Anti-interference high-robustness high-precision differential positioning method

Abstract

The invention discloses an anti-interference strong-robustness high-precision differential positioning method which is applied to real-time dynamic differential positioning of a Beidou No.3 receiver in a complex electromagnetic environment. Comprising the following steps: step 1, performing gross error combined processing: a, forming an LI combined observation value and an MW combined observation value by using double-difference phase observation values and double-difference pseudo-range observation values on B1 and B3 respectively; according to the method, a staged combined processing strategy is innovatively adopted, in the preprocessing stage, large gross errors are accurately eliminated through a median method (with the formula: XiM formula > k * MAD as the criterion, k = 5), and interference can be reduced from the source; in the parameter calculation stage, robust estimation iteration is only carried out on the residual small gross error, limitation of a single standard is avoided, the calculation amount is greatly reduced, balance of gross error processing effectiveness and real-time performance is achieved, and support is provided for efficient operation of an embedded processor.

Description

Technical Field

[0001] This invention belongs to the field of differential positioning, specifically relating to a robust and high-precision differential positioning method with strong anti-interference capabilities. Background Technology

[0002] In practical applications, the BeiDou-3 high-precision positioning system often faces complex electromagnetic environments, including various interferences such as deceptive signals and broadband suppression signals. This makes achieving fast and stable high-precision positioning under interference environments a current research hotspot and challenge.

[0003] In terms of gross error handling, accurate detection of gross errors is crucial for high-precision positioning due to their high frequency of occurrence. Currently, commonly used gross error handling techniques are mainly divided into two categories: one is gross error detection, which identifies and eliminates gross errors by constructing test statistics. However, accurately selecting the discrimination criteria is difficult; if the criteria are too broad, gross errors will remain, while if they are too strict, the reliability of the solution may be affected by insufficient observations. The other is robust estimation, which controls the impact of gross error observations through equivalent weights. However, this technique requires iterative calculation of equivalent weights in sync with parameter solving, which significantly increases the computational burden on the embedded processor of the high-precision anti-interference BeiDou-3 navigation receiver, hindering the implementation of real-time RTK solution processing.

[0004] In integer ambiguity processing, achieving highly reliable and rapid fixation requires ambiguity verification and partial ambiguity subset selection. Integer ambiguity search and fixation widely employs the integer least squares correlation adjustment method (LAMBDA). Commonly used ambiguity verification indicators include ambiguity accuracy factor (ADOP), bootstrapping success rate, ratio-test, and a "tight combination" of success rate indicators and ratio-test based on integer aperture estimation theory. Among these, the first three cannot accurately and reliably verify integer ambiguity solutions when used alone, while the "tight combination," although theoretically rigorous, is difficult to apply to practical data processing. Common techniques for partial ambiguity subset selection include elevation angle-first fixation, signal-to-noise ratio-first fixation, and ADOP-optimized fixation, but the applicability of these techniques in complex interference environments still needs improvement.

[0005] In summary, existing technologies struggle to balance the effectiveness and computational efficiency of gross error processing with the reliability and speed of integer ambiguity fixation in complex electromagnetic interference environments. A superior technical solution is urgently needed to meet the application requirements of BeiDou-3 high-precision differential positioning in anti-interference scenarios. Summary of the Invention

[0006] To overcome the challenges of balancing effectiveness and computational efficiency in gross error processing under complex electromagnetic interference environments, and the difficulty of balancing reliability and speed in fixing integer ambiguity, a robust and high-precision differential positioning method with strong anti-interference capabilities is proposed.

