obtained, which is of great significance for improving the efficiency of ambiguity fixation and improving positioning accuracy.

[0003] Many scholars at home and abroad have conducted certain research on multi-frequency combination positioning. At present, mature theoretical and practical results have been achieved in the three-frequency combination method, demonstrating the feasibility of multi-frequency combination solution, and indicating that the combination of multi-frequency observation values ​​plays a key role in fixing ambiguity and improving positioning accuracy. However, there is still a lot of room for exploration in the research of multi-frequency combination methods of four frequencies and above. Therefore, the present invention proposes a Beidou four-frequency combination positioning solution method under a short baseline, which effectively utilizes the multi-frequency observation data of Beidou satellites, thereby improving the efficiency and accuracy of positioning to a certain extent, and has good research and application prospects in the direction of high-precision positioning. Summary of the invention

[0004] Purpose of the invention: In view of the problem that dual-frequency narrow-lane ambiguity is sometimes difficult to fix, the present invention proposes a four-frequency dual-narrow-lane combination model, which increases redundant observations by combining two independent and unrelated dual-frequency narrow-lane observation equations, thereby improving the efficiency and reliability of ambiguity resolution.

[0005] Technical solution: To achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a Beidou four-frequency combination positioning solution method under a short baseline, comprising the following steps:

[0006] (1) Perform data preprocessing on the acquired Beidou four-frequency raw observation data, remove gross errors and calculate the instantaneous coordinates of the satellites. Then, perform dual-frequency narrow-lane combination on the B1C and B2a frequencies, and perform dual-frequency narrow-lane combination on the B1I and B3I frequencies to obtain the corresponding two sets of double-difference pseudoranges and carrier phase observation equations.

[0007] (2) Using the ambiguity as a parameter to construct a Kalman filter, the Kalman filter is used to obtain the integer ambiguity floating point solution and covariance matrix;

[0008] (3) The LAMBDA algorithm is used to calculate the ambiguity fixed solution, and the significance level Ratio value given in the ambiguity test is used as the test standard to evaluate the solution result. Finally, the ambiguity fixed solution is back-substituted to obtain the precise coordinate value.

[0009] Preferably, in step (1), dual-frequency narrow-lane combination is performed on B1C and B2a frequencies, and dual-frequency narrow-lane combination is performed on B1I and B3I frequencies, to obtain two corresponding sets of double-difference pseudorange and carrier phase observation equations, and the specific steps are as follows:

[0010] First, the combination coefficient (1, 0, 0, 1) is used to select B1C and B2a frequencies for dual-frequency narrow lane combination. Assuming the narrow lane combination of these two frequencies is NL1, the first set of double-difference pseudorange and carrier phase observation equations are obtained as follows:

[0011]

[0012] Then, the B1I and B3I frequencies are combined into a dual-frequency narrow lane combination using (0, 1, 1, 0). Assuming the narrow lane combination of these two frequencies is NL2, the second set of double-difference pseudorange and carrier phase observation equations are obtained as follows:

[0013]

[0014] In the formula, represents the double difference operator, i = 1, 2, The difference between the difference in pseudorange observations from the differential satellite to the mobile station and the reference station and the difference in pseudorange observations from the reference satellite to the mobile station and the reference station corresponding to NLi, The difference between the difference in distance from the differential satellite to the mobile station and the reference station and the difference in distance from the reference satellite to the mobile station and the reference station, represents the difference between the difference in tropospheric delay from the differential satellite to the rover and the reference station and the difference in tropospheric delay from the reference satellite to the rover and the reference station, represents the difference between the difference in ionospheric delay from the differential satellite to the rover and reference station and the difference in ionospheric delay from the reference satellite to the rover and reference station, represents the difference between the difference in pseudorange observation noise from the differential satellite to the mobile station and the reference station and the difference in pseudorange observation noise from the reference satellite to the mobile station and the reference station, λ NLi Indicates the wavelength of the corresponding frequency carrier after the dual-frequency narrow-lane combination, The difference between the difference in carrier phase observations from the differential satellite to the mobile station and the reference station and the difference in carrier phase observations from the reference satellite to the mobile station and the reference station corresponding to NLi, represents the difference between the difference in ambiguity between the differential satellite and the mobile station and the reference station and the difference in ambiguity between the reference satellite and the mobile station and the reference station corresponding to NLi, It represents the difference between the difference in carrier observation noise from the differential satellite to the mobile station and the reference station and the difference in carrier observation noise from the reference satellite to the mobile station and the reference station.

