A GNSS partial ambiguity fixing method based on the coupling of OST and ADOP

Abstract

The present invention discloses a method for fixing partial ambiguities of GNSS based on the coupling of OST and ADOP. The feature is that the optimal stopping theory is used to conduct a reliability test on all-set ambiguities. If it passes, the fixed solution of the current epoch is obtained and the process ends. Otherwise, the next step of screening is carried out, one satellite is removed and then the reliability test is conducted again. If it passes, the loop of the current epoch ends. Otherwise, another satellite is continuously removed until the ambiguity subset with the smallest ADOP and successful reliability test is selected. If there is still one satellite that fails the reliability test, the floating-point solution is maintained for the current epoch. Compared with the prior art, the present invention ensures that the obtained ambiguity subset is optimal, improves the search efficiency of partial ambiguities and guarantees the accuracy of the position result, reduces the complexity of searching a large number of ambiguity subsets, and is especially suitable for precise positioning in practical scenarios, having good application prospects.

Description

Technical Field

[0001] The present invention relates to the technical field of GNSS high-precision positioning, and particularly to a method for fixing partial ambiguities of GNSS (Global Navigation Satellite System) based on the coupling of OST (Optimal Stopping Theory) and ADOP (Ambiguity Dilution of Precision). Background Art

[0002] As an important observation value of GNSS, the correct fixation of carrier phase observations is crucial for obtaining high-precision GNSS parameter solutions. Thanks to stable solution models and precise ambiguity fixation algorithms, carrier phase ambiguities can be fixed relatively accurately in both relative positioning and precise point positioning. With the emergence of multi-system and multi-frequency observations and the increase of uncertain factors in the observation process, the difficulty of correctly fixing ambiguities increases and the fixation efficiency decreases, posing challenges to the development of GNSS high-precision precise positioning.

[0003] Although the strength of the GNSS observation model will continuously increase with the increase of redundant observations, and the accuracy of the corresponding real floating-point solution will also increase, the benefits brought by this redundant observation will decrease after reaching a certain level. Similarly, in the fixation of ambiguities, it is not necessary for all ambiguity observation values to participate in the fixation. Selecting a suitable subset of ambiguities from a high-dimensional ambiguity set for fixation can also obtain high-precision baseline results. The concept of partial ambiguities is proposed to find the most suitable subset of ambiguities. ADOP, as an index describing the accuracy of ambiguity parameters, can accurately capture the internal characteristics of the ambiguity variance-covariance matrix. Due to its extremely high approximation of the average accuracy information of ambiguities and its good approximation of the success rate of integer least squares ambiguities, it is used as an index to evaluate the accuracy of subsets of ambiguities in partial ambiguity fixation to help find the subset of ambiguities with the highest accuracy in the ambiguity set.

[0004] As a widely used method for fixing partial ambiguities, the ADOP minimum priority fixation method enumerates all subsets of ambiguities to calculate the ADOP value, selects the group of ambiguities with the minimum ADOP value for fixation, and conducts a reliability test after fixation. If the test fails, one satellite is deleted and then the subset with the minimum ADOP is searched for again for fixation and the ambiguity reliability test is performed. If the subset of ambiguities passes the ambiguity reliability test, the search stops; otherwise, satellites are continuously deleted and the search continues. It can be seen that when selecting the subset of ambiguities with the minimum ADOP, in the worst case, all subsets of ambiguities need to be enumerated for inspection.

[0005] Some of the ambiguity fixing methods in the prior art require a large number of searches for ambiguity subsets. As the number of ambiguities increases, the number of candidate ambiguity subsets will increase exponentially, increasing the difficulty of searching for the minimum ADOP subset, consuming a large amount of resources for program operation, having a low ambiguity search efficiency, reducing the efficiency of program operation, having poor accuracy of position results, and low positioning accuracy. Summary of the Invention

[0006] The object of the present invention is to provide a GNSS partial ambiguity fixing method based on the coupling of OST and ADOP in view of the deficiencies of the prior art. The optimal stopping theory is used for the search of GNSS partial ambiguities, which can search for the ambiguity subset corresponding to the minimum ADOP with the highest probability while greatly reducing the number of enumerated ambiguity subsets, thereby completing ambiguity fixing. The method is simple, has a good use effect, and has high positioning accuracy. It can effectively reduce the complexity of the large number of searches for ambiguity subsets required by the ordinary method of finding the minimum ADOP for partial ambiguities, and can ensure to the greatest extent that the obtained ambiguity subset is optimal, improve the search efficiency of partial ambiguities as much as possible, and ensure the accuracy of position results, effectively solving the problem of searching for a large number of ambiguity subsets in GNSS partial ambiguity fixing based on ADOP, especially suitable for precise positioning in actual scenarios, and having good application prospects.

