Complete cycle ambiguity resolving method based on hybrid adaptive differential evolution grey wolf algorithm

Abstract

The invention relates to the technical field of satellite navigation signal processing, in particular to an integer ambiguity resolving method based on a hybrid adaptive differential evolution grey wolf algorithm, which comprises the following steps of: loading GNSS (Global Navigation Satellite System) original data to carry out decorrelation, and calculating an adaptive integer search space boundary; calculating the solution of each individual, storing, comparing the fitness of each individual, and updating and recording globally optimal, suboptimal and third optimal solutions; executing a variation-crossover-selection process of differential evolution to generate a new generation of population; parameter self-adaption and Levy flight are executed; checking whether the current number of iterations reaches a preset maximum number of iterations, if not, adding one to the counter, returning and repeating the steps of comparing the fitness of each individual, updating and recording the global optimal solution, the suboptimal solution and the third optimal solution, and if yes, starting local search to find a better global optimal wolf; and the final calculation result finally recorded in the global optimal wolf variable is output, so that the premature convergence problem in the traditional algorithm solution is solved, and the solution success rate is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of satellite navigation signal processing, and particularly relates to a method for calculating integer ambiguity based on a hybrid adaptive differential evolution grey wolf algorithm. BACKGROUND

[0002] In a global satellite navigation system, high-precision positioning is usually performed by carrier phase technology. First, a double-difference carrier phase observation model is constructed, and then an algorithm is used to solve the integer number of carrier phases between satellites and receivers, i.e. integer ambiguity. Once the integer ambiguity is determined, the high-precision position coordinates can be calculated. The carrier phase is measured first, and then the ambiguity is fixed. Therefore, how to quickly and accurately fix the integer ambiguity is a key problem in carrier phase measurement. One of the core problems of precise positioning using carrier phase is to solve the integer ambiguity. The floating-point solution of the ambiguity parameter can be obtained by extended Kalman filtering, and the precision of the position parameter solution or baseline vector solution corresponding to the floating-point ambiguity parameter is usually poor. Only when the floating-point ambiguity parameter is correctly fixed to an integer value, can the position parameter solution or baseline vector solution achieve centimeter-level positioning accuracy.

[0003] However, with the development of GNSS systems and the increasing complexity of application scenarios, higher demands are placed on the real-time performance and reliability of ambiguity resolution. In recent years, metaheuristic algorithms, such as Particle Swarm Optimization (PSO), Differential Evolution (DE), and Grey Wolf Optimizer (GWO), have been introduced as a new approach to solving integer ambiguity problems due to their powerful global search capabilities and "black box" optimization characteristics. The advantages of using metaheuristic algorithms are: Global Parallel Search: By maintaining a population of candidate solutions, they conduct parallel and random exploration throughout the entire search space, theoretically making them more likely to escape local optima and find the global optimum than traditional sequential search methods. Simple Concept and Easy Implementation: Compared to the LAMBDA algorithm, which requires complex matrix transformations, the framework of metaheuristic algorithms is relatively unified, independent of the specific mathematical structure of the problem, and only requires defining a clear objective function for optimization. Flexibility and Scalability: The algorithm framework is easy to integrate with other technologies (such as machine learning and other heuristic rules), with the potential to build more powerful hybrid intelligent algorithms. However, directly applying existing standard metaheuristic algorithms to integer fuzzy search presents serious technical problems: Premature convergence: Standard metaheuristic algorithms (such as the original GWO) often exhibit a strong tendency to converge towards the optimal individual. In fuzzy search, a highly deceptive problem, the algorithm's population is easily attracted to a strong local optimum early on, causing the entire population to rapidly cluster there, prematurely ceasing its exploration of the global space and ultimately outputting incorrect solutions. Loss of population diversity: The root cause of the premature convergence problem is the rapid loss of population diversity. Once all candidate solutions become highly similar, the algorithm loses its evolutionary impetus and cannot generate new, promising search directions. Imbalance between exploration and exploitation: In high-dimensional fuzzy search, the algorithm needs extensive global exploration in the early stages of iteration to locate the region containing the correct solution with a high probability; in the later stages, it needs fine-grained local exploitation to precisely lock onto the optimal integer solution. The inherent, typically linear, exploration-exploitation mechanism of standard metaheuristic algorithms is ill-suited to this complex requirement.

