High-precision anti-interference navigation integer ambiguity fixing method

Abstract

The invention relates to the technical field of high-precision anti-interference satellite navigation, in particular to a high-precision anti-interference navigation integer ambiguity fixing method, which comprises the following steps of: S1, screening satellites of which the elevation angle is greater than 5 degrees from all visible satellites to form an available satellite set; s2, estimating by using a least square method to obtain an ambiguity floating point solution of an available satellite set; s3, integer Z transformation is carried out on the auto-covariance matrix of the ambiguity floating point solution, and an ordered ambiguity subset with ambiguity correlation weakened and precision ascending order arrangement is obtained; s4, removing the ambiguity of which the integer sequential rounding success rate is lower than a threshold value from the ordered ambiguity subset according to a positive sequence, and obtaining an initial value of a partial ambiguity subset; s5, searching ambiguity candidate integer solutions and sub-selected integer solutions of the partial ambiguity subsets; and S6, judging whether the candidate integer solution check is passed or not, and if yes, successfully fixing the ambiguity integer solution.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of high-precision anti-interference satellite navigation, and particularly relates to a high-precision anti-interference navigation integer ambiguity fixing method. BACKGROUND

[0002] Fast and reliable integer ambiguity fixing is one of the prerequisites for obtaining centimeter-level or even millimeter-level positioning accuracy. Compared with the full integer ambiguity fixing method which fixes all visible satellite ambiguity parameters, the partial integer ambiguity fixing (hereinafter referred to as partial ambiguity fixing) method which fixes only part of the visible satellite ambiguity parameters has shorter ambiguity fixing time, higher fixing success rate and higher fixing reliability, and is superior in terms of timeliness, reliability and practicability.

[0003] The core of the partial ambiguity fixing method is the selection of the partial ambiguity subset and the fixing of the integer ambiguity solution, wherein the selection of the partial ambiguity subset refers to selecting the optimal partial ambiguity subset under a certain criterion from the full ambiguity set; the fixing of the integer ambiguity solution includes: first searching for a candidate integer ambiguity solution that minimizes the objective function, and then checking the candidate integer ambiguity solution, if the checking metric is satisfied, the integer ambiguity solution is successfully fixed.

[0004] The main difference between existing partial ambiguity fixing methods lies in the selection criterion of the partial ambiguity subset and the checking metric of the integer ambiguity solution. The selection criterion of the partial ambiguity subset includes the greater the satellite elevation angle, the higher the satellite signal signal-to-noise ratio, the more the number of continuous tracking epochs of the satellite, the higher the ambiguity float solution accuracy, the smaller the ambiguity dilution of precision (ADOP), etc. The checking metric of the integer ambiguity solution includes ADOP less than an empirical threshold, ambiguity fixing success rate higher than an empirical threshold, Ratio value higher than an empirical threshold, Ratio value higher than an estimated threshold (calculated by reversing the preset value of ambiguity fixing failure rate), etc.

[0005] In existing partial ambiguity fixing methods, the selection criterion of the partial ambiguity subset and the checking metric of the integer ambiguity solution are either too many and harsh, time-consuming, or too few and lenient, one-sided, and compromise between fast fixing and reliable fixing of integer ambiguity.

[0006] The selection criteria of the above-mentioned partial ambiguity subset are multiple and strict, time-consuming, for example, the selection criteria are simultaneously satisfying satellite elevation angle, satellite signal signal-to-noise ratio, satellite continuous tracking epoch number, and ambiguity float solution precision. The check metrics are few and loose, one-sided, for example, the check metrics are that the ambiguity fixed Bootstrapping success rate is higher than the empirical threshold or the Ratio value is higher than the empirical threshold, wherein the Bootstrapping success rate can reflect the strength of the observation model, but cannot distinguish and distinguish the integer solution of the ambiguity because the real observation data is not considered; the Ratio value can compare the approximation degree of the ambiguity float solution and the integer solution, and can distinguish the distinguishability of the candidate integer solution and the sub-selected integer solution of the ambiguity, but cannot evaluate the strength of the observation model and the overall quality of the integer solution. SUMMARY

[0007] The present application aims to provide a high-precision anti-interference navigation integer ambiguity fixing method to solve the problems in the above background art.

