A GNSS Integer Ambiguity Fixation Method Integrating Intelligent Optimization Algorithm and VIB Strategy

Abstract

This invention discloses a GNSS integer ambiguity fixing method integrating intelligent optimization algorithms and VIB strategies, belonging to the field of satellite navigation and positioning technology. This method combines the advantages of VIB strategies and swarm intelligence fusion optimization algorithms. By directionally grouping the ambiguity floating-point solution covariance structure, the ambiguities are guided into groups. The PSOAF and AWDE intelligent optimization algorithms are used to perform parallel searches on the grouped ambiguities, improving search efficiency and positioning accuracy. Simultaneously, the probability assessment and fixing judgment of the integer solutions of each sub-block ambiguity and the overall ambiguity ensure the reliability of the ambiguity solutions, making it suitable for complex and dynamic GNSS positioning scenarios.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, and in particular to a GNSS integer ambiguity fixing method that integrates intelligent optimization algorithms and VIB strategies. Background Technology

[0002] With the rapid development of Global Navigation Satellite System (GNSS) technology and its widespread application in key areas such as national defense and security, smart cities, disaster monitoring and early warning, low-altitude economy, and autonomous driving, the requirements for high precision, reliability, and real-time performance in navigation and positioning systems are increasing. Among numerous navigation and positioning technologies, carrier phase observation, due to its centimeter-level or even millimeter-level measurement accuracy, has become one of the core methods for high-precision GNSS positioning. In high-precision GNSS carrier phase differential positioning, the correct fixation of integer ambiguity is a crucial step in achieving centimeter-level or even millimeter-level positioning accuracy.

[0003] While the LAMBDA algorithm (Least Squares Ambiguity Decorrelation) and its improved versions (such as MLAMBDA and C-LAMBDA) are currently the main solution techniques, they suffer from low search efficiency and low fixation rate when facing complex conditions such as dynamic scenes, multi-system fusion, and high-dimensional ambiguity. In recent years, swarm intelligence optimization algorithms (such as Particle Swarm Optimization (PSO) and Artificial Fish Swarm Optimization (AFSA)) have been introduced into the field of integer ambiguity solution to replace the integer least squares search process. These algorithms have achieved some success in static scenes with fusion strategies, but still suffer from problems such as search efficiency depending on the quality of covariance estimation and susceptibility to misjudgment. The VIB-BIE algorithm (Miao et al., J Geodesy), published in 2024, proposes to use a vector block self-guided (VIB) strategy for integer enumeration search within the "Best Integer Equivariant Estimation (BIE)" framework, effectively improving the enumeration efficiency and accuracy in high-dimensional spaces. However, this method has not yet incorporated an intelligent optimization mechanism or prior structural information, limiting its real-time performance and versatility. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides a GNSS integer ambiguity fixing method that integrates intelligent optimization algorithm and VIB strategy. This method integrates VIB strategy and intelligent optimization strategy to improve positioning performance and stability in complex and dynamic environments.

[0005] To achieve the above objectives, the present invention adopts the following technical solution, including:

[0006] A method for fixing GNSS integer ambiguities by integrating intelligent optimization algorithms and VIB strategies includes the following steps:

[0007] S1: Based on the received observation data, establish a carrier phase double difference model. Under the premise of ignoring the integer constraints of ambiguity, use the least squares method to calculate the floating-point solutions of the parameters to be determined and the ambiguity, as well as the corresponding variance-covariance matrix.

[0008] S2: Perform integer transformation on the floating-point solution of ambiguity and the variance-covariance matrix, and use the Cholesky decomposition method to reduce the correlation between the variance-covariance matrix, thereby reducing the correlation between ambiguity variables and narrowing the integer search space;

[0009] S3: Perform eigenvalue decomposition on the variance-covariance matrix, divide the ambiguity direction groups according to the magnitude of the eigenvalues, and set the inflation factor to dynamically adjust the covariance to adapt to different data quality.

[0010] S4: Based on the dimension of the sub-block and the objective function, select different intelligent optimization algorithms to perform parallel block integer optimal solution search. When the ambiguity dimension of the sub-block is less than or equal to the set dimension, select the PSOAF algorithm to search for ambiguity. When the ambiguity dimension of the sub-block is greater than the set dimension, select the AWDE algorithm to search for ambiguity.