[0004] In summary, although metaheuristic algorithms offer new possibilities for solving integer ambiguity problems, existing standard algorithms, due to inherent defects such as premature convergence and loss of diversity, fail to achieve significantly higher success rates and reliability in high-dimensional and complex GNSS application scenarios. Therefore, there is an urgent need for a high-performance metaheuristic optimization algorithm designed to effectively maintain population diversity, dynamically balance exploration and development, and efficiently solve high-dimensional integer ambiguity problems. Summary of the Invention

[0005] The purpose of this invention is to provide a method for solving integer ambiguity based on the hybrid adaptive differential evolution gray wolf algorithm, which aims to improve the success rate of fixation and accuracy of existing standard algorithms.

[0006] To achieve the above objectives, this invention provides a method for integer ambiguity resolution based on a hybrid adaptive differential evolution gray wolf algorithm, comprising the following steps:

[0007] Load raw GNSS data and perform downcorrelation, then dynamically calculate and set adaptive integer search space boundaries;

[0008] At the beginning of each generation, the solution for each individual is calculated using a pre-computed inverse matrix, and these values ​​are stored in an array. The program compares the fitness of each individual in real time and updates the records of the global best, second best, and third best solutions.

[0009] Matrix operations are used to perform a differential evolution mutation-crossover-selection process for the entire population to generate a new generation of population;

[0010] The intelligence and robustness of the execution parameter adaptation and Levy flight enhancement algorithm;

[0011] Check if the current iteration count has reached the preset maximum iteration count. If not, increment the iteration counter by one, return and repeat the real-time comparison of the fitness of each individual, and update the records of the global optimal, suboptimal and third optimal solutions. If so, start Nelder-Mead local search to try to find a better global optimal wolf.

[0012] The final calculation result is output as the global optimal integer solution vector and the corresponding optimal fitness value recorded in the global optimal wolf variable.

[0013] The raw GNSS data includes the floating-point modulus vector and the corresponding covariance matrix obtained from GNSS floating-point calculation.

[0014] In this process, the mutation-crossover-selection process is vectorized. Mutation: All mutation vectors are generated in parallel for the entire population through a one-time matrix operation. Crossover: A binomial crossover strategy is adopted to generate all trial vectors at once through a logical mask. Selection: The entire population is updated through a one-time fitness comparison and logical indexing.

[0015] The parameter adaptation is an online learning process based on a "reward and punishment" mechanism. Individuals that fail to evolve successfully in the selection process are considered invalid by the algorithm and need to be reset. When the algorithm detects that the global optimal solution has stalled, the Levy flight guides the search to a new and more promising area through a long-distance jump in a random direction.

[0016] This invention discloses an integer ambiguity resolution method based on a hybrid adaptive differential evolution gray wolf algorithm. The method loads raw GNSS data and performs decorrelation, dynamically calculating and setting an adaptive integer search space boundary. At the beginning of each generation, a pre-calculated inverse matrix is ​​used to calculate the solution for each individual, and these values ​​are stored in an array. The program compares the fitness of each individual in real time and updates the records of the globally optimal, second-best, and third-best solutions. Matrix operations are used to perform a differential evolution mutation-crossover-selection process for the entire population to generate a new generation. Parameter adaptation and Levy flight enhancement algorithms improve the intelligence and robustness of the algorithm. The method checks whether the current iteration count has reached the preset maximum iteration count; if not, then... The iteration counter is incremented, the program returns and repeats the real-time comparison of the fitness of each individual, and updates the records of the global optimal, suboptimal, and third-optimal solutions. If a solution is found, Nelder-Mead local search is initiated to try to find a better global optimal wolf. The global optimal integer solution vector and the corresponding optimal fitness value recorded in the global optimal wolf variable are output as the final calculation result. This method, through the DE core and parameter adaptive mechanism, successfully overcomes the premature convergence problem caused by the loss of population diversity in high-dimensional fuzzy solution of standard GWO and similar algorithms. The solution success rate is significantly improved, while the success rate of standard GWO algorithm is only 63%. The global search capability and reliability are greatly enhanced. The introduction of Lévy flight and Nelder-Mead strategy provides the algorithm with a powerful "escape trap" capability, ensuring that even if the algorithm is briefly trapped in a local optimum during iteration, it can successfully escape in subsequent iterations and eventually converge to the global optimal solution. Attached Figure Description

[0017] To make the technical solution and advantages of this application clearer, the embodiments of this application will be described in further detail below.

