Single-station robust time service estimation method for Beidou multi-frequency non-combination observation

Abstract

The invention discloses a single-station robust time service estimation method for Beidou multi-frequency non-combination observation, and the method comprises the steps: firstly carrying out the smoothing of a pseudo-range observation value through employing a carrier observation value based on Beidou multi-frequency observation data, and weakening the observation noise and multipath influence; then, giving play to the advantages of Beidou multi-frequency signals, making up the disadvantage that the number of single-mode Beidou satellites is insufficient with the frequency number, considering the Beidou satellite clock error reference and the correlation among all to-be-estimated parameters, and constructing a Beidou single-mode multi-frequency time service estimation model through parameter reforming, clock error reference unification and multi-frequency deviation compensation; and secondly, through two modes of comparison with the true value of a station coordinate and post-test residual chi-square hypothesis test, the abnormity of an observation value is eliminated, the precision and robustness of Beidou single-mode time service are improved, and the performance reaches and is even superior to that of a conventional GPS and a Beidou / GPS dual-system combination.

Description

Technical Field

[0001] The invention relates to a satellite timing method, in particular to a single-station robust timing estimation method. Background Art

[0002] Satellite navigation systems can provide all-weather, wide-area high-precision positioning, navigation and timing services, and are widely used in high-precision timing and time synchronization in power systems and other industries. At present, the most widely used and mature technical means is the timing estimation model based on the dual-frequency ionosphere-free combination standard single-point positioning. This model eliminates the influence of the ionosphere by combining observations, but it also causes the multipath and observation noise to be amplified by about 3 times. In addition, there are many ways to combine multi-frequency observations, and the dual-frequency ionosphere-free model does not make full use of multi-frequency observation information. If multiple dual-frequency ionosphere-free observations are used simultaneously, there are complex correlations between the observations that need to be processed, making it difficult to achieve a unified expression of the multi-frequency function model.

[0003] With the development of multi-frequency GNSS (Global Navigation Satellite System), especially the Beidou (BDS) system, it is currently possible to broadcast B1c / B2I / B2a / B6I / B2b multi-frequency observation data simultaneously. In theory, the more observation information the model uses, the higher the parameter estimation performance. However, compared with the dual-frequency observation situation, multi-frequency observation also means that more abnormal observations may be introduced, which poses a challenge to robust timing. In addition, most of the current mainstream satellite timing methods rely on the BDS / GPS dual-mode system. In addition, the timing performance is closely related to the number of satellites. The number of single-mode Beidou satellites is small, and the model redundancy is low, making Beidou single-mode robust timing challenging. Therefore, it is necessary to explore the advantages of Beidou system multi-frequency signals for Beidou single-mode application scenarios, make up for the disadvantage of insufficient number of satellites with frequency advantages, and realize Beidou single-mode multi-frequency robust timing estimation. Summary of the invention

[0004] Purpose of the invention: In view of the above-mentioned prior art, a single-station robust timing estimation method for Beidou multi-frequency non-combined observation is proposed, which is aimed at single-station Beidou multi-frequency timing scenario to improve the timing estimation accuracy and robustness.

[0005] Technical solution: A single-station robust timing estimation method for Beidou multi-frequency non-combined observation, including the following steps:

[0006] Step 1: The timing station receives the Beidou satellite B2I / B6I / B1c / B2a / B2b multi-frequency pseudorange and carrier observation data in real time. In the continuous observation arc without cycle slip, the carrier observation value is used to smooth the pseudorange to weaken the pseudorange noise and multipath influence;

[0007] Step 2: Construct Beidou multi-frequency non-combined observation model;

[0008] Step 3: For users who observe more than m BeiDou satellites at the same time, perform Taylor series expansion on the model constructed in step 2 and construct the least squares error equation. The parameter estimates of the model are obtained through least squares solution, and the posterior residual of each satellite is obtained; where m>4;

[0009] Step 4: Using the coupling between the parameters in step 3 and the statistical characteristics of the post-test residuals, check the coordinate correction order of magnitude and residual hypothesis test to improve the robustness of the timing estimation.