[0011] S5: Calculate the confidence level (ACP) of the fixed ambiguity of each sub-block, sort the sub-blocks from high to low confidence level, concatenate the ambiguities one by one, update the variance-covariance matrix, and filter out unreliable results;

[0012] S6: Calculate the global reliability ACP. If the threshold condition is met, output an integer solution. If the condition is not met, backtrack to a certain sub-block and search again or adjust the algorithm parameters until the reliability condition is met.

[0013] S7: Substitute the fixed ambiguity back into the original observation model to calculate the final coordinate parameters to be determined.

[0014] Preferably, in step S1, the carrier phase double-difference model is as follows:

[0015] GNSS carrier phase observations are expressed as follows:

[0016] (1)

[0017] Among them, subscript For receiver number, superscript Number the satellite; To from satellite to receiver The carrier phase measurement value; To from satellite to receiver geometric distance; The speed of light; Satellite signal transmission time Clock difference; For signal receiving timing receiver Clock difference; Wavelength; For ionospheric delay; For tropospheric delay; This is the carrier phase deviation term; This is carrier observation noise;

[0018] First, we use the single-difference observation equations obtained from different stations to form a single-difference observation equation, as shown below:

[0019] (2)

[0020] in, The difference in carrier phase measurement between different stations, The carrier phase measurement value of the reference station. The carrier phase measurement value of the monitoring station. This represents the difference in geometric distance from the satellite to the receiver at different stations. For the carrier phase deviation term of the reference station, For the carrier phase deviation term of the monitoring station, The difference in carrier observation noise between different stations;

[0021] Next, the single-difference observation equation is converted into a double-difference observation equation by inter-satellite double-difference, as shown in the following equation:

[0022] (3)

[0023] in, The carrier phase measurement difference between different satellites and different stations. This represents the difference in geometric distance from different satellites and different stations to the receiver. and Satellites Carrier phase deviation term at different stations, For carrier observation noise differences between different satellites and different stations;

[0024] In equations (2) and (3), , These represent the differences between different satellites and different receivers;

[0025] Equation (3) is linearized and transformed into an error equation based on Taylor series and parameter representation:

[0026] (4)

[0027] in, For the residual vector, The coefficient matrix, For an unknown parameter vector, For observation vectors;

[0028] In equation (4), The first three unknown parameters are the receiver's coordinates, and from the fourth parameter to the... n -1 parameter represents the difference in integer ambiguity. n This represents the number of satellites observed by the receiver.

[0029] Preferably, in step S1, the floating-point solution estimation of the ambiguity is specifically as follows:

[0030] The carrier phase observation equation is expressed as:

[0031] (5)

[0032] in, Represents the mathematical expectation operator. For the observation vector, For ambiguity parameters, Let be the coordinate parameters to be determined. To observe noise;

[0033] Based on the principle of least squares estimation, the objective function for solving equation (5) is:

[0034] (6)

[0035] in, Let be the variance matrix of the observation vectors;

[0036] The floating-point solution of the ambiguity parameter is calculated while ignoring the integer properties of ambiguity. Floating-point solution of coordinate parameters and the corresponding variance-covariance matrix ;

[0037] in, Let Variance be the variance matrix of the floating-point solution for ambiguity. Let Variance be the floating-point solution of the position parameters. and Let be the covariance matrix between the ambiguity floating-point solution and the position parameter floating-point solution.

[0038] Preferably, in step S2, the integer transformation and decorrelation processing are specifically as follows:

[0039] By performing an integer Gaussian transform on the ambiguity parameters and their variance-covariance matrix, The transformation, from the original space to a new space, achieves decorrelation of ambiguity:

[0040] (7)

[0041] in, , , These represent the real-valued ambiguity, integer-valued ambiguity, and variance-covariance matrix after integer transformation, respectively. It is an integer transformation matrix;

[0042] Since the variance-covariance matrix is ​​a symmetric positive definite matrix, and its principal minors are not zero, Choleskey decomposition is performed for computational convenience, i.e.:

[0043]

[0044] (8)

[0045] in, It is a lower triangular matrix. It is a diagonal matrix; after the decorrelation stage, The absolute value of the off-diagonal elements of a matrix is ​​less than or equal to 0.5. The diagonal elements are sorted in descending order.