[0018] The terms "first," "second," "third," and "fourth," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0019] It should be noted that all information (including but not limited to user device information, user personal information, etc.), data (including but not limited to data used for analysis, stored data, displayed data, etc.), and signals involved in this application have been authorized by the user or fully authorized by all parties, and the collection, use, and processing of related data must comply with the relevant laws, regulations, and standards of the relevant countries and regions. For example, the strain data, acceleration data, displacement data, pressure data, and video data involved in this application were all obtained with full authorization.

[0020] Figure 1 This is a schematic diagram illustrating the steps of an integer ambiguity resolution method based on the HADE-GWO algorithm according to the present invention.

[0021] Figure 2 This is a schematic diagram illustrating the specific process of an integer ambiguity resolution method based on the HADE-GWO algorithm of the present invention.

[0022] Figure 3 This is a schematic diagram of the HADE-GWO fitness value evolution curve in Example 2 of a specific embodiment of the present invention.

[0023] Figure 4 This is a graph showing the running time of solving the 3D fitness value of the GWO algorithm in Example 2 of a specific embodiment of the present invention.

[0024] Figure 5 This is a graph showing the running time of the HADE-GWO algorithm for solving the 3D fitness value in Example 2 of a specific embodiment of the present invention.

[0025] Figure 6 This is a graph showing the running time of the HADE-GWO algorithm for solving the 6-dimensional fitness value in Example 3 of a specific embodiment of the present invention.

[0026] Figure 7 This is a graph showing the running time of solving the 12-dimensional fitness value of the HADE-GWO algorithm in Example 3 of a specific embodiment of the present invention. Detailed Implementation

[0027] The embodiments of the present invention are described in detail below. Examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, but should not be construed as limiting the present invention.

[0028] Please see Figures 1 to 7 This invention provides a method for resolving integer ambiguities based on a hybrid adaptive differential evolution gray wolf algorithm, comprising the following steps:

[0029] S1 loads raw GNSS data and performs downcorrelation, dynamically calculating and setting adaptive integer search space boundaries;

[0030] In this embodiment of the invention, this is the preparatory work before the algorithm begins. First, the program loads the raw GNSS data (floating-point solution vectors and their covariance matrices). Next, the crucial LAMBDA method is executed to reduce correlation, yielding a new floating-point solution. Covariance Matrix This step aims to reduce the difficulty of subsequent searches. Then, let's move on to our first improvement: based on... The statistical properties of matrices are used to dynamically calculate and define a reasonable, adaptive integer search space boundary. Meanwhile, in order to significantly improve the efficiency of subsequent calculations, pre-calculation and storage are performed at this stage. inverse matrix Finally, within this search space, the initial positions of the wolf pack (population) are randomly initialized, and an independent set of adaptive differential evolution parameters is initialized for each individual in the population. and .

[0031] At the beginning of each generation, S2 uses a pre-computed inverse matrix to calculate the solution for each individual and stores these values ​​in an array. The program compares the fitness of each individual in real time and updates the records of the global best, second best, and third best solutions.

[0032] In this embodiment of the invention, the main iteration loop is entered. At the beginning of each generation, all individuals (wolves) in the current population are traversed first, using pre-calculated... The program efficiently calculates the fitness value of each individual and stores these values ​​in an array. During evaluation, the program compares the fitness of each individual in real time and updates the positions and fitness values ​​of the globally optimal (Alpha), second-best (Beta), and third-best (Delta) solutions. This step provides the basis for subsequent "elite selection" and "individual selection" decisions.

[0033] S3 performs a differential evolution mutation-crossover-selection process for the entire population through matrix operations, generating a new generation of population;

[0034] In this embodiment of the invention, the position update formula based on the mean of the leader wolf, which is used in the standard GWO, is replaced. A new generation of population is generated by performing a differential evolution "mutation-crossover-selection" process for the entire population through a one-time matrix operation (vectorization).

[0035] The intelligence and robustness of S4 execution parameter adaptation and Levy flight enhancement algorithm;

[0036] In this embodiment of the invention, after generating a new generation of population, an algorithmic check is performed using an adaptive parameter strategy to examine which individuals failed to evolve in the previous "selection" step (i.e., the newly generated solution was not accepted). For these "failed" individuals, the algorithm resets their corresponding... and The parameters force them to try entirely new and more diverse search behaviors in the next generation. Successfully evolved individuals retain their valid parameters, and then a Lévy flight stagnation detection is performed: checking if the alpha wolf has not improved for several consecutive generations. If a stagnation threshold is reached, the Lévy flight formula is executed on the alpha wolf to generate a new candidate solution; if it is better, the alpha wolf is updated.