[0015] Preferably, in step (1), when there are n+1 satellites in one epoch, the dual-frequency narrow lane combination NL1 lists n pseudo-range observation equations and n carrier phase observation equations respectively, and the dual-frequency narrow lane combination NL2 also lists n pseudo-range observation equations and n carrier phase observation equations respectively. There are only 2n+3 unknowns. All equations are combined to solve a single epoch, and the error equation obtained by linearization is:

[0016]

[0017] Among them, V L is the error matrix of the 2n×1-dimensional carrier observation equation, V p is the error matrix of the pseudorange observation equation of 2n×1 dimension, A is the coefficient matrix of the baseline vector of 2n×3 dimension, B is the double difference ambiguity coefficient matrix of 2n×2n dimension, δX, δY, δZ are the three-dimensional coordinate correction values, is a 2n×1 dimensional double difference ambiguity matrix, L L , L P are the constant matrices of the carrier phase and pseudorange observation equations respectively.

[0018] Preferably, in step (2), the double difference ambiguity is used as a parameter to construct a Kalman filter, and the specific steps are as follows:

[0019] Assuming that the number of common-view satellites observed in a certain epoch is n, there are corresponding 3 coordinate correction values ​​and 2n ambiguities to be determined, and 4n observation equations for pseudorange and carrier can be obtained. Therefore, the state vector X of the kth epoch is k and the observation equation coefficient matrix H k Set to:

[0020]

[0021] Where δX, δY, δZ are the three-dimensional coordinate correction values, i = 1, 2, represents the double difference ambiguity to be determined for the nth satellite dual-frequency narrow lane combination NLi, α ni ,β ni ,γ ni are the coefficients of δX, δY, δZ of ​​the n-th satellite dual-frequency narrow lane combination NLi, and λ is the double-difference ambiguity coefficient to be determined consisting of the carrier wavelength;

[0022] Substitute this state vector and observation equation coefficient matrix into the state equation and observation equation of the Kalman filter respectively to construct the Kalman filter.

[0023] Preferably, the specific description of obtaining the precise coordinate value in step (3) is that, based on the integer ambiguity floating point solution and covariance matrix obtained in step (2), the significance level Ratio value given in the ambiguity test is used as the reliability test standard of the ambiguity fixed solution in step (3), and its expression is:

[0024]

[0025] In the formula, σ 1 and σ 2 It represents the residual sum of squares corresponding to the suboptimal and optimal solutions of the ambiguity integer solution; if the Ratio value is greater than the set threshold, the ambiguity is considered to be fixed successfully.

[0026] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0027] The present invention aims at the problem that dual-frequency narrow lane ambiguity is sometimes difficult to fix, and observes that the current positioning solution method that does not fully utilize Beidou four-frequency data is insufficient. By combining two independent and unrelated dual-frequency narrow lane observation equations, a Beidou four-frequency combined positioning solution method under a short baseline is proposed. This method makes full use of the linear combination of multi-frequency data, and can obtain a combined observation value with the advantages of long wavelength, weak ionospheric delay, and small observation noise, which can effectively improve the ambiguity fixing efficiency and the positioning accuracy, and improve the accuracy of positioning solution to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a flow chart of the Beidou four-frequency combination positioning solution method under short baseline;

[0029] Figure 2 The coordinate error statistics of the baseline SJTH-JSJN obtained by the BDS single-frequency method, where (a) is the N direction error, (b) is the E direction error, and (c) is the U direction error;

[0030] Figure 3 The coordinate error statistics of the baseline SJTH-JSJN obtained by the BDS-3 three-frequency TCAR method, where (a) is the N direction error, (b) is the E direction error, and (c) is the U direction error;

[0031] Figure 4 The coordinate error statistics of the baseline SJTH-JSJN obtained by the BDS-3 four-frequency method, where (a) is the N direction error, (b) is the E direction error, and (c) is the U direction error;