[0007] The technical solution of this invention is: a robust and high-precision differential positioning method with strong anti-interference capabilities, applied to real-time dynamic differential positioning of Beidou-3 receivers in complex electromagnetic environments, comprising the following steps: Step 1: Coarse error joint processing: a. First, use the double-difference phase observations and double-difference pseudorange observations on B1 and B3 to form LI combined observations respectively. Combined observations with MW The calculation expression is as follows: ; In the formula , , , These represent the double-difference carrier phase observations and pseudorange observations on B1 and B3, respectively. , , , b. Represent the frequency and wavelength of B1 and B3 respectively; and c. Generate a test sequence by subtracting differences between epochs; d. Use the median method to identify outliers, with the criterion being ||, where M is the sequence median, MAD is the median absolute deviation, and k=5; e. For small outliers that are not eliminated, use robust estimation iterative calculation of equivalent weights during the parameter solution stage; Step 2: Integer ambiguity processing: Use an optimized partial ambiguity subset selection technique, specifically including: e. In the preprocessing stage, based on the limit of a cutoff elevation angle of 10° and a ambiguity estimation standard deviation of 1.5 weeks, filter out low-precision ambiguities; f. Perform integer downcorrelation processing on the usable original ambiguity parameters obtained after filtering in step e, and generate the modulus... g. Sort the fuzzy linear combinations in ascending order of variance; h. Use LAMBDA technique to search for fixed solutions in the selected fuzzy subset; h. Calculate the bootstrapping success rate and ratio-test threshold of the fixed solution. If at least one of them does not meet the preset requirements, remove the last fuzzy linear combination in the sort and return to step g to repeat the process; if there are more than 3 remaining fuzzy linear combinations, and both the bootstrapping success rate and the ratio-test threshold meet the preset requirements, then determine the fuzzy subset as the final fixed solution; otherwise, retain the floating-point solution.

[0008] Furthermore, in step one, the standard deviation of the LI combined observation ΔL1 ranges from 0.01 to 0.02 weeks, and the standard deviation of the MW combined observation ΔL2 ranges from 0.1 to 0.2 weeks.

[0009] Furthermore, in step two g, the preset requirements are: bootstrapping success rate not less than 95%, and ratio-test threshold not less than 3.0.

[0010] Furthermore, in step one c, the testing logic of the median method is as follows: when a certain observation value in the sequence of observations to be tested is greater than the critical value S, it is determined that the observation value has a gross error.

[0011] Furthermore, in step two f, the integer decorrelation processing is performed by constructing a transformation matrix to reduce the correlation of the original ambiguity parameters, thereby reducing the correlation of the ambiguity search space.

[0012] Furthermore, in step b, the test sequence sum is the result of the difference between epochs of the LI combination observations and the difference between epochs of the MW combination observations, and the sums both follow a normal distribution.

[0013] Furthermore, in step e, the specific method for filtering low-precision ambiguities is as follows: ambiguities that simultaneously satisfy a cutoff elevation angle ≥ 10° and a ambiguity estimation standard deviation ≤ 1.5 cycles are retained; otherwise, they are filtered out.

[0014] Furthermore, in step twoh, the termination condition "more than 3 remaining linear combinations of ambiguity" means that the number of retained linear combinations of ambiguity is 4 or more, to ensure that the subset has sufficient observation redundancy.

[0015] Furthermore, in step one c, the critical value S of the median method is calculated based on the median M and the median absolute deviation MAD of the sequence, specifically using the formula S=k×MAD, where k=5.

[0016] Furthermore, the stage division method of the joint processing of gross errors in step one is as follows: the preprocessing stage removes large gross errors through gross error detection, and the parameter calculation stage processes small gross errors through robust estimation, so as to achieve staged targeted processing of gross errors of different magnitudes.

[0017] The beneficial effects of this invention are as follows: 1. In terms of gross error processing, this technology innovatively adopts a "stage-by-stage joint processing" strategy: in the preprocessing stage, large gross errors are accurately eliminated using the median method (with |Xi−M|>k×MAD as the criterion, k=5), which can reduce interference from the source; in the parameter calculation stage, robust estimation iteration is only performed on the residual small gross errors, which avoids the limitations of a single standard and significantly reduces the amount of computation, achieving a balance between the effectiveness and real-time performance of gross error processing, and providing support for the efficient operation of embedded processors; 2. In terms of integer ambiguity processing, this technology achieves dual optimization... To overcome bottlenecks: On the one hand, a "dual-index verification" of bootstrapping success rate (≥95%) and ratio-test threshold (≥3.0) is adopted to make up for the shortcomings of a single index and significantly improve the reliability of ambiguity fixation; on the other hand, low-precision ambiguity is filtered by preprocessing with "elevation angle + standard deviation", and subset selection is optimized by combining integer decorrelation and iterative elimination strategies. Under the premise of ensuring at least 4 redundant combinations, the search efficiency of LAMBDA technology is accelerated, enabling it to obtain fixed solutions quickly and stably in complex electromagnetic environments. Attached Figure Description