[0046] Preferably, in step S3, the ambiguity vector is dynamically grouped, as shown below:

[0047] Perform eigenvalue decomposition on the covariance matrix:

[0048] (9)

[0049] in, This is the eigenvector matrix, where each column represents a principal direction of ambiguity; For the covariance eigenvalues ​​arranged in descending order, when Large indicates high uncertainty in the search space; when A number of hours indicates high reliability of the search space;

[0050] Ambiguity direction groups are divided according to the magnitude of the eigenvalues:

[0051] (10)

[0052] in, The first set based on the covariance eigenvalue k Layer-by-layer threshold; K The number of blocks; For ambiguity direction groups;

[0053] To dynamically adapt to different data qualities, a continuous adaptive expansion method is used for each group. Set an expansion factor:

[0054] (11)

[0055] in, It is the expansion factor; It is a parameter that adjusts the degree of expansion; The larger the value, the lower the confidence level.

[0056] Inflation factor matrix Represented as:

[0057] (12)

[0058] Covariance inflation is:

[0059] (13)

[0060] in, For covariance.

[0061] Preferably, in step S4, the parallel block search is performed as follows:

[0062] Sub-block The search for integer solutions is transformed into the following minimization problem:

[0063] (14)

[0064] in, Size of a superellipsoid Let be the real number of ambiguity. For integer ambiguity, The variance corresponding to the ambiguity. Integer space;

[0065] When the dimension of the fuzzy sub-block is less than or equal to 6, the PSOAF algorithm is used, as follows:

[0066]

[0067] (15)

[0068] in, For the individual's historical best; For the group optimal; , , These are the inertia weight and the learning factor, respectively. , It is a random number; and They are respectively t +1、 tThe residual, and Don't t +1、 t Integer ambiguity;

[0069] When the dimension of the ambiguity sub-block is greater than 6, the AWDE algorithm is used, as follows:

[0070] First, in each sub-block search, the search population size is defined as... Set the upper and lower bounds of each dimension of the floating-point solution to integers as follows:

[0071] (16)

[0072] in, The radius of the integer search window is used, and the initial population is represented by real number encoding. Let be the real number of ambiguity. Integer ambiguity;

[0073] Perform differential mutation to generate a mutation vector:

[0074] (17)

[0075] in, , , Different individuals randomly selected from the population; The difference weighting factor;

[0076] Secondly, candidate individuals are constructed using the site crossover operator, and adaptive crossover operation is performed:

[0077] (18)

[0078] in, Crossover rate; For experimental individuals, and As a mutated individual, It is a random number;

[0079] Finally, a greedy selection strategy is used to update the population:

[0080] (19)

[0081] in, and For fitness value, For experimental subjects.

[0082] Preferably, in step S5, the sub-block credibility calculation and splicing are as follows:

[0083] For each sub-block search result, calculate the probability estimate (ACP) that the integer solution of that sub-block is the true solution:

[0084] (20)

[0085] in, For sub-blocks k ACP value;

[0086] Sort all sub-block solution results in descending order of ACP value:

[0087] (twenty one)

[0088] By sequentially concatenating the integer solutions of the sub-blocks, a candidate complete ambiguity vector is constructed. :

[0089] (twenty two).

[0090] Preferably, step S6 is as follows:

[0091] After each concatenation, the joint covariance matrix is ​​used to construct the current overall confidence level. :

[0092] (twenty three)

[0093] like If the condition is met, accept this concatenation as the final solution; otherwise, backtrack to the lowest trustworthy sub-block and re-optimize or replace the algorithm until the criterion is satisfied.

[0094] Preferably, an interruption-based splicing mechanism is introduced, if in the... j After the individual blocks are pieced together If the result is not found, stop splicing, keep the result of the spliced ​​sub-blocks, and reselect the algorithm, mutate, or increase the search step size for the remaining sub-blocks.

[0095] The present invention also provides a computer program product, which includes a computer program / instruction that, when executed by a processor, implements the aforementioned GNSS integer ambiguity fixing method that integrates intelligent optimization algorithm and VIB strategy.

[0096] The advantages of this invention are:

[0097] (1) This invention proposes a GNSS integer ambiguity fixing method that integrates intelligent optimization algorithm and VIB strategy, which aims to improve the fixing efficiency, accuracy and stability of integer ambiguity in carrier phase differential positioning. It is particularly suitable for high-dimensional ambiguity resolution, complex observation environment and dynamic positioning scenario.

[0098] (2) This invention adopts integer transformation and decorrelation processing combined with VIB grouping strategy to effectively reduce the integer search space, and introduces eigenvalue decomposition and covariance inflation factor to realize dynamic grouping, thereby enhancing the algorithm's adaptability to different observation data quality and environmental conditions.