[0032] Figure 5The coordinate error statistics of the baseline Coor1650-JSJN obtained by the BDS single-frequency method, where (a) is the N direction error, (b) is the E direction error, and (c) is the U direction error;

[0033] Figure 6 The coordinate error statistics of the baseline Coor1650-JSJN obtained by the BDS-3 three-frequency TCAR method, where (a) is the N direction error, (b) is the E direction error, and (c) is the U direction error;

[0034] Figure 7 The coordinate error statistics of the baseline Coor1650-JSJN obtained by the BDS-3 four-frequency method, where (a) is the N direction error, (b) is the E direction error, and (c) is the U direction error;

[0035] Figure 8 The standard deviation and root mean square error statistics of the coordinate results are obtained for the baseline SJTH-JSJN by using the BDS single-frequency method, the BDS-3 three-frequency TCAR method, and the BDS-3 four-frequency method, where (a) is the standard deviation and (b) is the root mean square error;

[0036] Fig. 9 The standard deviation and root mean square error statistics of the coordinate results are obtained for the baseline Coor1650-JSJN by using the BDS single-frequency method, BDS-3 triple-frequency TCAR method and BDS-3 quad-frequency method, where (a) is the standard deviation and (b) is the root mean square error. DETAILED DESCRIPTION

[0037] The present invention will be further described below in conjunction with the accompanying drawings.

[0038] like Figure 1 As shown, an embodiment of the present invention discloses a Beidou four-frequency combined positioning and solving method under a short baseline. First, a data preprocessing operation is performed on the Beidou four-frequency original observation data to eliminate gross errors and calculate the instantaneous coordinates of the satellite. The four-frequency observation data are combined in pairs to form two groups of independent and unrelated dual-frequency narrow lane observation values. The double difference observation model is used to obtain the corresponding pseudorange and carrier double difference observation equations; secondly, a Kalman filter with attached parameters is used to perform multi-epoch processing to obtain the integer ambiguity floating point solution and covariance matrix; finally, the integer ambiguity fixed solution is calculated according to the LAMBDA algorithm and back-substituted into the original carrier pseudorange narrow lane combination double difference equation to obtain the precise coordinates of the current position.

[0039] The above method comprises the following specific steps:

[0040] Step 1) Perform dual-frequency narrow-lane combination on B1C and B2a frequencies, and perform dual-frequency narrow-lane combination on B1I and B3I frequencies to obtain two corresponding sets of double-difference pseudorange and carrier phase observation equations. The specific steps are as follows:

[0041] First, the combination coefficient (1, 0, 0, 1) is used to select B1C and B2a frequencies for dual-frequency narrow lane combination. Assuming the narrow lane combination of these two frequencies is NL1, the first set of double-difference pseudorange and carrier phase observation equations are obtained as follows:

[0042]

[0043] Then, the B1I and B3I frequencies are combined into a dual-frequency narrow lane combination using (0, 1, 1, 0). Assuming the narrow lane combination of these two frequencies is NL2, the second set of double-difference pseudorange and carrier phase observation equations are obtained as follows:

[0044]

[0045] In the formula, represents the double difference operator, i = 1, 2, The difference between the difference in pseudorange observations from the differential satellite to the mobile station and the reference station and the difference in pseudorange observations from the reference satellite to the mobile station and the reference station corresponding to NLi, The difference between the difference in distance from the differential satellite to the mobile station and the reference station and the difference in distance from the reference satellite to the mobile station and the reference station, represents the difference between the difference in tropospheric delay from the differential satellite to the rover and the reference station and the difference in tropospheric delay from the reference satellite to the rover and the reference station, represents the difference between the difference in ionospheric delay from the differential satellite to the rover and reference station and the difference in ionospheric delay from the reference satellite to the rover and reference station, represents the difference between the difference in pseudorange observation noise from the differential satellite to the mobile station and the reference station and the difference in pseudorange observation noise from the reference satellite to the mobile station and the reference station, λ NLi Indicates the wavelength of the corresponding frequency carrier after the dual-frequency narrow-lane combination, The difference between the difference in carrier phase observations from the differential satellite to the mobile station and the reference station and the difference in carrier phase observations from the reference satellite to the mobile station and the reference station corresponding to NLi, represents the difference between the difference in ambiguity between the differential satellite and the mobile station and the reference station and the difference in ambiguity between the reference satellite and the mobile station and the reference station corresponding to NLi, It represents the difference between the difference in carrier observation noise from the differential satellite to the mobile station and the reference station and the difference in carrier observation noise from the reference satellite to the mobile station and the reference station.