[0018] Figure 1 The flowchart shown is of the high-precision solution unit of the present invention; Figure 2 The flowchart shown is a process for detecting gross errors in satellite observations according to the present invention. Figure 3 The flowchart shown is a partial ambiguity fixing algorithm based on bootstraping success rate and ratio-test verification of the present invention. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Example 1: Please refer to Figures 1-3 A robust and high-precision differential positioning method with strong anti-interference capabilities is characterized by its application to real-time dynamic differential positioning of BeiDou-3 receivers in complex electromagnetic environments, comprising the following steps: Step 1: Gross Error Co-processing: a. First, use the double-difference phase observations and double-difference pseudorange observations on B1 and B3 to form LI combined observations respectively. Combined observations of MW The calculation expression is as follows: ; In the formula , , , These represent the double-difference carrier phase observations and pseudorange observations on B1 and B3, respectively. , , , These represent the frequency and wavelength of B1 and B3, respectively; because and Simultaneously satisfying the following relationship: In the formula This represents the residual ionospheric delay after double-difference. denoted as double difference ambiguity, and c is the speed of light.

[0021] Therefore, when the same satellite does not experience cycle slips, the equation... , The right side of the equation should be a constant. The left side is mainly affected by ionospheric residuals The effect of this is reduced by 65% ​​due to the preceding coefficient. And the equation... The left side is mainly affected by noise in the double-difference pseudorange observations.

[0022] Numerous experiments have shown that: and It generally fluctuates around a constant, with standard deviations of approximately 0.01-0.02 weeks and 0.1-0.2 weeks, respectively.

[0023] right and The difference between epochs yields two sets of normally distributed sequences of the observed values ​​to be tested. and We tested both sets of observation sequences separately. If either set was found to contain a gross error at any epoch, that epoch was considered to contain a gross error. We used the median method to avoid the destructive impact of excessively large outlier observations on the test. The criteria for this determination are as follows: In the formula, S is the critical value; values ​​greater than S are considered gross errors, while values ​​less than S are considered normal. M is the median of the test sequence. k is a constant, usually taken as 3, but after extensive experimentation, we have set it to 5 to appropriately relax the testing criteria. Using the above method, the identification and removal of large gross errors can be completed during the data preprocessing stage.

[0024] For the remaining minor gross errors, we use robust estimation in the parameter solution stage to eliminate or reduce their impact. That is, in the data preprocessing stage, we use the median method and a relatively lenient gross error discrimination criterion to remove large gross errors; in the parameter solution stage, we use robust estimation to eliminate or reduce the impact of minor gross errors.

[0025] The gross error handling method based on the combination of gross error detection and robust estimation can not only effectively control and resist the influence of gross errors, but also reduce the computational load and improve the calculation speed compared with using robust estimation method alone. b. For and c. Generate a test sequence by subtracting from each epoch; d. Use the median method to identify outliers, with the following criteria: Where M is the median of the sequence, MAD is the median absolute deviation, and k=5; d. For minor outliers that are not eliminated, robust estimation is used to iteratively calculate the equivalent weights during the parameter solution stage.

[0026] Step 2: Integer Ambiguity Processing: An optimized partial ambiguity subset selection technique is adopted, specifically including: e. Preprocessing stage: Based on the limits of a cutoff elevation angle of 10° and a standard deviation of 1.5 weeks for ambiguity estimation, low-precision ambiguities are filtered out; f. The usable original ambiguity parameters obtained after filtering in step e are subjected to integer downcorrelation processing, and the resulting linear combinations of ambiguities are sorted in ascending order of variance; g. LAMBDA technique is used to search for fixed solutions of the selected ambiguity subset; h. The bootstrapping success rate and ratio-test threshold of the fixed solution are calculated. If at least one of them does not meet the preset requirements, the last linear combination of ambiguities in the sorting is removed, and step g is returned to be repeated; if the number of remaining linear combinations of ambiguities is more than 3, and both the bootstrapping success rate and the ratio-test threshold meet the preset requirements, the ambiguity subset is determined as the final fixed solution; otherwise, the floating-point solution is retained.