[0099] (3) This invention improves the efficiency and accuracy of solving high-dimensional fuzziness by using the parallel block search mechanism and employing PSOAF and AWDE intelligent optimization algorithms for fuzzy sub-blocks of different dimensions.

[0100] (4) The present invention introduces sub-block and global credibility (ACP) evaluation, rollback and interrupt splicing mechanism, which reduces the risk of incorrect fixation and significantly improves the stability and robustness of the solution results.

[0101] (5) By back-substituting the observation model after fixing the ambiguity, the present invention can output a higher precision coordinate parameter solution, ensuring that GNSS positioning maintains a high fixation rate and reliability in dynamic environments and complex conditions. Attached Figure Description

[0102] Figure 1 This is a flowchart of a GNSS integer ambiguity fixing method that integrates intelligent optimization algorithm and VIB strategy according to the present invention.

[0103] Figure 2 This is a diagram of a carrier phase double-difference model.

[0104] Figure 3 This is a flowchart of the PSOAF algorithm.

[0105] Figure 4 This is a flowchart of the AWDE algorithm. Detailed Implementation

[0106] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0107] This invention achieves GNSS ambiguity fixation through the following technical solution: Navigation and observation data are collected by a receiver; a double-difference model is established based on carrier phase observations; the parameters to be determined and the floating-point solution of ambiguity, along with the corresponding variance-covariance matrix, are calculated using the least squares method; integer transformation and decorrelation processing are performed on the floating-point solution of ambiguity and the variance-covariance matrix; the high-dimensional ambiguity vector is divided into multiple sub-blocks; different intelligent optimization algorithms are selected according to the sub-block dimension for parallel block search; the ambiguity of each sub-block and the global reliability are calculated; reliable integer ambiguity is obtained; and a fixed solution for the coordinate parameters to be determined is obtained.

[0108] Depend on Figure 1 As shown, the present invention provides a GNSS integer ambiguity fixing method that integrates intelligent optimization algorithms and VIB strategies, specifically including the following steps:

[0109] S1: Based on the received observation data, establish a differential model of the carrier phase. Ignore the integer constraints of ambiguity and use the least squares method to calculate the floating-point solutions of the parameters to be determined and the ambiguity, as well as the corresponding variance-covariance matrix.

[0110] S2: Perform integer transformation on the floating-point solution of ambiguity and the variance-covariance matrix, and use the Cholesky decomposition method to reduce the correlation between the variance-covariance matrix, thereby reducing the correlation between ambiguity variables and narrowing the integer search space;

[0111] S3: Perform eigenvalue decomposition on the variance-covariance matrix, divide the ambiguity direction groups according to the magnitude of the eigenvalues, and set the inflation factor to dynamically adjust the covariance to adapt to different data quality.

[0112] S4: Based on the dimension of the sub-block and the objective function, select different intelligent optimization algorithms to perform parallel block integer optimal solution search. When the ambiguity dimension of the sub-block is less than or equal to 6, select the PSOAF algorithm to search for ambiguity. When the ambiguity dimension of the sub-block is greater than 6, select the AWDE algorithm to search for ambiguity.

[0113] S5: Calculate the confidence level (ACP) of the fixed ambiguity of each sub-block, sort the sub-blocks from high to low confidence level, concatenate the ambiguities one by one, update the variance-covariance matrix, and filter out unreliable results;

[0114] S6: Calculate the global ACP. If the threshold condition is met, output the integer solution. If the condition is not met, backtrack to a certain sub-block and search again or adjust the algorithm parameters until the reliability condition is met.

[0115] S7: Substitute the fixed ambiguity back into the original observation model to calculate the final coordinate parameters to be determined.

[0116] The specific techniques involved in the above method are as follows:

[0117] (1) Carrier phase double difference model

[0118] Carrier phase double difference model, such as Figure 2 As shown, Receiver represents a receiver, and Satellite represents a satellite.

[0119] GNSS carrier phase observations are expressed as follows:

[0120] (1)

[0121] Among them, subscript For receiver number, superscript Number the satellite; To from satellite to receiver The carrier phase measurement value, in units of ; To from satellite to receiver geometric distance, in units of ; The speed of light, with a value of ; Satellite signal transmission time Clock difference, unit: ; For signal receiving timing receiver Clock difference, unit: ; Wavelength, unit: ; Ionospheric delay, in units of ; Tropospheric delay, in units of ; This is the carrier phase deviation term; Carrier observation noise, in units of .