[0046] In step 1), when there are n+1 satellites in one epoch, the NL1 dual-frequency narrow lane combination can list n pseudo-range observation equations and n carrier phase observation equations respectively, and the corresponding NL2 dual-frequency narrow lane combination can also list n pseudo-range observation equations and n carrier phase observation equations. There are only 2n+3 unknowns. All equations can be solved for a single epoch by combining them. The error equation can be obtained by linearization as follows:

[0047]

[0048] Among them, V L is the error matrix of the 2n×1-dimensional carrier observation equation, V p is the error matrix of the pseudorange observation equation of 2n×1 dimension, A is the coefficient matrix of the baseline vector of 2n×3 dimension, B is the double difference ambiguity coefficient matrix of 2n×2n dimension, δX, δY, δZ are the three-dimensional coordinate correction values, is a 2n×1 dimensional double difference ambiguity matrix, L L , L P are the constant matrices of the carrier phase and pseudorange observation equations respectively.

[0049] Step 2) Use the double difference ambiguity as a parameter to construct a Kalman filter. The specific steps are as follows:

[0050] Assuming that the number of common-view satellites observed in a certain epoch is n, there are corresponding 3 coordinate correction values ​​and 2n ambiguities to be determined, and 4n observation equations for pseudorange and carrier can be obtained. Therefore, the state vector X of the kth epoch is k and the observation equation coefficient matrix H k Set to:

[0051]

[0052] Where δX, δY, δZ are the three-dimensional coordinate correction values, i = 1, 2, represents the double difference ambiguity to be determined for the nth satellite dual-frequency narrow lane combination NLi, α ni ,β ni ,γ ni are the coefficients of δX, δY, δZ of ​​the n-th satellite dual-frequency narrow lane combination NLi, and λ is the double-difference ambiguity coefficient to be determined consisting of the carrier wavelength;

[0053] Substitute this state vector and observation equation coefficient matrix into the state equation and observation equation of the Kalman filter respectively to construct the Kalman filter.

[0054] Step 3) Based on the integer ambiguity floating point solution and covariance matrix obtained in step (2), the significance level Ratio value given in the ambiguity test is used as the reliability test standard of the ambiguity fixed solution in step (3), and its expression is:

[0055]

[0056] In the formula, σ 1 and σ 2 It represents the residual sum of squares corresponding to the suboptimal and optimal solutions of the ambiguity integer solution; if the Ratio value is greater than the set threshold, the ambiguity is considered to be fixed successfully.

[0057] The accuracy verification of the method of the present invention is as follows: two sets of GNSS data are collected by using a receiver in the field, namely the baseline SJTH-JSJN with a length of 17m and the baseline Coor1650-JSJN with a length of 3km; the baseline SJTH-JSJN data observation time is from UTC 00:00:00 to 00:20:00 on January 15, 2021, with a sampling interval of 1s, a total of 1200 epochs of data; the baseline Coor1650-JSJN data observation time is from UTC 08:00:00 to 14:00:00 on June 14, 2021, with a sampling interval of 30s, a total of 720 epochs of data. The two sets of data are processed by three schemes: BDS single-frequency method, BDS-3 three-frequency TCAR method and BDS-3 four-frequency method, and finally the solution results are compared with the true value of the coordinates to analyze their positioning accuracy.

[0058] Figures 2 to 4 The positioning error results obtained by three solution methods for baseline SJTH-JSJN are respectively the BDS single-frequency method, the BDS-3 three-frequency TCAR method and the BDS-3 four-frequency method. The horizontal axis represents the epoch number, the vertical axis represents the coordinate error in each direction, and the coordinate system is the WGS84 coordinate system. It can be seen that in this short baseline, the four-frequency combination method of the present invention has a significant improvement in plane accuracy, and is close to the other two models in the elevation direction.