[0027] Please see Figure 1 In this embodiment, in step one, the standard deviation range of the LI combined observation value ΔL1 is 0.01-0.02 weeks, and the standard deviation range of the MW combined observation value ΔL2 is 0.1-0.2 weeks. Please refer to [link / reference]. Figure 1 In this embodiment, in step two (g), the preset requirements are: a bootstrapping success rate of not less than 95% and a ratio-test threshold of not less than 3.0. Please refer to [link / reference]. Figure 1 In this embodiment, in step one c, the testing logic of the median method is as follows: when an observation in the sequence of observations to be tested is greater than the critical value S, it is determined that the observation has a gross error. Please refer to [link to relevant documentation]. Figure 1 In this embodiment, in step two f, the integer decorrelation processing involves constructing a transformation matrix to reduce the correlation of the original ambiguity parameters, thereby decreasing the correlation of the ambiguity search space. Please refer to [link to previous text]. Figure 1 In this embodiment, in step b, the test sequence sum is the result of subtracting the observations between epochs of the LI combination and the MW combination, and both sums follow a normal distribution. Please refer to [link to relevant documentation]. Figure 1 In this embodiment, step e specifically filters low-precision ambiguities as follows: ambiguities that simultaneously satisfy a cutoff elevation angle ≥ 10° and a ambiguity estimation standard deviation ≤ 1.5 cycles are retained; otherwise, they are filtered out. Please refer to [link to relevant documentation]. Figure 1 In this embodiment, in step twoh, the termination condition "more than 3 remaining linear combinations of ambiguities" means that the number of retained linear combinations of ambiguities is 4 or more, to ensure that the subset has sufficient observation redundancy. Please refer to [link to relevant documentation]. Figure 1 In this embodiment, in step one c, the critical value S of the median method is calculated based on the median M and the median absolute deviation MAD of the sequence, specifically using the formula S = k × MAD, where k = 5. Please refer to [link to relevant documentation]. Figure 1 In this embodiment, the stage division method of the gross error joint processing in step one is as follows: the preprocessing stage removes large gross errors through gross error detection, and the parameter calculation stage processes small gross errors through robust estimation, so as to realize the staged targeted processing of gross errors of different magnitudes.

[0028] Example 2: The difference from Example 1 is that this application provides a technical solution: a. The LI combined observation value ΔL1 (expression is the same as in Example 1) is formed by using the double-difference phase observation value and the double-difference pseudorange observation value on B1, and the MW combined observation value is no longer used; c. When using the median method to identify gross errors, the criterion is |Xi−M|>k×MAD, where k=4 (instead of k=5), and the critical value S=4×MAD; d. For small gross errors that are not eliminated, a simplified robust estimation is used (equivalent weights are calculated only 2 times) to further reduce the computational load. Step 2: In integer ambiguity processing, the preprocessing and fixed solution conditions are optimized, specifically including: e. In the preprocessing stage, the cutoff elevation angle is adjusted to 15°, and the standard deviation limit of ambiguity estimation is adjusted to 2.0 weeks; h. In the termination condition, when "the number of remaining linear combinations of ambiguities is more than 2" (i.e. ≥ 3), if the dual indicators meet the requirements, it is determined as a fixed solution (instead of more than 3), to adapt to scenarios with fewer observations.

[0029] Example 3: The difference from Example 1 is that this application provides a technical solution: Step 1: Gross error joint processing introduces inertial navigation auxiliary data (combined with prior information in a high-dynamic environment), specifically including: a. In addition to the LI combined observation value ΔL1 and the MW combined observation value ΔL2, the approximate position and velocity of the carrier provided by the inertial navigation are introduced, and the prior residuals of the double-difference observations are calculated; b. The verification sequence is generated by weighted fusion of the inter-epoch difference of the LI combination and the MW combination with the prior residuals; c. The gross error discrimination criterion is |Xi−M|>k×MAD (k=5) of the fused sequence, and at the same time, combined with the auxiliary criterion of whether the prior residual exceeds 0.5m, the gross error recognition rate in complex dynamic scenes is improved. Step 2: In integer ambiguity processing, the verification index is adjusted, specifically including: h. The dual index verification of "bootstrapping success rate (≥95%) + ADOP (ambiguity accuracy factor ≤0.6 weeks)" is adopted (replacing the ratio-test threshold). ADOP is calculated through the ambiguity covariance matrix to further improve the reliability of the fixed solution in a high-dynamic environment.