[0007] The specific technical solution to achieve the object of the present invention is: a GNSS partial ambiguity fixing method based on the coupling of OST and ADOP, characterized in that the optimal stopping theory is used for the search of GNSS partial ambiguities, and the ambiguity subset corresponding to the minimum ADOP is searched with the highest probability while reducing the number of enumerated ambiguity subsets. The ambiguity fixing specifically includes the following steps:

[0008] Step 1: Perform Kalman filter parameter calculation on the combined GNSS multi-system observation data to obtain the floating-point solution of the ambiguity and the variance-covariance matrix;

[0009] Step 2: Perform a preliminary screening on the floating-point solution of the ambiguity from the cycle slip index, elevation angle index, and continuous tracking epoch index to obtain m floating-point ambiguities to be fixed;

[0010] Step 3: Use the LAMBDA algorithm to fix the full-set ambiguity and perform a reliability test. If the reliability test is passed, the fixed solution of the current epoch is obtained and the process ends. If the reliability test fails, the next screening is performed;

[0011] Step 4: Exclude one satellite, select m - 1 floating-point ambiguities from the m floating-point ambiguities in turn to generate ambiguity subsets, record the minimum ADOP value in the first 37% of the ambiguity subsets as the reference value; calculate the ADOP of the remaining ambiguity subsets in turn and compare it with the reference value. If it is greater than the reference value, continue to compare the remaining ambiguity subsets. If it is less than the reference value, stop the subsequent comparison and use LAMBDA to fix and perform reliability test on this ambiguity subset;

[0012] Step 5: If the reliability test is successful, end the loop of the current epoch. If the reliability test fails, continue to exclude one satellite, and then repeat Step 4 until the ambiguity subset with the minimum ADOP and successful reliability test is selected. If there is still one satellite that fails the reliability test, keep the floating-point solution for the current epoch.

[0013] In the above Step 1, no additional satellite selection is required, and the floating-point solution of the ambiguity can be directly obtained by using the Kalman filter.

[0014] In the above Step 2, the floating-point solution of the ambiguity is preliminarily screened from the cycle slip index, elevation angle index, and continuous tracking epoch index to exclude satellites with poor observation quality, and m floating-point ambiguities to be fixed are obtained.

[0015] In the above Step 3, the full set and the ambiguity are fixed to ensure that the ambiguity with the minimum ADOP is selected. The ADOP adopted in the present invention is obtained by the following formula (1):

[0016]

[0017] where is the average of the square roots of the variances of different-frequency carrier phase observations; σ φj represents the square root of the variance of the phase observation data in the j frequency band; is the factorial of the wavelengths of different frequencies; m is the number of satellites; s represents the s-th satellite; w s represents the weight of the s-th satellite elevation angle for weight determination; is the average of the square roots of the variances of different-frequency pseudorange observations; σ pj represents the square root of the variance of the pseudorange observation data in the j frequency band; k represents the number of systems.

[0018] In the above Step 4, select n satellites from the m floating-point ambiguities, and calculate the ADOP for the ambiguity subsets of the first 37% of the nodes generated each time, then the reference ADOP value can be obtained.

[0019] In step 5, after removing one satellite, it is not necessary to calculate the ADOP of all remaining ambiguity subsets. It is only necessary to compare the ADOP of each ambiguity subset with the ADOP reference value. If it is less than the reference value, stop further searching; otherwise, continue to find a suitable ambiguity subset.

[0020] Compared with the prior art, the present invention has the advantages of simple method, good use effect, high positioning accuracy. It can search for the ambiguity subset corresponding to the minimum ADOP with the highest probability to complete ambiguity fixing while greatly reducing the number of enumerated ambiguity subsets, effectively reducing the complexity of the method of searching a large number of ambiguity subsets for the part with the minimum ordinary ADOP, and can ensure to the greatest extent that the obtained ambiguity subset is optimal, improve the search efficiency of the partial ambiguity as much as possible, and ensure the accuracy of the position result, effectively solving the problem of searching a large number of ambiguity subsets in GNSS partial ambiguity fixing based on ADOP, especially suitable for precise positioning in actual scenarios, and having good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flowchart of the present invention;

[0022] Figure 2 is a graph of the number of visible GPS and GALILEO satellites on the 313th day of the year 2022;

[0023] Figure 3 is a graph of the ambiguity fixing rate on the day of the year without any partial ambiguity fixing algorithm;

[0024] Figure 4 is a graph of the number of ambiguities in the ambiguity subset finally selected by the OST-ADOP coupling model at each epoch on the 313th day of the year 2022;