[0010] Furthermore, in step 1, the observation equation corresponding to the original observation value is as follows:

[0011]

[0012] In the formula, the superscript s and subscript r, i represent the satellite, receiver and frequency respectively, where i = 1, 2, 3, 4, 5 correspond to the frequency B2I / B6I / B1c / B2a / B2b respectively; and are the original pseudorange observation value and the carrier observation value respectively; Indicates the station-to-star distance; represents the tropospheric delay on the signal propagation path; c represents the speed of light in a vacuum; t r and t s Represent the receiver clock error and satellite clock error respectively; represents the ionospheric delay corresponding to frequency 1 on the signal propagation path; γ i =f1 2 / f i 2 is the ionospheric delay amplification factor of frequency i relative to frequency 1, where f i Represents the frequency of the i-th frequency signal; λ i Indicates the carrier wavelength of frequency i; Indicates floating point ambiguity; d r,i and They represent the pseudorange hardware delays of the receiver and satellite at the corresponding frequency point i respectively; and They represent the pseudorange and carrier observation noise including multipath respectively;

[0013] When the pseudorange is smoothed using carrier observations, corresponding to a certain epoch t n ,

[0014]

[0015] Where, t n-1 and t n Two represents two different epochs; n represents the smoothed epoch count; represents the smoothed pseudorange observation value; Indicates t n-1 and t n The change in carrier observations between two epochs.

[0016] Furthermore, in step 2, the parameters to be estimated in the observation equation are decoupled by parameter renormalization, and the following abbreviations are defined corresponding to the frequency points i and j:

[0017]

[0018] Among them, α ij and β ij are the ionospheric-free combination coefficients corresponding to frequency points i and j respectively; and are the pseudorange hardware delays of the satellite and receiver in the ionosphere-free combination form respectively; corresponding to frequency points i and j, the differential code deviation of the satellite and receiver is defined as follows:

[0019]

[0020] In the formula, is the differential code deviation at the satellite end, DCB r,ij is the differential code deviation at the receiver;

[0021] Based on the above abbreviation, the receiver clock difference t r and the satellite clock error t s Reparameterization is performed; specifically, the receiver clock error benchmark depends on the pseudorange observation value. Based on frequency points 1 and 2, the receiver clock error is firstly compared with the ionosphere-free combined pseudorange hardware delay corresponding to these two frequency points. Reparameterization is performed, and the reparameterized receiver clock error for,

[0022]

[0023] Then, based on the Beidou satellite clock error and taking the B6I frequency as the reference, the reparameterized form of the satellite clock error is:

[0024]

[0025] In the formula, is the reparameterized satellite clock error;

[0026] Finally, the ionospheric delay and pseudorange hardware delay are reparameterized, that is, the ionospheric delay and the differential code bias representing the pseudorange hardware delay are combined into one term.

[0027]

[0028] In the formula, is the reparameterized ionospheric delay;

[0029] At the same time, the reparameterization process of equations (5), (6), and (7) is implemented, and the inconsistency between the Beidou satellite clock error reference and the multi-frequency pseudorange observation values ​​is converted and unified to obtain the following Beidou multi-frequency non-combined observation model:

[0030]

[0031] Where D ref and The specific form is as follows:

[0032]

[0033] Where D ref Used to realize Beidou satellite clock error reference conversion, Used to compensate for the inconsistency between multi-frequency observations and the clock reference.

[0034] Furthermore, in step 3, the model of equation (8) is subjected to Taylor series expansion, converted into a linear equation for solution, and the least squares error equation is constructed as follows:

[0035]

[0036] In the formula, V represents the residual, represents the residual error of satellite m at frequency point i; B is the design matrix, They represent the corresponding direction cosines respectively; X is the parameter to be estimated, including the three-dimensional coordinate correction number, the tilt ionospheric delay of each satellite after reparameterization, and the receiver clock error; ΔX, ΔY, and ΔZ represent the coordinate correction number respectively. represents the ionospheric delay of each satellite reparameterization; L is the observation matrix, including the smoothed pseudorange observation value and various error correction terms, represents the observation value corresponding to frequency point i of satellite m;

[0037] Based on the error equation of formula (10), the estimation of each parameter is solved by least squares, and the posterior residual of each satellite is obtained.

[0038] X=(B T B) -1 ·B T ·L (11)

[0039] Where the superscript T represents the matrix rank transformation.