[0008] To achieve the above-mentioned purpose, the present application provides the following technical scheme: A high-precision anti-interference navigation integer ambiguity fixing method, comprising the following steps: Step S1: selecting satellites with an elevation angle greater than 5° from all visible satellites to form a set of available satellites; Step S2: obtaining ambiguity float solutions of the set of available satellites by using least squares estimation; Step S3: performing integer Z transformation on the autocovariance matrix of the ambiguity float solutions to obtain an ordered ambiguity subset with reduced ambiguity correlation and ascending order of precision; Step S4: removing ambiguities with integer sequential rounding success rate lower than a threshold value in the ordered ambiguity subset in ascending order to obtain a partial ambiguity subset initial value; Step S5: searching for ambiguity candidate integer solutions and sub-selected integer solutions of the partial ambiguity subset; Step S6: judging whether the candidate integer solution check passes, and if so, the ambiguity integer solution is fixed successfully.

[0009] Preferably, step S2 specifically comprises: obtaining the float solution of the ambiguity parameter from the observation value of the available satellite by using the least squares method , the float solution of the position and atmospheric delay parameter , and the corresponding covariance matrix, specifically as follows (1) ; (2) ; In formula (1) and formula (2), is the coefficient matrix of the ambiguity parameter; a coefficient matrix of the position and atmospheric delay parameters; an observation vector composed of the pseudo-range and carrier phase observations, a self-covariance matrix of the observation vector an inverse matrix of a self-covariance matrix of , a self-covariance matrix of , a self-covariance matrix of , a cross-covariance matrix of , a cross-covariance matrix of ; is a vector or matrix transposition symbol.

[0010] Preferably, the integer Z transformation in step S3 specifically comprises: upper triangular decomposition: upper triangular decomposition is performed on to obtain (3); in formula (3), is an M-order unit lower triangular matrix with elements on the diagonal being 1, and M is the dimension of the ambiguity vector; is an M-order diagonal matrix with elements on the diagonal being the ambiguity condition variance; integer Gaussian elimination: if the absolute value of a non-diagonal element of exceeds 0.5, Gaussian elimination is performed on and the lower and same column elements thereof according to the following formula to make the absolute value thereof not greater than 0.5: (4); (5); … (6); in formulas (4) to (6), ; is an assignment operator, is a rounding operator; condition variance sorting: if , the adjacent two condition variances are exchanged: (7); (8); correspondingly, the matrix becomes , matrix becomes : (9); after transformation , and , , remain unchanged, and , , respectively as follows: (10); (11); in formula (11) .

[0011] After the integer Z transformation, an ordered ambiguity subset with ambiguity precision in ascending order is obtained , a conditional variance diagonal matrix , and the relationship before and after ambiguity ordering, is the ambiguity float solution of each satellite in the set of available satellites after the integer Z transformation.

[0012] Preferably, the integer Z transformation further comprises: first determine whether to perform integer Gaussian elimination, then determine , whether to order the variance, and finally determine whether to perform integer Gaussian elimination.

[0013] Preferably, step S4 comprises: from the ordered ambiguity subset , according to the ascending order, sequentially eliminate the ambiguities with integer sequential rounding success rate below the empirical threshold to obtain the partial ambiguity subset initial value; here the empirical threshold is usually 99% or 99.9%; The calculation formula of the integer sequential rounding success rate is as follows: (12); in formula (12) is a multiplication operation; is the subscript of the multiplication factor in the multiplication operation; is the cardinality of the partial ambiguity subset, ; is the distribution function of the standard normal distribution, and the calculation method is as follows: (13).

[0014] In formula (13), is the upper limit of integration, is the integral variable.