[0025] Figure 5 is a graph of the ambiguity fixing rate of the OST-ADOP coupling model and the ordinary ADOP model for consecutive days; Figure 6 is a graph of the ambiguity fixing success rate of the OST-ADOP coupling model and the ordinary ADOP model;

[0026] Figure 7 is a graph of the time consumption of the multi-day solution of the OST-ADOP coupling model and the ordinary ADOP model;

[0027] Figure 8 is a graph of the root mean square error of the multi-day solution of the baselines in the east, north, and zenith directions of the OST-ADOP coupling model and the ordinary ADOP model. DETAILED DESCRIPTION OF THE INVENTION

[0028] Refer to Figure 1 , the present invention specifically includes the following steps:

[0029] Step 1: Perform single-epoch solution on the GNSS multi-system short-baseline relative positioning observation data for consecutive days to obtain the ambiguity float solution and variance-covariance under Kalman filtering;

[0030] Step 2: Perform preliminary screening on the ambiguity float solution according to indicators such as cycle slips, elevation angles, and consecutive tracking epochs;

[0031] Step 3: Fix the full set of ambiguities using the LAMBDA algorithm and set ratio to 3 for reliability test after ambiguity fixing. If the test passes, end the ambiguity fixing for the current epoch to obtain the parameter fixed solution. If the reliability test fails, prepare for partial ambiguity fixing by coupling OST and ADOP. ADOP is calculated by the following formula (1):

[0032]

[0033] where, is the average of the square roots of the variances of carrier phase observations at different frequencies; σ φj represents the square root of the variance of the phase observation data in the j frequency band; is the factorial of the phase wavelengths at different frequencies; m is the number of satellites; s represents the s-th satellite; w s represents the weight for weighting the elevation angle of the s-th satellite; is the average of the square roots of the variances of pseudorange observations at different frequencies; σ pj represents the square root of the variance of the pseudorange observation data in the j frequency band; k represents the number of systems;.

[0034] Step 4: Exclude any one satellite from the m floating ambiguity parameters, record (n = m - i, i = 1) The minimum ADOP value in the first 37% of the ambiguity subsets is used as the reference value, and then the ADOP values of the remaining ambiguity subsets are compared with the reference value in turn. If it is less than the reference value, stop the subsequent comparison, and use LAMBDA to fix and test the current ambiguity subset. If the test passes, end the search for the optimal ambiguity subset for the current epoch to obtain the parameter fixed solution. If it is greater than the reference ADOP, continue the comparison until all the remaining 63% of the ambiguity subsets have been compared, and make a judgment on i.

[0035] Step 5: If the parameter fixed solution still cannot be obtained when i = m - 1, output the floating solution for the current epoch. If i < m - 1, then i += 1, and repeat Step 4.

[0036] The following further illustrates the present invention through specific embodiments on the 313th - 320th day of the year 2022 in terms of the day of the year.

[0037] Embodiment 1

[0038] In step 1, taking short - distance relative positioning as an example, two consecutive observation points with a distance of about 20 m are selected to form a baseline. The GPS and GALILEO single - frequency dual - system observation data from the 313th to 320th day of the year 2022 are selected as the experimental data. The Kalman filter solution is used to perform single - epoch solution on the experimental data to obtain the float ambiguity solution and the float variance - covariance matrix.

[0039] In step 2, the float ambiguities are preliminarily screened using cycle - slip indicators, elevation angle indicators, and the number of consecutive tracking epochs indicators to eliminate low - quality ambiguities and reduce the number of ambiguities as much as possible.

[0040] Refer to Figure 2 , for the GPS and GALILEO on the 313th day of the year 2022, the number of visible satellites in most epochs is about 11 - 14.

[0041] In step 3, first, the LAMBDA algorithm is used to fix all - set ambiguities and perform reliability tests.

[0042] Refer to Figure 3 , for the period from the 313th to 320th day of the year 2022 without any partial - ambiguity - fixing algorithms, the ambiguity - fixing rates are 80.5%, 80.9%, 76.3%, 80.4%, 78.5%, 78.7%, 78.9%, and 77.1% respectively.

[0043] In step 4, each time (n = m - i, i += 1) ambiguity sets are detected using the OST - ADOP coupling model, and the ambiguity subset with the minimum ADOP is selected for LAMBDA fixing and reliability testing.

[0044] Refer to Figure 4 , for all epochs on the 313th day of the year 2022, the number of ambiguities in the optimal ambiguity subset finally selected by the OST - ADOP coupling model is about 6 - 12.

[0045] In step 5, according to the reliability test results in step 4, the current epoch is ended or step 4 is repeated.