[0040] Furthermore, the step 4 includes the following specific steps:

[0041] First, for stations with accurate known coordinates, the coordinates obtained by least squares solution are compared with the true values ​​to preliminarily determine whether the results are usable; then, according to the set significance level, the residuals of each satellite are analyzed. Based on the theoretical knowledge of mathematical statistics, the residuals of each satellite should obey the chi-square distribution with a degree of freedom of (4m-4).

[0042]

[0043] In the formula, δ chisqr is the test quantity, χ represents the chi-square test;

[0044] If the residuals of one or more satellites exceed the limit, the satellites are eliminated one by one in a loop, and the least squares solution and chi-square test are performed again. During the loop, for the satellite combination that can pass the chi-square test, the RMS value of its residual after the test is calculated at the same time as the criterion for subsequent judgment; after all cycles are completed, the satellite combination solution with the smallest RMS value is selected as the final result; if the chi-square test is not passed during the loop, there is no solution result for the current site, and an early warning message is sent to the administrator.

[0045] Beneficial effect: The present invention proposes a single-station robust timing estimation method for Beidou multi-frequency non-combined observation, which is aimed at the single-station Beidou multi-frequency timing scenario. By giving full play to the advantages of Beidou system multi-frequency signals, the frequency advantage makes up for the disadvantage of insufficient number of satellites. This method constructs a Beidou multi-frequency non-combined robust clock error estimation model, which makes it compatible with multi-frequency observation information and improves the performance of Beidou single-mode timing. At the same time, for possible anomalies in multi-frequency observation values, it is supplemented by hypothesis testing and other gross error identification strategies to improve the accuracy and robustness of timing estimation. Compared with the conventional dual-frequency situation, the performance of Beidou single-mode multi-frequency timing is better than that of GPS and Beidou / GPS dual system combination. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of a single-station robust timing estimation method for Beidou multi-frequency non-combined observation of the present invention;

[0047] Figure 2 is a flow chart of step 4 of the present invention;

[0048] Figure 3 The method of the present invention is used to compare the timing accuracy of Beidou single-mode multi-frequency and GPS;

[0049] Figure 4 The method of the present invention is used to compare the timing accuracy of Beidou single-mode multi-frequency and conventional Beidou / GPS dual-system combination;

[0050] Figure 5 It is the statistical result of different sites using the method of the present invention. DETAILED DESCRIPTION

[0051] The present invention will be further explained below in conjunction with the accompanying drawings.

[0052] like Figure 1 As shown in FIG. 1 , a robust timing estimation algorithm for Beidou multi-frequency non-combined observation is shown in FIG. 1 . The specific steps are as follows:

[0053] Step 1. Noise smoothing of raw observation values: The timing station receives Beidou satellite B2I / B6I / B1c / B2a / B2b multi-frequency pseudorange and carrier observation data in real time. The observation equation corresponding to the raw observation value is as follows:

[0054]

[0055] In the formula, the superscript s and subscript r, i represent the satellite, receiver and frequency respectively, where i = 1, 2, 3, 4, 5 correspond to the frequency B2I / B6I / B1c / B2a / B2b respectively; and are the original pseudorange observation value and the carrier observation value respectively; Indicates the station-to-star distance; represents the tropospheric delay on the signal propagation path; c represents the speed of light in a vacuum; t r and t s Represent the receiver clock error and satellite clock error respectively; represents the ionospheric delay corresponding to frequency 1 on the signal propagation path; γ i =f1 2 / f i 2 is the ionospheric delay amplification factor of frequency i relative to frequency 1, where f i Indicates the frequency of the i-th frequency point signal. The corresponding frequencies of B2I / B6I / B1c / B2a / B2b are 1561.098MHz, 1268.52MHz, 1575.42MHz, 1176.45MHz, and 1207.14MHz respectively. i Indicates the carrier wavelength of frequency i; Indicates floating point ambiguity; d r,i and They represent the pseudorange hardware delays of the receiver and satellite at the corresponding frequency point i respectively; and represent the pseudorange and carrier observation noise including multipath, respectively.