[0037] S5 checks whether the current iteration count has reached the preset maximum iteration count. If not, the iteration counter is incremented by one, the program returns and repeats the real-time comparison of the fitness of each individual, and updates the records of the global optimal, suboptimal and third optimal solutions. If so, Nelder-Mead local search is started to try to find a better global optimal wolf.

[0038] In this embodiment of the invention, it is checked whether the current iteration count has reached the preset maximum iteration count. If not, the iteration counter is incremented, the program returns and repeats step S2 to start a new round of iteration. If yes, the main loop ends, and the program continues to execute step S6.

[0039] S6 outputs the global optimal integer solution vector and the corresponding optimal fitness value, which are finally recorded in the global optimal wolf variable, as the final calculation result.

[0040] In this embodiment of the invention, after the iteration is completed, the algorithm outputs the final recorded Alpha_pos (global optimal integer solution vector) and Alpha_score (global optimal fitness value) as the final result.

[0041] To better understand this technical solution, the following embodiments are provided for further explanation, and the specific execution flow is as follows: Figure 2 As shown:

[0042] Step 1: This stage lays the foundation for the algorithm's global search. Through a series of mathematical transformations and intelligent settings, an efficient and reasonable optimization environment is created. The algorithm's input is the floating-point modulus vector obtained after GNSS floating-point calculation. and its corresponding covariance matrix ,in To determine the ambiguity dimension, a Z-transform matrix is ​​found using the Integer Gaussian Transform. Its determinant is The original data is transformed as follows:

[0043]

[0044] After this transformation, the original least squares problem... It is equivalently transformed into a new problem of finding the best mathematical properties:

[0045]

[0046] in, It is the negative integer ambiguity vector. This step transforms a geometrically dimensional "narrow oblique ellipsoid" search space into a regular space that is closer to a "standard sphere", greatly reducing the difficulty of subsequent searches.

[0047] Next, we will optimize efficiency and define the objective function. To avoid repeatedly performing complex matrix inversion operations during iteration, we will pre-calculate and store the results at this stage. Inverse matrix: Therefore, during the entire algorithm's execution, the objective function (i.e., the cost function) used to evaluate individual fitness is ultimately determined as:

[0048]

[0049] in It is a subject to evaluation. A vector of candidate solutions of dimensional integers.

[0050] Simultaneously, an adaptive space range is set, and the search center of the algorithm is set to a floating-point solution. The nearest integer point: Search radius Depend on The statistical characteristics are dynamically determined. First, calculate the standard deviation vector for each dimension: Then, a uniform integer search radius is determined:

[0051]

[0052] in This is a minimum radius threshold. Ultimately, the upper and lower bounds of the search space are defined as:

[0053]

[0054] In the aforementioned dynamically determined boundary Inside, randomly generate a containing The initial population of individuals And all individuals are rounded down to ensure they are integer vectors, and an independent set of adaptive differential evolution control parameters is initialized:

[0055] Step Two: This stage marks the beginning of each iteration. Its core task is to assess the current population's "combat strength" and provide a basis for subsequent evolutionary operations. The algorithm traverses all individuals (wolves) in the current population, efficiently calculating the fitness value of each individual using the inverse matrix pre-calculated in step S1. At the start of the next iteration, the algorithm first processes the current population. Conduct a comprehensive fitness assessment for each individual in the population. Using a pre-calculated objective function Calculate its candidate solutions:

[0056]

[0057] The candidate solutions for all individuals are stored in a vector. middle.

[0058] While evaluating the overall fitness, the algorithm compares the fitness value of each individual in real time and updates the records of the three elite wolves: the global best (Alpha), the second best (Beta), and the third best (Delta). The record of the Alpha wolf is crucial because it represents the best candidate solution found so far in the entire search history.

[0059] Step 3: This step is the core of the algorithm. It completely replaces the centripetal mean-guided formula of the standard GWO and efficiently performs the "mutation-crossover-selection" process of differential evolution for the entire population through parallel matrix operations.

[0060] Mutation: For the first mutation in a population Each individual randomly selects three distinct indices from the population. Its variation vector The formula for generating it is:

[0061]

[0062] This process is vectorized, generating all mutation vectors in parallel for the entire population through a single matrix operation. Crossover: A binomial crossover strategy is used. For the ... The individual's first dimension, its test vector The amount The generating formula is:

[0063]

[0064] in, It is in The random integers between these parameters ensure that at least one component of each experimental vector originates from the mutation vector. This process is also vectorized, generating all experimental vectors at once using a logical mask.