[0046] Refer to Figure 5 , through the ambiguity - fixing rates of the OST - ADOP coupling model and the ordinary ADOP model, it shows that without the premise of finding the ambiguity subset corresponding to the minimum ADOP, the OST - ADOP coupling model can ensure a fixing rate equivalent to that of the ordinary ADOP model.

[0047] Refer to Figure 6, the ambiguity fixing success rates of the OST-ADOP coupling model and the ordinary ADOP model indicate that without the need to find the ambiguity subset corresponding to the minimum ADOP, the OST-ADOP coupling model can ensure a comparable fixing success rate to the ordinary ADOP model.

[0048] See Figure 7 , the multi-day solution time consumption of the OST-ADOP coupling model and the ordinary ADOP model indicates that without the need to find the ambiguity subset corresponding to the minimum ADOP, the OST-ADOP coupling model can save the time required for ambiguity fixing.

[0049] See Figure 8 a. The root mean square error of the baseline multi-day solution of the eastward OST-ADOP coupling model and the ordinary ADOP model indicates that without the need to find the ambiguity subset corresponding to the minimum ADOP and with less time required, the eastward baseline accuracy of the OST-ADOP coupling model is comparable to that of the ordinary ADOP model.

[0050] See Figure 8 b. The root mean square error of the baseline multi-day solution of the northward OST-ADOP coupling model and the ordinary ADOP model indicates that without the need to find the ambiguity subset corresponding to the minimum ADOP and with less time required, the northward baseline accuracy of the OST-ADOP coupling model is comparable to that of the ordinary ADOP model.

[0051] See Figure 8 c. The root mean square error of the baseline multi-day solution of the upward OST-ADOP coupling model and the ordinary ADOP model indicates that without the need to find the ambiguity subset corresponding to the minimum ADOP and with less time required, the upward baseline accuracy of the OST-ADOP coupling model is comparable to that of the ordinary ADOP model.

[0052] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claimed rights.

[0053] In addition, it should be understood that although this specification is described in terms of embodiments, not every embodiment contains only one independent technical solution. This narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A GNSS partial ambiguity fixing method based on the coupling of OST and ADOP, characterized in that: The optimal stopping theory is adopted to search for the GNSS partial ambiguities. The ambiguity fixing specifically includes the following steps: Step 1: Solve the Kalman filter parameters for the GNSS multi-system combined observation data to obtain the floating-point solution of the ambiguities and the variance-covariance matrix; Step 2: Preliminarily screen the floating-point solution of the ambiguities based on the cycle slip index, elevation angle index, and continuous tracking epoch number index to obtain m floating-point ambiguities to be fixed; Step 3: Use the LAMBDA algorithm to fix the full set of ambiguities and perform a reliability test. If the reliability test is passed, the fixed solution of the current epoch is obtained and the process ends. If the reliability test fails, the next screening is carried out; Step 4: Exclude one satellite, select m - 1 floating-point ambiguities from the m floating-point ambiguities to generate ambiguity subsets in sequence, record the minimum ADOP value in the first 37% of the ambiguity subsets as the reference value; calculate the ADOP of the remaining ambiguity subsets in sequence and compare it with the reference value. If it is greater than the reference value, continue to compare the remaining ambiguity subsets; if it is less than the reference value, stop the subsequent comparison, and use LAMBDA to fix and perform a reliability test on this ambiguity subset; Step 5: If the reliability test is successful, end the loop of the current epoch. If the reliability test fails, continue to exclude one satellite, and then repeat Step 4 until the ambiguity subset with the minimum ADOP and successful reliability test is selected; if there is still one satellite that fails the reliability test, keep the floating-point solution for the current epoch.

2. The GNSS partial ambiguity fixing method based on the coupling of OST and ADOP according to claim 1, wherein In Step 4, n satellites are selected from the m floating-point ambiguities, and the ADOP of the ambiguity subsets of the first 37% of the nodes generated each time is calculated to obtain the ADOP reference value. The ADOP is obtained through the following formula (1): Among them, is the average of the square roots of the carrier phase observation variances at different frequencies; σ φj represents the square root of the variance of the phase observation data in the j frequency band; is the factorial of the phase wavelengths at different frequencies; m is the number of satellites; s represents the s-th satellite; w s represents the weight for weighting by the elevation angle of the s-th satellite; is the average of the square roots of the pseudorange observation variances at different frequencies; σ pj represents the square root of the variance of the pseudorange observation data in the j frequency band; k represents the number of systems.

3. The GNSS partial ambiguity fixing method based on the coupling of OST and ADOP according to claim 1, characterized in that, In Step 5, if the reliability test fails, continue to exclude one satellite. The ADOP of each ambiguity subset needs to be compared with the ADOP reference value. If it is less than the reference value, stop the continuous search; otherwise, continue to find a suitable ambiguity subset.

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