[0015] Preferably, step S5 specifically comprises: In a half-axial-length- respectively , , dimensional ellipsoid, search for ambiguity candidate integer solutions and sub-integer solutions that make the objective function take the minimum value and the second minimum value respectively; is the square root of the maximum value of the objective function, the expression of (14). In formula (14), is the ambiguity floating-point solution corresponding to is the conditional evaluation of ; Starting from the last component , the integer nodes of the feasible interval are solved; then the integer nodes of the feasible interval of , , are solved in turn; the feasible integer nodes of each component are combined, and from among the numerous combinations and that make take the minimum value and the second minimum value respectively are selected; Combine , with the rejected ambiguity in place, and then obtain the ambiguity candidate integer solution and the ambiguity sub-integer solution corresponding to the available satellite set through the inverse transformation of the integer Z transformation.

[0016] Preferably, the judgment in step S6 whether the candidate integer solution passes the check specifically comprises: The Ratio test method is used to check whether the ambiguity candidate integer solution and the ambiguity floating-point solution proximity, and its distinguishability from the ambiguity sub-integer solution Ratio value is higher than an empirical threshold , the test is passed; otherwise, the test is failed. The calculation formula of the Ratio value is as follows: (15).

[0017] Preferably, the ambiguity integer solution fixing success in step S6 specifically comprises: If the ambiguity candidate integer solution passes the test, it is accepted as the correct ambiguity value, i.e. the integer solution of the ambiguity is , and the ambiguity integer solution fixing is successful; otherwise, the first element of the partial ambiguity subset is removed, and the cardinality of the partial ambiguity subset is decreased by 1; if the cardinality of the partial ambiguity subset ≥4 and the positioning accuracy factor PDOP≤4, the ambiguity candidate integer solution in the low-dimensional space is searched and tested again, and if a low-dimensional candidate integer solution passes the test, it is accepted as the correct ambiguity value, and the ambiguity integer solution fixing is successful. If all the dimensional ambiguity candidate integer solutions fail the test, i.e. the ambiguity integer solution fixing is failed, the ambiguity floating point solution is reserved.

[0018] Compared with the prior art, the present application has the following beneficial effects: ​The application provides a high-precision anti-interference navigation integer ambiguity fixing method, which considers the cardinality of a partial ambiguity subset and the ambiguity precision, and optimizes the selection of the partial ambiguity subset as coarse selection and fine selection. The low-elevation-angle satellites with an elevation angle less than a cutoff height angle of 5° are removed from all visible satellite sets to form a usable satellite set through coarse selection; the fine selection process includes: obtaining an ordered ambiguity subset with ambiguity precision from low to high by using integer Z transformation, and then removing the ambiguities with a low integer sequential integer success rate below an empirical threshold in a normal order; the partial ambiguity subset initial value with reasonable cardinality, high precision and strong observation model strength is quickly and reliably obtained; the approximation degree of the ambiguity candidate integer solution and the floating point solution, and the distinguishability from the secondary integer solution are considered, and the ratio value is selected as the checking measurement of the ambiguity integer solution; the ratio value is defined as the ratio of the residual quadratic form of the ambiguity secondary integer solution and the ambiguity candidate integer solution, and is a reliability measurement of the ambiguity fixed solution based on actual observation value information; the closer the ambiguity candidate integer solution to the ambiguity floating point solution, the more different the candidate integer solution from the secondary integer solution, the larger the ratio value of the ambiguity candidate integer solution, and the higher the correct fixing reliability of the ambiguity integer solution; the application is different from the existing partial ambiguity fixing method in the selection of the partial ambiguity subset and the checking measurement of the ambiguity integer solution, and the fixing time of the integer ambiguity is shorter and the fixing reliability is higher. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 A flowchart of the high-precision anti-interference navigation integer ambiguity fixing method provided by the application is shown in the figure. Figure 2 A joint processing flowchart of integer Gaussian elimination and conditional variance sorting in the integer Z transformation in the high-precision anti-interference navigation integer ambiguity fixing method provided by the application is shown in the figure. DETAILED DESCRIPTION