[0059] Figures 5 to 7 The positioning error results obtained by three solution methods for baseline Coor1650-JSJN, namely, the BDS single-frequency method, the BDS-3 three-frequency TCAR method and the BDS-3 four-frequency method. The horizontal axis represents the epoch number, the vertical axis represents the coordinate error in each direction, and the coordinate system is the WGS84 coordinate system. It can be seen that in this short baseline, the solution results of the three methods can reach about 3mm in the N and E directions and about 7mm in the U direction. Since some epochs of this baseline have insufficient number of satellites receiving four-frequency observations, the calculation results of some epochs have large jumps. However, in this baseline, the positioning effect of the four-frequency combination method is still close to that of the other two models, and is always not weaker than the other two models.

[0060] Figure 8The standard deviation and root mean square error statistics of the baseline SJTH-JSJN, where the horizontal axis is the statistical classification of the east direction, north direction and elevation direction, and the vertical axis represents the difference statistics of each method. As can be seen from the figure, in the baseline SJTH-JSJN, the standard deviations of the three methods are about 1.5mm in the N and E directions, and about 2.5mm in the U direction, among which the BDS-3 four-frequency combination method has better positioning stability; the root mean square errors of the three methods are less than 3mm in the N and E directions, and about 5mm in the U direction, among which the BDS four-frequency combination solution is the best, with a plane accuracy better than 2mm and an elevation accuracy of 3.6mm; it can be found that among the three methods, the four-frequency combination method is better than the other two solution models in the plane, and the positioning performance of the three models in the elevation direction is close, and the four-frequency combination method is always slightly better than the other two models.

[0061] Fig. 9 The standard deviation and root mean square error statistics of the baseline Coor1650-JSJN, where the horizontal axis is the statistical classification of the east direction, north direction and elevation direction, and the vertical axis represents the difference statistics of each method. As can be seen from the figure, in the baseline Coor1650-JSJN, the standard deviations of the three methods are all within 2mm in the N and E directions, and about 2.5mm in the U direction. Among them, the BDS-3 four-frequency combination method is within 1.5mm in the N and E directions, and within 2mm in the U direction; the root mean square error plane accuracy of the three methods is within 5mm, and the best solution result of the BDS-3 four-frequency combination method in the elevation direction is about 5.5mm, and the worst solution result of the three-frequency TCAR method is about 7.5mm. The standard deviation and root mean square error of the four-frequency combination method in each direction are slightly better than the other two models, and the overall positioning effect is improved compared with the other two positioning models.

[0062] It should be pointed out that the description of the above embodiments is only used to help understand the method of the present application and its core idea. For ordinary technicians in this technical field, several improvements and modifications can be made to the present application without departing from the principles of the present application. These improvements and modifications are also within the scope of protection of the claims of the present application.