[0056] Considering that the pseudorange observation value has large noise, which is generally hundreds of times that of the carrier observation value, and the multipath effect in the pseudorange observation value is also much greater than that of the carrier observation value. In order to ensure the accuracy and smoothness of the subsequent timing solution, firstly, in the continuous observation arc segment without cycle slip, the pseudorange is smoothed using the carrier observation value to weaken the pseudorange noise and multipath effect. n ,

[0057]

[0058] Where, t n-1 and t n Two represents two different epochs; n represents the smoothed epoch count; represents the smoothed pseudorange observation value; Indicates t n-1 and t n The change in carrier observations between two epochs. In order to avoid ionospheric accumulation during the smoothing process, the smoothing window should not be too large.

[0059] Step 2. Beidou multi-frequency non-combined observation model construction: Considering that the observation equation has many parameters to be estimated and they are coupled to each other, it is impossible to estimate all of them at the same time. Therefore, it is necessary to use the idea of ​​parameter reorganization to decouple. For the convenience of subsequent expression, the following abbreviations are defined for frequency points i and j:

[0060]

[0061] Among them, α ij and β ij are the ionospheric-free combination coefficients corresponding to frequency points i and j respectively; and are the pseudorange hardware delays in the form of ionospheric-free (IF) combinations at the satellite and receiver ends, respectively. It should be noted that the absolute amount of pseudorange hardware delay cannot be determined, but the relative hardware deviation between different code observations can be obtained, namely, differential code bias (DCB). Corresponding to frequency points i and j, the DCB at the satellite and receiver ends is usually defined as follows:

[0062]

[0063] In the formula, is the differential code deviation at the satellite end, DCB r,ij is the differential code deviation at the receiver.

[0064] Based on the above abbreviation, the receiver clock error t r and the satellite clock error t sThe receiver clock error reference depends on the pseudorange observation value. Based on frequency points 1 and 2, the receiver clock error is firstly compared with the ionosphere-free combined pseudorange hardware delay corresponding to these two frequency points. Reparameterization is performed, and the reparameterized receiver clock error for,

[0065]

[0066] Then, considering that the Beidou satellite clock error is usually based on the B6I frequency, the reparameterized form of the satellite clock error is,

[0067]

[0068] In the formula, is the reparameterized satellite clock error.

[0069] Finally, considering the correlation between the ionosphere and pseudorange hardware delay, the two cannot be separated in the absence of external ionosphere information constraints. Therefore, the ionosphere delay and pseudorange hardware delay are further reparameterized, that is, the ionosphere delay and the DCB representing the pseudorange hardware delay are combined into one item.

[0070]

[0071] In the formula, is the reparameterized ionospheric delay.

[0072] By implementing the reparameterization process of equations (5), (6), and (7) at the same time and converting and unifying the inconsistencies between the Beidou satellite clock error reference and the multi-frequency pseudorange observation values, the following function model can be obtained:

[0073]

[0074] Where D ref Used to realize Beidou satellite clock error reference conversion, Used to compensate for the inconsistency between multi-frequency observations and clock reference. ref and The specific form is as follows:

[0075]

[0076] Step 3. Least square positioning and timing solution: For users who simultaneously observe more than m (m>4) BeiDou satellites, perform Taylor series expansion on the model of equation (8), convert it into a linear equation and solve it, and construct the least square error equation as follows:

[0077]

[0078] In the formula, V represents the residual, represents the residual error of satellite m at frequency point i; B is the design matrix, They represent the corresponding direction cosines respectively; X is the parameter to be estimated, including the three-dimensional coordinate correction number, the tilt ionospheric delay of each satellite after reparameterization, and the receiver clock error; ΔX, ΔY, and ΔZ represent the coordinate correction number respectively. represents the ionospheric delay of each satellite reparameterization; L is the observation matrix, which is composed of smoothed pseudorange observations and various error correction terms, Represents the observation value corresponding to frequency point i of satellite m.

[0079] Based on the error equation of formula (10), the estimation of each parameter is solved by least squares, and the posterior residual of each satellite is obtained.

[0080] X=(B T B) -1 ·B T ·L (11)

[0081] Where the superscript T represents the matrix rank transformation.

[0082] Step 4. Abnormal elimination and robust timing:

[0083] Due to the limited accuracy of orbital clock error and atmospheric prior model, and the large pseudo-range multipath effect in the actual observation environment, the observation data inevitably have abnormalities or gross errors. All of these factors will affect the accuracy of positioning and timing, especially when some errors are not handled properly or gross errors are not effectively eliminated, which may even lead to wrong results. For satellite observations with gross errors, they will also affect the accuracy of the estimated parameters and the distribution of the post-test residuals. Therefore, the coupling between the parameters in step 3 and the statistical characteristics of the post-test residuals are used to check the magnitude of coordinate correction and residual hypothesis test, respectively, to improve the robustness of timing estimation.