[0020] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0021] Figure 1 A flowchart of the high-precision anti-interference navigation integer ambiguity fixing method provided by the application is shown in the figure. Figure 1 As shown in the figure, the embodiment of the application provides a high-precision anti-interference navigation integer ambiguity fixing method, which includes the following steps: Step S1: selecting the satellites with an elevation angle greater than 5° from all visible satellites to form a usable satellite set; Step S2: obtain the ambiguity float solution of the available satellite set by least square estimation; Step S3: integer Z transform the self-covariance matrix of the ambiguity float solution, to obtain an ordered ambiguity subset with reduced ambiguity correlation and ascending order of precision; Step S4: from the ordered ambiguity subset, remove the ambiguities with integer sequential rounding success rate lower than the threshold in the positive order, to obtain the partial ambiguity subset initial value; Step S5: search for the ambiguity candidate integer solution and the secondary integer solution of the partial ambiguity subset; Step S6: judge whether the candidate integer solution check passes, and if yes, the ambiguity integer solution is fixed successfully.

[0022] The integer ambiguity fixing method for high-precision anti-interference navigation provided by the application is different from the existing partial ambiguity fixing method in terms of partial ambiguity subset selection and ambiguity integer solution check measurement, and the fixing time of the integer ambiguity is shorter and the fixing reliability is higher.

[0023] It is considered that: 1) the lower the satellite elevation angle, the greater the influence of the multipath error and the ionospheric / tropospheric delay error on the satellite observation value, wherein the influence of the multipath error on the pseudo-range observation value can reach 10-20 cm, and the influence on the carrier phase observation value can reach 1 / 4 wavelength at most; 2) the low-elevation satellite is usually a rising satellite, and the accuracy of the observation value is not stable; 3) the satellite signal signal-to-noise ratio is usually positively correlated with the satellite elevation angle (that is, the satellite signal signal-to-noise ratio is low, and the satellite elevation angle is usually low), and one of the two criteria can be taken.

[0024] Therefore, in step S1, before calculating the float solution of the ambiguity vector, rough selection is performed, and the low-elevation satellites with an elevation angle less than the cutoff height angle of 5° are removed from the set of all visible satellites, and the set of high-elevation satellites greater than 5° is screened to form the available satellite set.

[0025] In an embodiment of the application, step S2 specifically comprises: ignoring the integer constraint of the ambiguity, estimating the float solution of the ambiguity parameter from the available satellite observation value by using the least square method , the float solution of the position and the atmospheric delay parameter , and the corresponding covariance matrix, specifically as follows (1) ; (2) ; In formula (1) and formula (2), is the coefficient matrix of the ambiguity parameter; is the coefficient matrix of the position and the atmospheric delay parameter; is the observation vector composed of the pseudo-range and the carrier phase observation value, The autocovariance matrix of the observed vector The inverse matrix; for The autocovariance matrix, for The autocovariance matrix, for , The cross-covariance matrix, for , The cross-covariance matrix; This is the symbol for the transpose of a vector or matrix.

[0026] Because there is correlation among the ambiguity floating-point solutions of the available satellite set, therefore The matrix is ​​not diagonal. Firstly, its diagonal elements cannot accurately reflect the ambiguity precision. Secondly, the multidimensional ellipsoid corresponding to its quadratic residual is long and narrow, resulting in low efficiency and poor accuracy when searching for integer nodes within this ellipsoidal space. Therefore, we first perform an integer Z-transform on the autocovariance matrix of the ambiguity floating-point solution, i.e., an upper triangular Cholesky (L... T The algorithm employs DL decomposition, integer Gaussian elimination, and conditional variance sorting to obtain an ordered subset of fuzzinesses sorted from low to high fuzziness precision, a conditional variance diagonal matrix sorted from large to small diagonal elements, and the relationship between fuzzinesses before and after reordering.