[0122] Differential positioning can reduce or eliminate some systematic errors and improve positioning accuracy. If the two receivers are close to each other, the clock error, ionospheric delay and tropospheric delay of the satellite can be eliminated by single-difference between the receiver stations.

[0123] First, we use the single-difference observation equations obtained from different stations to form a single-difference observation equation, as shown below:

[0124] (2)

[0125] in, The difference in carrier phase measurement between different stations, The carrier phase measurement value of the reference station. The carrier phase measurement value of the monitoring station. This represents the difference in geometric distance from the satellite to the receiver at different stations. For the carrier phase deviation term of the reference station, For the carrier phase deviation term of the monitoring station, This represents the difference in carrier observation noise between different stations.

[0126] Next, the single-difference observation equation is converted into a double-difference observation equation by inter-satellite double-difference, as shown in the following equation:

[0127] (3)

[0128] in, The carrier phase measurement difference between different satellites and different stations. This represents the difference in geometric distance from different satellites and different stations to the receiver. and Satellites j , k Carrier phase deviation term at different stations, This represents the difference in carrier observation noise between different satellites and different stations.

[0129] In equations (2) and (3), , These represent the differences between different satellites and different receivers.

[0130] Equation (3) is linearized and transformed into an error equation based on Taylor series and parameter representation:

[0131] (4)

[0132] in, For the residual vector, The coefficient matrix, For an unknown parameter vector, This is the observation vector.

[0133] In equation (4), The first three unknown parameters are the receiver's coordinates, and from the fourth parameter to the... n -1 parameter represents the difference in integer ambiguity, where n The number of satellites observed by the temporary receiver.

[0134] (2) Estimation of fuzzy floating-point solutions

[0135] For ease of calculation and representation, the carrier phase observation equation can be expressed as:

[0136] (5)

[0137] in, Represents the mathematical expectation operator. For the observation vector, For ambiguity parameters, Let be the coordinate parameters to be determined. To observe noise.

[0138] Based on the principle of least squares estimation, the objective function for solving equation (5) is:

[0139] (6)

[0140] in, Let be the variance matrix of the observation vectors.

[0141] Ignoring the integer properties of ambiguity, the floating-point solution of the ambiguity parameters can be calculated. Floating-point solution of coordinate parameters and the corresponding variance-covariance matrix .

[0142] in, Let Variance be the variance matrix of the floating-point solution for ambiguity. Let Variance be the floating-point solution of the position parameters. and Let be the covariance matrix between the ambiguity floating-point solution and the position parameter floating-point solution.

[0143] (3) Integer transformation and decorrelation processing

[0144] By performing an integer Gaussian transform on the ambiguity parameters and their variance-covariance matrix ( Transformation), transforming them from the original space to a new space, to reduce the correlation of ambiguity:

[0145] (7)

[0146] in, , , These represent the real-valued ambiguity, integer-valued ambiguity, and variance-covariance matrix after integer transformation, respectively. It is an integer transformation matrix.

[0147] Since the variance-covariance matrix is ​​a symmetric positive definite matrix, and its principal minors are not zero, for computational convenience, they can be decomposed using Choleskey decomposition, i.e.:

[0148]

[0149] (8)

[0150] in, It is a lower triangular matrix. It is a diagonal matrix. After the decorrelation stage, The absolute value of the off-diagonal elements of a matrix is ​​less than or equal to 0.5. The diagonal elements are sorted in descending order.

[0151] (4) Dynamic grouping of ambiguity vectors

[0152] Perform eigenvalue decomposition on the covariance matrix:

[0153] (9)

[0154] in, This is the eigenvector matrix, where each column represents a principal direction of ambiguity; For the covariance eigenvalues ​​arranged in descending order, when A large search space indicates high uncertainty and a high risk of misjudgment; when... A number of hours indicates a high level of reliability in the search space and a level of ambiguity that makes it easy to find the correct answer.

[0155] Ambiguity direction groups are divided according to the magnitude of the eigenvalues:

[0156] (10)

[0157] in, The first set based on the covariance eigenvalue k Layer-by-layer threshold; K The number of blocks (number of layers); This is the ambiguity direction group.

[0158] To dynamically adapt to different data qualities, a continuous adaptive expansion method is used for each group. Set an expansion factor ( ):

[0159] (11)

[0160] in, It is a parameter that adjusts the degree of expansion; It is the expansion factor; The larger the value, the lower the confidence level.