[0084] like Figure 2 As shown in Figure 1, first, for stations with accurate known coordinates, the coordinates obtained by least squares solution are compared with the true values ​​to preliminarily determine whether the results are usable; then, according to the set significance level, the residuals of each satellite are analyzed. Based on the theoretical knowledge of mathematical statistics, the residuals of each satellite should obey the chi-square distribution with a degree of freedom of (4m-4).

[0085]

[0086] In the formula, δ chisqr is the test quantity, and χ represents the chi-square test.

[0087] If the residual error of one or more satellites exceeds the limit, the satellites are removed one by one in a loop, and the least squares solution and chi-square test are performed again. During the loop, for the satellite combination that can pass the chi-square test, the RMS value of the residual error after the test is calculated as the criterion for subsequent judgment. After all the loops are completed, the satellite combination solution with the smallest RMS value can be selected as the final result. If the chi-square test is not passed during the loop, there is no solution result for the current site, and an early warning message is sent to the administrator.

[0088] Figure 3 By comparing the results of the Beidou single-mode multi-frequency robust timing estimation method of the present invention with the timing results of the conventional GPS single system, it can be found that the results of the method of the present invention have smaller fluctuations and an accuracy of 2.87ns, which is 34.9% higher than the 4.41ns of GPS.

[0089] Figure 4 By comparing the results of the Beidou single-mode multi-frequency robust timing estimation method of the present invention with the timing results of the Beidou / GPS dual system, it can be found that the results of the method of the present invention have smaller fluctuations and an accuracy of 2.87ns. The accuracy of the conventional Beidou / GPS dual system is 3.47ns, which is an improvement of 17.3%.

[0090] Figure 5 By comparing the results of the method of the present invention with those of the conventional single GPS and Beidou / GPS dual system combination for different test sites, it can be seen that the proposed method has a certain universality, and different sites have the same phenomenon. The performance of the proposed Beidou single-mode multi-frequency robust timing method is better than that of the conventional single GPS and Beidou / GPS dual system combination.

[0091] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A single-station robust timing estimation method for Beidou multi-frequency non-combined observation, characterized in that: The steps include: Step 1: The timing station receives the Beidou satellite B2I / B6I / B1c / B2a / B2b multi-frequency pseudorange and carrier observation data in real time. In the continuous observation arc without cycle slip, the carrier observation value is used to smooth the pseudorange to weaken the pseudorange noise and multipath influence; Step 2: Construct Beidou multi-frequency non-combined observation model; Step 3: For users who observe more than m BeiDou satellites at the same time, perform Taylor series expansion on the model constructed in step 2 and construct the least squares error equation. The parameter estimates of the model are obtained through least squares solution, and the posterior residual of each satellite is obtained; where m>4; Step 4: Using the coupling between the parameters in step 3 and the statistical characteristics of the post-test residuals, check the coordinate correction order of magnitude and residual hypothesis test to improve the robustness of the timing estimation.

2. The single-station robust timing estimation method for Beidou multi-frequency non-combined observation according to claim 1, characterized in that: In step 1, the observation equation corresponding to the original observation value is as follows: In the formula, the superscript s and subscript r, i represent the satellite, receiver and frequency respectively, where i = 1, 2, 3, 4, 5 correspond to the frequency B2I / B6I / B1c / B2a / B2b respectively; and are the original pseudorange observation value and the carrier observation value respectively; Indicates the station-to-star distance; T r s represents the tropospheric delay on the signal propagation path; c represents the speed of light in a vacuum; t r and t s Represent the receiver clock error and satellite clock error respectively; represents the ionospheric delay corresponding to frequency 1 on the signal propagation path; γ i =f1 2 / f i 2 is the ionospheric delay amplification factor of frequency i relative to frequency 1, where f i Represents the frequency of the i-th frequency signal; λ i Indicates the carrier wavelength of frequency i; Indicates floating point ambiguity; d r,i and They represent the pseudorange hardware delays of the receiver and satellite at the corresponding frequency point i respectively; and They represent the pseudorange and carrier observation noise including multipath respectively; When the pseudorange is smoothed using carrier observations, corresponding to a certain epoch t n , Where, t n-1 and t n Two represents two different epochs; n represents the smoothed epoch count; represents the smoothed pseudorange observation value; Indicates t n-1 and t n The change in carrier observations between two epochs.