[0027] Figure 2 This invention provides a flowchart illustrating the joint processing of integer Gaussian elimination and conditional variance sorting in the integer Z-transform of a high-precision anti-interference navigation integer ambiguity fixing method. Specifically, as shown... Figure 2 As shown, in one embodiment of the present invention, the integer Z-transform in step S3 specifically includes: Upper triangular decomposition: right Performing upper triangular decomposition, we obtain: (3); In equation (3), It is an M-order unit lower triangular matrix with all diagonal elements being 1, where M is the dimension of the ambiguity vector; It is an M-order diagonal matrix whose diagonal elements are the conditional variance of ambiguity; Integer Gaussian elimination: like off-diagonal elements If the absolute value exceeds 0.5, apply the following formula: Perform Gaussian elimination on the elements in the same column and below it, ensuring that their absolute values ​​are no greater than 0.5. (4); (5); … (6); In equations (4) to (6), ; For assignment operators, This is the rounding operator; Conditional variance sorting: like Swap the conditional variances of two adjacent pairs: (7); (8); Accordingly, matrix Become ,matrix Become : (9); After transformation , as well as , , remain unchanged. as well as , , They are as follows: (10); (11); In formula (11) .

[0028] After integer Z-transformation, an ordered subset of fuzzy values ​​is obtained, arranged in ascending order of fuzziness precision. Conditional variance diagonal matrix And the relationship between the ambiguity before and after reordering. It is the ambiguity floating-point solution after performing an integer Z-transform on the ambiguity floating-point solutions of each satellite in the available satellite set.

[0029] In one embodiment of the present invention, the integer Z-transform further includes: like Figure 2 The combined processing flow shown indicates that: first determine Whether to perform integer Gaussian elimination before making a decision , Whether the variance is reordered is determined later. Whether to perform integer Gaussian elimination.

[0030] In one embodiment of the present invention, step S4 includes: From the ordered fuzziness subset Success rate of sequentially rounding down integers in ascending order (i.e., the success rate of bootstrapping) is below the empirical threshold. The ambiguity is obtained, and a subset of the ambiguity is obtained. Initial value; here is an empirical threshold. Usually, 99% or 99.9% is used; Integer sequential rounding success rate The calculation formula is as follows: (12); In equation (12), This is a series multiplication operation; The index of the multiplicative factor in a multiplication operation; The cardinality of a subset of ambiguities. ; The distribution function of the standard normal distribution is calculated as follows: (13).

[0031] In equation (13), This is the maximum number of points. It is the integral variable.

[0032] In one embodiment of the present invention, step S5 specifically includes: With semi-axis lengths respectively , … of Within a 3D ellipsoid, the search makes the objective function Candidate integer solutions for ambiguity, taking the minimum and second minimum values ​​respectively. and second-choice integer solutions ; The square root of the maximum value of the objective function. The expression is as follows: (14); In equation (14), To and The corresponding fuzzy floating-point solution, for Conditional valuation; From the last component First, solve for the integer nodes of its feasible interval; then solve for them sequentially. , , …, integer nodes of the feasible interval; combining the feasible integer nodes of each component, selecting from the numerous combinations the one that makes respectively take the minimum value, the second minimum value and ; combining , respectively with the eliminated ambiguity in situ, and then through inverse transformation of the integer Z transformation to obtain ambiguity candidate integer solution and ambiguity second integer solution .

[0033] In an embodiment of the present application, the judgment in step S6 whether the candidate integer solution passes the check specifically includes: using the Ratio test method to check the closeness of the ambiguity candidate integer solution to the ambiguity float solution , and the distinguishability of the ambiguity candidate integer solution to the ambiguity second integer solution : if the Ratio value of is higher than the empirical threshold value , then the check passes; otherwise, the check fails; here, the empirical threshold value is usually taken as 2.5 or 3; The calculation formula of the Ratio value is as follows: (15).

[0034] In an embodiment of the present application, the ambiguity integer solution fixing success in step S6 specifically includes: if the ambiguity candidate integer solution passes the check, then it is accepted as the correct ambiguity value, that is, the integer solution of the ambiguity is , and the ambiguity integer solution fixing success; otherwise, the first element of the partial ambiguity subset is eliminated, and the cardinality of the partial ambiguity subset decreases by 1; if the cardinality of the partial ambiguity subset ≥4 and the positioning accuracy factor PDOP≤4, then the ambiguity candidate integer solution and the ambiguity second integer solution in the low-dimensional space are re-searched and checked; if a certain low-dimensional candidate integer solution passes the check, then it is accepted as the correct ambiguity value, and the ambiguity integer solution fixing success; if all the dimensional ambiguity candidate integer solutions fail the check, that is, the ambiguity integer solution fixing fails, then the ambiguity float solution is retained.