[0161] Inflation factor matrix It can be represented as:

[0162] (12)

[0163] Covariance inflation is:

[0164] (13)

[0165] in, For covariance.

[0166] This operation amplifies the ambiguity covariance of high-risk directions, improving the ability to identify false fixations; and maintains the search convergence of high-confidence directions, reducing unnecessary convergence delays.

[0167] (5) Parallel block search

[0168] For sub-blocks The search for integer solutions can be transformed into the following minimization problem:

[0169] (14)

[0170] in, Size of a superellipsoid Let be the real number of ambiguity. For integer ambiguity, The variance corresponding to the ambiguity. Integer space;

[0171] When the ambiguity sub-block dimension is less than or equal to 6, the PSOAF algorithm is used. The PSOAF algorithm flowchart is as follows: Figure 3 As shown, the details are as follows:

[0172]

[0173] (15)

[0174] in, For the individual's historical best; For the group optimal; , , These are the inertia weight and the learning factor, respectively. , It is a random number; and The residuals for t+1 and t are respectively. and Do not specify the integer ambiguity of t and t+1.

[0175] When the dimension of the ambiguity sub-block is greater than 6, the AWDE algorithm is used. The flowchart of the AWDE algorithm is as follows: Figure 4 As shown, the details are as follows:

[0176] First, in each sub-block search, the search population size is defined as... Set the upper and lower bounds of each dimension of the floating-point solution to integers as follows:

[0177] (16)

[0178] in, The search window radius is an integer (e.g., 3 to 5), and the initial population is represented by real number encoding. Let be the real number of ambiguity. The ambiguity is an integer.

[0179] Perform differential mutation to generate a mutation vector:

[0180] (17)

[0181] in, , , Different individuals randomly selected from the population; This is the differential weighting factor, whose value is adaptively adjusted with the number of iterations. , This represents the maximum number of iterations.

[0182] Secondly, candidate individuals are constructed using the site crossover operator, and adaptive crossover operation is performed:

[0183] (18)

[0184] in, The crossover rate is initialized to 0.5 and gradually adjusted for a more refined search. For experimental individuals, and As a mutated individual, It is a random number.

[0185] Finally, a greedy selection strategy is used to update the population:

[0186] (19)

[0187] in, For fitness value, For experimental subjects.

[0188] (6) Sub-block credibility calculation and splicing

[0189] ACP (Ambiguity Confidence Probability) represents the probability estimate that the integer solution of a sub-block is a true solution; the closer the value is to 1, the higher the confidence level. The ACP is calculated for each sub-block search result.

[0190] (20)

[0191] in, For sub-blocks k The ACP value.

[0192] Sort all sub-block solution results in descending order of ACP value:

[0193] (twenty one)

[0194] By sequentially concatenating the integer solutions of the sub-blocks, a candidate complete ambiguity vector is constructed. :

[0195] (twenty two)

[0196] (7) Global decision and result output

[0197] After each concatenation, the joint covariance matrix is ​​used to construct the current overall confidence level. :

[0198] (twenty three)

[0199] like If the concatenation is accepted as the final solution, then backtrack to the least reliable sub-block and re-optimize or replace the algorithm until the criterion is met.

[0200] In addition, an interruption-based splicing mechanism is introduced, if in the... j After the individual blocks are pieced together If the result is not found, stop splicing; keep the result of the spliced ​​sub-blocks; reselect the algorithm, mutate or increase the search step size for the remaining sub-blocks; reduce the risk of early misunderstandings propagating to later stages.

[0201] This invention reduces the correlation between fuzzy variables by using integer transformation and Cholesky decomposition, thereby effectively compressing the integer search space.

[0202] This invention utilizes eigenvalue decomposition combined with dilation factor to dynamically group ambiguities in a directional manner, thereby enhancing the algorithm's adaptability to different observation data qualities and complex environments.

[0203] This invention flexibly selects two intelligent optimization algorithms, PSOAF and AWDE, for sub-block dimensions, and performs integer solution search in parallel to achieve efficient solution of high-dimensional fuzziness.

[0204] This invention ensures a high accuracy rate in the solution by calculating and sorting the credibility (ACP) of sub-blocks and the overall ambiguity solution.

[0205] When the global confidence level does not reach the threshold, this invention supports reverting to the low-confidence sub-block for re-optimization, or interrupting the splicing process and adjusting the search strategy to improve the robustness of the results.