[0030] Example 4: The difference from Example 1 is that this application provides a technical solution: Step 1: Gross error joint processing optimizes robust estimation method, specifically including: d. For small gross errors that have not been eliminated, use Huber weight function (instead of equivalent weight iteration) for robust estimation. The function form is: when |v_i|≤c, weight w_i=1; when |v_i|>c, w_i=c / |v_i| (c=1.345), reducing the number of iterations and improving real-time performance. Step 2: Integer ambiguity processing adjusts search and fixing strategies, specifically including: f. Sort ambiguity linear combinations in descending order of variance (instead of ascending order); g. Use ARCE (Integer Least Squares Ambiguity Regression Adjustment) technology instead of LAMBDA technology to search for fixed solutions; h. The preset requirements are adjusted to: bootstrapping success rate ≥90%, ratio-test threshold ≥2.5, and the number of remaining ambiguity linear combinations is more than 3, which is determined as a fixed solution, so as to balance the fixing speed and accuracy in complex environments.

[0031] This invention addresses the real-time dynamic differential positioning requirements of BeiDou-3 receivers in complex electromagnetic environments. Through the coordinated operation of coarse error joint processing and integer ambiguity optimization processing, it achieves an organic unity of anti-interference, strong robustness, and high-precision positioning. The specific working principle is as follows.

[0032] I. Anti-interference mechanism for gross error joint processing: Interference such as deceptive signals and broadband suppression signals in complex electromagnetic environments can easily lead to gross errors (including large and small gross errors) in observations, directly affecting positioning accuracy. This invention adopts a "staged targeted processing" strategy to accurately suppress gross error interference.

[0033] Preprocessing stage: Rapid removal of major gross errors. Using double-difference phase and pseudorange observations from the B1 and B3 bands of BeiDou-3, LI combined observations (ΔL1) and MW combined observations (ΔL2) are constructed. Among them, the LI combination is less affected by ionospheric residuals (the coefficient is reduced by 65%), while the MW combination is clearly affected by pseudorange noise. The two complement each other to improve the reliability of gross error identification.

[0034] Interepoch difference calculations are performed on ΔL1 and ΔL2 to generate a test sequence that follows a normal distribution. Based on the median method (discrimination criterion: |Xᵢ−M|>5×MAD, where M is the median and MAD is the median absolute deviation), large gross errors can be quickly identified and eliminated, reducing the impact of strong interference on subsequent solutions from the source and avoiding the limitations of a single observation type.

[0035] Parameter calculation stage: Precise suppression of minor gross errors. For minor gross errors remaining after preprocessing, equivalent weights are dynamically reduced in the solution by iteratively calculating robust estimation. This process only iterates for minor gross errors, significantly reducing computational load compared to full robust estimation, balancing processing accuracy and real-time performance, and ensuring efficient operation of the embedded processor in complex environments.

[0036] II. High-precision assurance of integer ambiguity processing: The rapid and reliable fixation of integer ambiguity is the core of high-precision differential positioning. This invention overcomes the challenge of ambiguity fixation in complex environments through a process of "preprocessing filtering + dynamic subset optimization + dual index verification".

[0037] Preprocessing: Low-precision ambiguity screening is performed based on a cutoff elevation angle ≥10° (removing satellites that are easily obstructed / interfered at low altitudes) and a standard deviation of ambiguity estimation ≤1.5 weeks (removing observations with high noise). This filters out low-precision ambiguities, reduces unnecessary computation, and lays a high-quality data foundation for subsequent processing.

[0038] Subset optimization and fixed solution search are employed. The filtered ambiguity parameters undergo integer decorrelation processing (reducing correlation through a transformation matrix) and are sorted in ascending order of variance, prioritizing high-reliability ambiguities for solution calculation. LAMBDA technology is used to search for fixed solutions within the ambiguity subset, combined with dual-indicator verification of "bootstrapping success rate ≥ 95%" and "ratio-test threshold ≥ 3.0" to compensate for the shortcomings of single-indicator omissions / false positives.

[0039] Dynamic iteration and solution decision-making: If the dual indicators do not meet the requirements, the ambiguity combination with the largest variance is eliminated iteratively and the search is restarted until the indicators meet the requirements or there are fewer than 4 remaining combinations. When there are ≥4 remaining combinations and the indicators meet the requirements, it is determined as a fixed solution (to ensure observation redundancy and improve reliability); otherwise, the floating-point solution is retained to avoid positioning deviation caused by forced fixing.