[0035] The application provides a high-precision anti-interference navigation fast and reliable integer ambiguity fixing method, which takes into account the cardinality of partial ambiguity subsets and ambiguity precision, and optimizes partial ambiguity subsets to be selected as coarse selection and fine selection. Low-elevation-angle satellites with an elevation angle less than a cutoff height angle of 5° are removed from all visible satellite sets to form a usable satellite set through coarse selection; the fine selection process includes: first, obtaining an ordered ambiguity subset with ambiguity precision from low to high by using integer Z transformation, and then removing ambiguities with a low success rate of integer sequential rounding in a positive order; fast and reliable partial ambiguity subset initial values with reasonable cardinality, higher precision and strong observation model are obtained; the approximation degree of ambiguity candidate integer solution and floating point solution, and the distinguishability from the secondary integer solution are taken into account, and the ratio value is selected as the check measure of the ambiguity integer solution. The ratio value is defined as the ratio of the residual quadratic form of the ambiguity secondary integer solution and the ambiguity candidate integer solution, and is a reliability measure of the ambiguity fixed solution based on actual observation value information; the closer the ambiguity candidate integer solution to the ambiguity floating point solution, the more different the candidate integer solution from the secondary integer solution, the larger the ratio value of the ambiguity candidate integer solution, and the higher the correct fixing reliability of the ambiguity integer solution.

[0036] Although embodiments of the application have been shown and described, it is to be understood that various modifications, substitutions, replacements and variations can be made to these embodiments without departing from the principles and spirit of the application, and the scope of the application is defined by the appended claims and their equivalents.

Claims

1. A high-precision anti-interference navigation integer ambiguity fixing method, characterized in that, The method comprises the following steps: Step S1: selecting satellites with an elevation angle greater than 5° from all visible satellites to form a set of available satellites; Step S2: obtaining a float ambiguity solution of the set of available satellites by using a least square estimation method; Step S3: performing an integer Z transformation on a self-covariance matrix of the float ambiguity solution to obtain an ordered ambiguity subset with weakened ambiguity correlation and ascending order of precision; Step S4: removing ambiguities with a success rate of integer sequential rounding lower than a threshold value in a positive order from the ordered ambiguity subset to obtain a partial ambiguity subset initial value; Step S5: searching for an ambiguity candidate integer solution and a secondary integer solution of the partial ambiguity subset; Step S6: judging whether the candidate integer solution passes a check, and if yes, fixing the ambiguity integer solution successfully.

2. The method according to claim 1, wherein the method is characterized by, Step S2 specifically comprises: Least squares method for estimating float solution of ambiguity parameters from available satellite observations , position and atmospheric delay parameters and the corresponding covariance matrix, as follows （1）； （2）； in formula (1) and formula (2), is a coefficient matrix of the ambiguity parameters; is a coefficient matrix of the position and atmospheric delay parameters; is an observation vector composed of the pseudo-range and carrier phase observations, is a self-covariance matrix of the observation vector is an inverse matrix of is is a self-covariance matrix of is is a self-covariance matrix of is , is a cross-covariance matrix of is , is a cross-covariance matrix of is a vector or matrix transpose symbol.

3. The method according to claim 2, wherein the method is characterized by, The integer Z transformation in Step S3 specifically comprises: Upper triangular decomposition: To perform upper triangular decomposition, we get: （3）； In formula (3), is an M-order unit lower triangular matrix with 1 on the diagonal, and M is the dimension of the ambiguity vector; is an M-order diagonal matrix with the ambiguity condition variance on the diagonal. Integer Gaussian elimination: If the absolute value of the non-diagonal element of is more than 0.5, the Gauss elimination is performed on and its lower, same column element according to the following formula, so that the absolute value is not more than 0.5: （4）； （5）； … （6）； In formulas (4) to (6), ; is an assignment operator, is a rounding operator; Conditional variance sorting: If Swap the two adjacent conditional variances: （7）； （8）； Accordingly, the matrix becomes , the matrix becomes : （9）； after the transformation , and , , remain unchanged, and , , respectively as follows: （10）； （11）； In formula (11) . After the integer Z transformation, the ordered ambiguity subset arranged in ascending order of ambiguity precision is obtained , the conditional variance diagonal matrix , and the relationship before and after the ambiguity ordering, is the ambiguity float solution of each satellite in the available satellite set after the integer Z transformation.