3. The single-station robust timing estimation method for Beidou multi-frequency non-combined observation according to claim 2 is characterized in that: In step 2, the parameters to be estimated in the observation equation are decoupled by parameter renormalization. Corresponding to the frequency points i and j, the following abbreviations are defined: Among them, α ij and β ij are the ionospheric-free combination coefficients corresponding to frequency points i and j respectively; and are the pseudorange hardware delays of the satellite and receiver in the ionosphere-free combination form respectively; corresponding to frequency points i and j, the differential code deviation of the satellite and receiver is defined as follows: In the formula, is the differential code deviation at the satellite end, DCB r,ij is the differential code deviation at the receiver; Based on the above abbreviation, the receiver clock difference t r and the satellite clock error t s Reparameterization is performed; specifically, the receiver clock error benchmark depends on the pseudorange observation value. Based on frequency points 1 and 2, the receiver clock error is firstly compared with the ionosphere-free combined pseudorange hardware delay corresponding to these two frequency points. Reparameterization is performed, and the reparameterized receiver clock error for, Then, based on the Beidou satellite clock error and taking the B6I frequency as the reference, the reparameterized form of the satellite clock error is: In the formula, is the reparameterized satellite clock error; Finally, the ionospheric delay and pseudorange hardware delay are reparameterized, that is, the ionospheric delay and the differential code bias representing the pseudorange hardware delay are combined into one term. In the formula, is the reparameterized ionospheric delay; At the same time, the reparameterization process of equations (5), (6), and (7) is implemented, and the inconsistency between the Beidou satellite clock error reference and the multi-frequency pseudorange observation values ​​is converted and unified to obtain the following Beidou multi-frequency non-combined observation model: Where D ref and The specific form is as follows: Where D ref Used to realize Beidou satellite clock error reference conversion, Used to compensate for the inconsistency between multi-frequency observations and the clock reference.

4. The single-station robust timing estimation method for Beidou multi-frequency non-combined observation according to claim 3 is characterized in that: In step 3, the model of formula (8) is expanded by Taylor series, converted into a linear equation for solution, and the least squares error equation is constructed as follows: In the formula, V represents the residual, represents the residual error of satellite m at frequency point i; B is the design matrix, They represent the corresponding direction cosines respectively; X is the parameter to be estimated, including the three-dimensional coordinate correction number, the tilt ionospheric delay of each satellite after reparameterization, and the receiver clock error; ΔX, ΔY, and ΔZ represent the coordinate correction number respectively. represents the ionospheric delay of each satellite reparameterization; L is the observation matrix, including the smoothed pseudorange observation value and various error correction terms, represents the observation value corresponding to frequency point i of satellite m; Based on the error equation of formula (10), the estimation of each parameter is solved by least squares, and the posterior residual of each satellite is obtained. X=(B T ·B) -1 ·B T ·L(11) Where the superscript T represents the matrix rank transformation.

5. The single-station robust timing estimation method for Beidou multi-frequency non-combined observation according to claim 4 is characterized in that: The step 4 comprises the following specific steps: First, for stations with accurate known coordinates, the coordinates obtained by least squares solution are compared with the true values ​​to preliminarily determine whether the results are usable; then, according to the set significance level, the residuals of each satellite are analyzed. Based on the theoretical knowledge of mathematical statistics, the residuals of each satellite should obey the chi-square distribution with a degree of freedom of (4m-4). In the formula, δ chisqr is the test quantity, χ represents the chi-square test; If the residuals of one or more satellites exceed the limit, the satellites are eliminated one by one in a loop, and the least square solution and chi-square test are performed again. During the loop, for the satellite combination that can pass the chi-square test, the RMS value of its residual after the test is calculated at the same time as the criterion for subsequent judgment; after all the loops are completed, the satellite combination solution with the smallest RMS value is selected as the final result; If the chi-square test fails during the cycle, there is no solution result for the current site, and a warning message is sent to the administrator.

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