[0065] choose:

[0066] First, for all newly generated test vectors is Perform boundary checks and calculate fitness values. .

[0067] Subsequently, a greedy selection strategy is adopted to determine the next generation. Individual populations:

[0068]

[0069] This process is also vectorized, and the entire population is updated through a one-time fitness comparison and logical indexing.

[0070] Step 4: After the new generation of population is generated, two independent enhancement strategies are executed. Parameter adaptation: This is an online learning process based on a "reward and punishment" mechanism. For those that failed to evolve successfully in the selection in step 3 (i.e., The For each individual, the algorithm considers its current control parameters. and It might be invalid, so reset it:

[0071]

[0072] in, Indicates the interval Uniformly random numbers are generated. For individuals that successfully evolve, their effective parameter combinations are preserved: and Lévy Flight: This strategy provides the algorithm with a powerful "trap-jumping" mechanism. As a powerful global exploration and "trap-jumping" mechanism, when the algorithm detects that the global optimum is stuck, it triggers a Lévy flight, which guides the search to a new and potentially more promising region through a long-distance jump in a random direction.

[0073] When stagnation is triggered, a new candidate solution is generated. :

[0074]

[0075] in, It is the step size control factor (e.g., 0.01). It is a random step-size vector generated by the Lévy distribution. It is the Lévy index (usually 1.5).

[0076] Step 5: Apply Nelder-Mead periodic refinement. The algorithm checks if the current iteration count has reached the preset maximum iteration count, Max_iter. If not, the iteration counter is incremented, and the program returns with the updated population and adaptive parameters, repeating step S2 to begin a new round of iterative optimization. If the maximum iteration count has been reached, the Nelder-Mead algorithm is invoked to perform a high-intensity local search on the alpha wolf. If a better solution is found, the alpha wolf is updated. The main loop then ends, marking the completion of the search process.

[0077] Step Six: Once the termination condition is met, the algorithm outputs the final calculation result, which includes the globally optimal integer solution vector Alpha_pos and the corresponding optimal fitness value Alpha_score, both recorded in the Alpha wolf variable. This is the final answer to the GNSS integer ambiguity problem.

[0078] To further clarify the function of this invention, example 1 is provided for illustration.

[0079] Example 1: Solving 3D Double-Difference Integer Ambiguity

[0080] For three-dimensional double-difference integer ambiguity floating-point solutions and covariance matrix

[0081]

[0082] After searching for the above ambiguity using the integer ambiguity resolution method based on the hybrid adaptive differential evolution gray wolf algorithm provided by this invention, the optimal solution for the integer ambiguity is obtained as follows:

[0083]

[0084] Algorithm 2: Performance Analysis and Comparison of Multiple Algorithms

[0085] This example compares and analyzes the solution performance of four algorithms: GWO, HADE-GWO, LAMBDA, and MLAMBDA. The floating-point solution and covariance matrix of the double-difference integer ambiguity in 3D are as follows:

[0086]

[0087] After the decorrelation operation, the floating-point solution and the transformation of the covariance matrix are as follows:

[0088]

[0089] Assume an initial gray wolf population of 30, a population dimension of 3, and a maximum number of iterations of 200. Compare the search performance of the new algorithm with the GWO, HADE-GWO, LAMBDA, and MLAMBDA algorithms. The fitness change curve of the OBL-DEGWO algorithm is shown below. Figure 3 As shown in the figure. Multiple experiments have demonstrated that the HADE-GWO algorithm, through differential evolution, improves its ability to escape local optima, reaching the vicinity of the optimal fitness value region in approximately six iterations.

[0090] To gain a more accurate understanding of the computation time for each experiment, the computation time of the GWO and HADE-GWO algorithms is displayed in a bar chart as follows: Figure 4 and Figure 5 As shown. By comparing the running time of the three algorithms each time, the GWO algorithm has the shortest solution time, while the HADE-GWO algorithm has a slightly longer solution time.

[0091] To compare and analyze the accuracy and reliability of the solutions in 3D, the four algorithms were repeated 100 times, with a maximum of 200 iterations per iteration. The results, average solution time, and success rate are shown in Table 1.

[0092] Table 1 Comparison of Five Algorithms

[0093]

[0094] While the GWO algorithm is fast, its success rate is low. The HADE-GWO algorithm is slightly slower, but has a high success rate. Compared with the LAMBDA and M-LAMBDA algorithms, HADE-GWO is superior in terms of computation time; its success rate is the same as both algorithms. The HADE-GWO algorithm can effectively solve 3D ambiguity problems.