4. The method according to claim 3, wherein the method is characterized by, The integer Z transformation further comprises: First determine whether to perform integer Gaussian elimination, and then determine , whether to reorder the variances, and then determine whether to perform integer Gaussian elimination.

5. The method according to claim 4, wherein the method is characterized by, Step S4 specifically comprises: from the ordered ambiguity subset , sequentially eliminate the integer sequential rounding success rate in accordance with the positive order below the empirical threshold of ambiguity, get the partial ambiguity subset initial value; Integer sequential rounding success rate The calculation formula is as follows: （12）； In formula (12), is a product operation; is an index of a multiplication factor in the product operation; is a cardinality of a partial ambiguity subset, ; is a distribution function of a standard normal distribution, and is calculated as follows: （13）。 In formula (13), is the upper limit of integration, is the integration variable.

6. The integer ambiguity fixing method for high-precision anti-jamming navigation according to claim 5, characterized in that, Step S5 specifically comprises: With semi-axis lengths respectively , … of Within a 3D ellipsoid, the search makes the objective function Candidate integer solutions for ambiguity, taking the minimum and second minimum values ​​respectively. and second-choice integer solutions ; The square root of the maximum value of the objective function. The expression is as follows: （14）； In formula (14), corresponding to the corresponding ambiguity float solution, is the conditional estimate; from the last component Start, solve the integer nodes of its feasible interval; then solve the integer nodes of the feasible interval in turn , ,… Combine the feasible integer nodes of each component, select the combination that makes respectively take the minimum value, the second minimum value and ; The ambiguity candidates are combined with the in-situ combined ambiguity candidates and the ambiguity candidates are combined with the in-situ combined ambiguity candidates , respectively, and the ambiguity candidates are combined with the in-situ combined ambiguity candidates and the ambiguity candidates are combined with the in-situ combined ambiguity candidates and the ambiguity candidates are combined with the in-situ combined ambiguity candidates and the ambiguity candidates are combined with the in-situ combined ambiguity candidates .

7. The method according to claim 6, wherein the method is characterized by, The judgment of whether the candidate integer solution passes the check in Step S6 specifically comprises: The Ratio test method is used to evaluate candidate integer solutions for ambiguity. With ambiguity floating-point solution The degree of closeness, and its relationship with the second-choice integer solution of ambiguity. The degree of distinguishability is checked: if The Ratio value is higher than the empirical threshold. If yes, the check passes; otherwise, the check fails. A calculation formula of the Ratio value is as follows: （15）。 8. The integer ambiguity fixing method for high-precision anti-jamming navigation according to claim 7, characterized in that, The fixing of the ambiguity integer solution successfully in Step S6 specifically comprises: If the ambiguity candidate integer solution is accepted as the correct ambiguity value, i.e. the integer solution of ambiguity is , the ambiguity integer solution is fixed successfully; otherwise, the first element of the partial ambiguity subset is rejected, the cardinality of the partial ambiguity subset is decreased by 1; if the cardinality of the partial ambiguity subset is greater than or equal to 4 and the positioning dilution of precision PDOP is less than or equal to 4, the ambiguity candidate integer solution in the low-dimensional space is re-searched and checked; if a low-dimensional candidate integer solution passes the check, it is accepted as the correct ambiguity value, and the ambiguity integer solution is fixed successfully; If none of the dimension ambiguity candidates integer solution passes the check, i.e. ambiguity integer solution fixing fails, the ambiguity float solution is kept .

Images