[0206] This invention obtains a high-precision coordinate solution by substituting the fixed ambiguity back into the original observation model, and can still maintain a high fixation rate and reliability in dynamic environments and complex conditions.

[0207] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy, characterized in that, Includes the following steps: S1: Based on the received observation data, establish a carrier phase double difference model. Under the premise of ignoring the integer constraints of ambiguity, use the least squares method to calculate the floating-point solutions of the parameters to be determined and the ambiguity, as well as the corresponding variance-covariance matrix. S2: Perform integer transformation on the floating-point solution of ambiguity and the variance-covariance matrix, and use the Cholesky decomposition method to reduce the correlation between the variance-covariance matrix, thereby reducing the correlation between ambiguity variables and narrowing the integer search space; S3: Perform eigenvalue decomposition on the variance-covariance matrix, divide the ambiguity direction groups according to the magnitude of the eigenvalues, and set the inflation factor to dynamically adjust the covariance to adapt to different data quality. S4: Based on the dimension of the sub-block and the objective function, select different intelligent optimization algorithms to perform parallel block integer optimal solution search. When the ambiguity dimension of the sub-block is less than or equal to the set dimension, select the PSOAF algorithm to search for ambiguity. When the ambiguity dimension of the sub-block is greater than the set dimension, select the AWDE algorithm to search for ambiguity. S5: Calculate the confidence level (ACP) of the fixed ambiguity of each sub-block, sort the sub-blocks from high to low confidence level, concatenate the ambiguities one by one, update the variance-covariance matrix, and filter out unreliable results; S6: Calculate the global reliability ACP. If the threshold condition is met, output an integer solution. If the condition is not met, backtrack to a certain sub-block and search again or adjust the algorithm parameters until the reliability condition is met. S7: Substitute the fixed ambiguity back into the original observation model to calculate the final coordinate parameters to be determined.

2. The GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy according to claim 1, characterized in that, In step S1, the carrier phase double-difference model is as follows: GNSS carrier phase observations are expressed as follows: （1） Among them, subscript For receiver number, superscript Number the satellites; To from satellite to receiver The carrier phase measurement value; To from satellite to receiver geometric distance; The speed of light; Satellite signal transmission time Clock difference; For signal receiving timing receiver Clock difference; Wavelength; For ionospheric delay; For tropospheric delay; This is the carrier phase deviation term; This is carrier observation noise; First, we use the single-difference observation equations obtained from different stations to form a single-difference observation equation, as shown below: （2） in, The difference in carrier phase measurement between different stations, The carrier phase measurement value of the reference station. The carrier phase measurement value of the monitoring station. This represents the difference in geometric distance from the satellite to the receiver at different stations. For the carrier phase deviation term of the reference station, For the carrier phase deviation term of the monitoring station, The difference in carrier observation noise between different stations; Next, the single-difference observation equation is converted into a double-difference observation equation by inter-satellite double-difference, as shown in the following equation: （3） in, The carrier phase measurement difference between different satellites and different stations. This represents the difference in geometric distance from different satellites and different stations to the receiver. and Satellites Carrier phase deviation term at different stations, For carrier observation noise differences between different satellites and different stations; In equations (2) and (3), , These represent the differences between different satellites and different receivers; Equation (3) is linearized and transformed into an error equation based on Taylor series and parameter representation: （4） in, For the residual vector, The coefficient matrix, For an unknown parameter vector, For observation vectors; In equation (4), The first three unknown parameters are the receiver's coordinates, and from the fourth parameter to the... n -1 parameter represents the difference in integer ambiguity. n This represents the number of satellites observed by the receiver.

3. The GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy according to claim 1, characterized in that, In step S1, the floating-point solution estimation of the ambiguity is specifically as follows: The carrier phase observation equation is expressed as: （5） in, Represents the mathematical expectation operator. For the observation vector, For ambiguity parameters, Let be the coordinate parameters to be determined. To observe noise; Based on the principle of least squares estimation, the objective function for solving equation (5) is: （6） in, Let be the variance matrix of the observation vectors; The floating-point solution of the ambiguity parameter is calculated while ignoring the integer properties of ambiguity. Floating-point solution of coordinate parameters and the corresponding variance-covariance matrix ; in, Let Variance be the variance matrix of the floating-point solution for ambiguity. Let Variance be the floating-point solution of the position parameters. and Let be the covariance matrix between the ambiguity floating-point solution and the position parameter floating-point solution.