[0095] Example 3: Experiment on Multidimensional Integer Ambiguity Resolution

[0096] With the development of satellite systems in various countries and the introduction of multiple systems, the number of satellites involved in the ambiguity resolution has increased, raising the complexity of ambiguity search and resolution. Therefore, the performance of multidimensional integer ambiguity resolution is one of the key indicators of integer ambiguity resolution algorithms. This invention conducts 3D, 6D, and 12D ambiguity resolution experiments for the HADE-GWO algorithm. The 3D experimental data is consistent with Example 3, and the floating-point solution matrices for 6D and 12D are as follows:

[0097]

[0098]

[0099] The fitness change curves of the 6-dimensional and 12-dimensional HADE-GWO algorithms are shown below. Figure 3 As shown. Regardless of whether it's 6D or 12D ambiguity resolution, the HADE-GWO algorithm, even if it gets stuck in a local optimum for a short time, can escape it subsequently. The running times of the 6D and 12D HADE-GWO algorithms are as follows: Figure 6 and Figure 7 As shown, the complexity of ambiguity resolution increases with the increase of the ambiguity dimension, and the resolution time increases accordingly.

[0100] To compare and analyze the accuracy and reliability of the HADE-GWO algorithm under different dimensions, the HADE-GWO algorithm was repeatedly tested 100 times for 3D, 6D, and 12D ambiguities, with a maximum of 200 iterations per test. The average solution time and solution success rate are shown in Table 2.

[0101] Table 2 Comparison of HADE-GWO algorithm under different dimensions

[0102]

[0103] As the fuzzy dimension increases, the average solution time of the algorithm increases accordingly, and the solution success rate also decreases. However, the solution speed and solution success rate of the algorithm can still meet the engineering requirements.

[0104] The above-disclosed method is merely a preferred embodiment of the integer ambiguity resolution method based on the hybrid adaptive differential evolution gray wolf algorithm of this application. It should not be construed as limiting the scope of the claims of this application. Those skilled in the art can understand that all or part of the process of implementing the above embodiments and the equivalent changes made in accordance with the claims of this application still fall within the scope of this application.

Claims

1. A method for resolving integer ambiguities based on a hybrid adaptive differential evolution gray wolf algorithm, characterized in that, Includes the following steps: Load raw GNSS data and perform downcorrelation, then dynamically calculate and set adaptive integer search space boundaries; At the beginning of each generation, the solution for each individual is calculated using a pre-computed inverse matrix, and these values ​​are stored in an array. The program compares the fitness of each individual in real time and updates the records of the global best, second best, and third best solutions. Matrix operations are used to perform a differential evolution mutation-crossover-selection process for the entire population to generate a new generation of population; The intelligence and robustness of the execution parameter adaptation and Levy flight enhancement algorithm; Check if the current iteration count has reached the preset maximum iteration count. If not, increment the iteration counter by one, return and repeat the real-time comparison of the fitness of each individual, and update the records of the global optimal, suboptimal and third optimal solutions. If so, start Nelder-Mead local search to try to find a better global optimal wolf. The final calculation result is output as the global optimal integer solution vector and the corresponding optimal fitness value recorded in the global optimal wolf variable.

2. The integer ambiguity resolution method based on the hybrid adaptive differential evolution gray wolf algorithm as described in claim 1, characterized in that, The raw GNSS data includes the floating-point modulus vector and the corresponding covariance matrix obtained from GNSS floating-point calculation.

3. The integer ambiguity resolution method based on the hybrid adaptive differential evolution gray wolf algorithm as described in claim 1, characterized in that, The mutation-crossover-selection process is vectorized. Mutation: All mutation vectors are generated in parallel for the entire population through a one-time matrix operation. Crossover: A binomial crossover strategy is adopted to generate all trial vectors at once through a logical mask. Selection: The entire population is updated through a one-time fitness comparison and logical indexing.

4. The integer ambiguity resolution method based on the hybrid adaptive differential evolution gray wolf algorithm as described in claim 1, characterized in that, The parameter adaptation is an online learning process based on a "reward and punishment" mechanism. Individuals that fail to evolve successfully in the selection process are considered invalid by the algorithm and need to be reset. When the algorithm detects that the global optimal solution has stalled, the Levy flight guides the search to a new and more promising area through a long-distance jump in a random direction.

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