Claims

1. A short baseline Beidou four-frequency combination positioning solution method, It is characterized in that The method comprises the following steps: (1) The acquired Beidou four-frequency raw observation data is preprocessed to eliminate gross errors and calculate the instantaneous coordinates of the satellites. Then, the B1C and B2a frequencies are combined with dual-frequency narrow lanes, and the B1I and B3I frequencies are combined with dual-frequency narrow lanes to obtain the corresponding two sets of double-difference pseudoranges and carrier phase observation equations. (2) The double difference ambiguity is used as a parameter to construct a Kalman filter, and the integer ambiguity floating point solution and covariance matrix are obtained using the Kalman filter; (3) Calculate the ambiguity fixation solution using the LAMBDA algorithm and substitute the ambiguity fixation solution back to obtain the precise coordinates of the current position; In the step (1), the B1C and B2a frequencies are combined with dual-frequency narrow lanes, and the B1I and B3I frequencies are combined with dual-frequency narrow lanes to obtain two corresponding sets of double-difference pseudoranges and carrier phase observation equations. The specific steps are as follows: First, the combination coefficient (1, 0, 0, 1) is used to select B1C and B2a frequencies for dual-frequency narrow lane combination. Assuming the narrow lane combination of these two frequencies is NL1, the first set of double-difference pseudorange and carrier phase observation equations are obtained as follows: Then, the B1I and B3I frequencies are combined into a dual-frequency narrow lane combination using (0, 1, 1, 0). Assuming the narrow lane combination of these two frequencies is NL2, the second set of double-difference pseudorange and carrier phase observation equations are obtained as follows: In the formula, represents the double difference operator, i = 1, 2, The difference between the difference in pseudorange observations from the differential satellite to the mobile station and the reference station and the difference in pseudorange observations from the reference satellite to the mobile station and the reference station corresponding to NLi, The difference between the difference in distance from the differential satellite to the mobile station and the reference station and the difference in distance from the reference satellite to the mobile station and the reference station, represents the difference between the difference in tropospheric delay from the differential satellite to the rover and the reference station and the difference in tropospheric delay from the reference satellite to the rover and the reference station, represents the difference between the difference in ionospheric delay from the differential satellite to the rover and reference station and the difference in ionospheric delay from the reference satellite to the rover and reference station, represents the difference between the difference in pseudorange observation noise from the differential satellite to the mobile station and the reference station and the difference in pseudorange observation noise from the reference satellite to the mobile station and the reference station, λ NLi Indicates the wavelength of the corresponding frequency carrier after the dual-frequency narrow-lane combination, The difference between the difference in carrier phase observations from the differential satellite to the mobile station and the reference station and the difference in carrier phase observations from the reference satellite to the mobile station and the reference station corresponding to NLi, represents the difference between the difference in ambiguity between the differential satellite and the mobile station and the reference station and the difference in ambiguity between the reference satellite and the mobile station and the reference station corresponding to NLi, It represents the difference between the difference in carrier observation noise from the differential satellite to the mobile station and the reference station and the difference in carrier observation noise from the reference satellite to the mobile station and the reference station.

2. According to the short baseline Beidou four-frequency combined positioning solution method of claim 1, It is characterized in that When there are n+1 satellites in one epoch, the dual-frequency narrow lane combination NL1 lists n pseudo-range observation equations and n carrier phase observation equations respectively, and the dual-frequency narrow lane combination NL2 also lists n pseudo-range observation equations and n carrier phase observation equations respectively. There are only 2n+3 unknowns. All equations are combined to solve a single epoch, and the error equation obtained by linearization is: Among them, V L is the error matrix of the 2n×1-dimensional carrier observation equation, V p is the error matrix of the pseudorange observation equation of 2n×1 dimension, A is the coefficient matrix of the baseline vector of 2n×3 dimension, B is the double difference ambiguity coefficient matrix of 2n×2n dimension, δX, δY, δZ are the three-dimensional coordinate correction values, is a 2n×1 dimensional double difference ambiguity matrix, L L , L P are the constant matrices of the carrier phase and pseudorange observation equations respectively.

3. The short baseline Beidou four-frequency combined positioning solution method according to claim 1, It is characterized in that In step (2), the double difference ambiguity is used as a parameter to construct a Kalman filter, and the specific steps are as follows: Assuming that the number of common-view satellites observed in a certain epoch is n, there are corresponding 3 coordinate correction values ​​and 2n ambiguities to be determined, and 4n observation equations for pseudorange and carrier can be obtained. Therefore, the state vector X of the kth epoch is k and the observation equation coefficient matrix H k Set to: Where δX, δY, δZ are the three-dimensional coordinate correction values, i = 1, 2, represents the double difference ambiguity to be determined for the nth satellite dual-frequency narrow lane combination NLi, α ni ,β ni ,γ ni are the coefficients of δX, δY, δZ of ​​the n-th satellite dual-frequency narrow lane combination NLi, and λ is the double-difference ambiguity coefficient to be determined consisting of the carrier wavelength; Substitute this state vector and observation equation coefficient matrix into the state equation and observation equation of the Kalman filter respectively to construct the Kalman filter.

4. The short baseline Beidou four-frequency combined positioning solution method according to claim 1, It is characterized in that The significance level Ratio value given in the fuzziness test is used as the reliability test standard of the fuzziness fixed solution in step (3), and its expression is: In the formula, σ 1 and σ 2 It represents the residual sum of squares corresponding to the suboptimal and optimal solutions of the ambiguity integer solution; if the Ratio value is greater than the set threshold, the ambiguity is considered to be fixed successfully.

Images