[0040] III. Overall Effectiveness of Collaborative Work: Gross error joint processing provides clean observation data for ambiguity processing by suppressing interference errors of different magnitudes in stages; integer ambiguity optimization processing improves positioning accuracy through high-precision fixed solutions. The two form a closed loop of "interference suppression - data purification - accurate solution". This mechanism can resist strong interference in complex electromagnetic environments (anti-interference capability) and maintain solution stability (robustness) when gross errors and ambiguity anomalies occur, ultimately achieving real-time dynamic high-precision differential positioning for BeiDou-3 receivers.

[0041] Furthermore, the present invention can be flexibly adapted to actual scenarios (such as introducing inertial navigation auxiliary data to improve the gross error recognition rate in highly dynamic environments, or adjusting the verification index to adapt to scenarios with fewer observations), further expanding its applicability in complex dynamic scenarios.

Claims

1. A robust and high-precision differential positioning method with strong anti-interference capabilities, characterized in that, The real-time dynamic differential positioning method applied to BeiDou-3 receivers in complex electromagnetic environments includes the following steps: Step 1: Gross Error Co-processing: a. First, use the double-difference phase observations and double-difference pseudorange observations on B1 and B3 to form LI combined observations respectively. Combined observations with MW b. To and c. Generate a test sequence by subtracting from each epoch; d. Use the median method to identify outliers; e. For small outliers that are not eliminated, use robust estimation to iteratively calculate the equivalent weights during the parameter solution stage. Step 2: Integer Ambiguity Processing: An optimized partial ambiguity subset selection technique is adopted, specifically including: e. Preprocessing stage: Based on the limits of a cutoff elevation angle of 10° and a standard deviation of 1.5 weeks for ambiguity estimation, low-precision ambiguities are filtered out; f. The usable original ambiguity parameters obtained after filtering in step e are subjected to integer downcorrelation processing, and the resulting linear combinations of ambiguities are sorted in ascending order of variance; g. LAMBDA technique is used to search for fixed solutions of the selected ambiguity subset; h. The bootstrapping success rate and ratio-test threshold of the fixed solution are calculated. If at least one of them does not meet the preset requirements, the last linear combination of ambiguities in the sorting is removed, and step g is returned to be repeated; if the number of remaining linear combinations of ambiguities is more than 3, and both the bootstrapping success rate and the ratio-test threshold meet the preset requirements, the ambiguity subset is determined as the final fixed solution; otherwise, the floating-point solution is retained.

2. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, In step one, the LI combined observations Combined observations with MW The calculation expression is as follows: ; In the formula These represent the double-difference carrier phase observations and pseudorange observations on B1 and B3, respectively. These represent the frequency and wavelength of B1 and B3, respectively.

3. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, In step one, the standard deviation of the LI combination observation ΔL1 ranges from 0.01 to 0.02 weeks, and the standard deviation of the MW combination observation ΔL2 ranges from 0.1 to 0.2 weeks. The median method in step one is used to identify outliers, and the criterion is... , where M is the median of the sequence, MAD is the median absolute deviation, and k=5.

4. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, In step two g, the preset requirements are: bootstrapping success rate not less than 95%, and ratio-test threshold not less than 3.

0.

5. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, In step 1c, the testing logic of the median method is as follows: when a certain observation value in the sequence of observations to be tested is greater than the critical value S, it is determined that the observation value has a gross error.

6. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, In step 2f, the integer decorrelation processing involves constructing a transformation matrix to reduce the correlation of the original ambiguity parameters, thereby reducing the correlation in the ambiguity search space.

7. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, In step b, the test sequence sum is the result of the difference between epochs of the LI combination observations and the difference between epochs of the MW combination observations, and the sums both follow a normal distribution.

8. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, In step e, the specific method for filtering low-precision ambiguities is as follows: ambiguities that simultaneously satisfy a cutoff elevation angle ≥ 10° and a ambiguity estimation standard deviation ≤ 1.5 cycles are retained; otherwise, they are filtered out.

9. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, In step 1c, the critical value S of the median method is calculated based on the median M and the median absolute deviation MAD of the sequence, with the specific formula S=k×MAD, where k=5.

10. The anti-interference, robust, high-precision differential positioning method according to claim 1, characterized in that, The stage division method of the joint processing of gross errors in step one is as follows: the preprocessing stage removes large gross errors through gross error detection, and the parameter calculation stage processes small gross errors through robust estimation, so as to achieve staged targeted processing of gross errors of different magnitudes.

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