4. The GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy according to claim 3, characterized in that, In step S2, the integer transformation and decorrelation processing are specifically as follows: By performing an integer Gaussian transform on the ambiguity parameters and their variance-covariance matrix, The transformation, from the original space to a new space, achieves decorrelation of ambiguity: （7） in, , , These represent the real-valued ambiguity, integer-valued ambiguity, and variance-covariance matrix after integer transformation, respectively. It is an integer transformation matrix; Since the variance-covariance matrix is ​​a symmetric positive definite matrix, and its principal minors are not zero, Choleskey decomposition is performed for computational convenience, i.e.: （8） in, It is a lower triangular matrix. It is a diagonal matrix; after the decorrelation stage, The absolute value of the off-diagonal elements of a matrix is ​​less than or equal to 0.

5. The diagonal elements are sorted in descending order.

5. The GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy according to claim 1, characterized in that, In step S3, the ambiguity vector is dynamically grouped, as shown below: Perform eigenvalue decomposition on the covariance matrix: （9） in, This is the eigenvector matrix, where each column represents a principal direction of ambiguity; For the covariance eigenvalues ​​arranged in descending order, when Large indicates high uncertainty in the search space; when A number of hours indicates high reliability of the search space; Ambiguity direction groups are divided according to the magnitude of the eigenvalues: （10） in, The first set based on the covariance eigenvalue k Layer-by-layer threshold; K The number of blocks; For ambiguity direction groups; To dynamically adapt to different data qualities, a continuous adaptive expansion method is used for each group. Set an expansion factor: （11） in, It is the expansion factor; It is a parameter that adjusts the degree of expansion; The larger the value, the lower the confidence level. Inflation factor matrix Represented as: （12） Covariance inflation is: （13） in, For covariance.

6. The GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy according to claim 1, characterized in that, In step S4, parallel block search is performed, as detailed below: Sub-block The search for integer solutions is transformed into the following minimization problem: （14） in, Size of a superellipsoid Let be the real number of ambiguity. For integer ambiguity, The variance corresponding to the ambiguity. Integer space; When the dimension of the fuzzy sub-block is less than or equal to the set dimension, the PSOAF algorithm is used, as follows: （15） in, For the individual's historical best; For the group optimal; , , These are the inertia weight and the learning factor, respectively. , It is a random number; and They are respectively t +1、 t The residual, and Don't t +1、 t Integer ambiguity; When the dimension of the ambiguity sub-block is greater than the set dimension, the AWDE algorithm is used, as follows: First, in each sub-block search, the search population size is defined as... Set the upper and lower bounds of each dimension of the floating-point solution to integers as follows: （16） in, The radius of the integer search window is used, and the initial population is represented by real number encoding. Let be the real number of ambiguity. Integer ambiguity; Perform differential mutation to generate a mutation vector: （17） in, , , Different individuals randomly selected from the population; The difference weighting factor; Secondly, candidate individuals are constructed using the site crossover operator, and adaptive crossover operation is performed: （18） in, Crossover rate; For experimental individuals, and As a mutated individual, It is a random number; Finally, a greedy selection strategy is used to update the population: （19） in, and For fitness value, For experimental subjects.

7. The GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy according to claim 6, characterized in that, In step S5, the sub-block credibility calculation and splicing are as follows: For each sub-block search result, calculate the probability estimate (ACP) that the integer solution of that sub-block is the true solution: （20） in, For sub-blocks k ACP value; Sort all sub-block solution results in descending order of ACP value: （21） By sequentially concatenating the integer solutions of the sub-blocks, a candidate complete ambiguity vector is constructed. : （22）。 8. The GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy according to claim 7, characterized in that, Step S6 is detailed below: After each concatenation, the joint covariance matrix is ​​used to construct the current overall confidence level. : （23） like If the condition is met, accept this concatenation as the final solution; otherwise, backtrack to the lowest trustworthy sub-block and re-optimize or replace the algorithm until the criterion is satisfied.

9. A GNSS integer ambiguity fixing method integrating intelligent optimization algorithm and VIB strategy according to claim 8, characterized in that, Introducing an interrupt-type splicing mechanism, if in the first... j After the individual blocks are pieced together If the result is not found, stop splicing, keep the result of the spliced ​​sub-blocks, and reselect the algorithm, mutate, or increase the search step size for the remaining sub-blocks.

10. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements the GNSS integer ambiguity fixing method that integrates intelligent optimization algorithm and VIB strategy as described in any one of claims 1 to 9.

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