A low earth orbit satellite positioning satellite selection method, device, equipment and medium

Abstract

The application relates to a low-orbit satellite positioning satellite selection method, device, equipment and medium. The method comprises the following steps: acquiring adaptive parameters such as the population dimension of an alternative scheme and the number of satellite selection, and designing an alternative scheme matrix and a random step matrix. The alternative scheme matrix is resampled to generate an evolution matrix, and a decay factor is calculated according to the number of iterations and the number of fitness evaluations. A basis vector is obtained through the number of iterations, the number of evaluations and the alternative scheme matrix, and after the fitness of the evolution matrix is calculated, a dominant solution and a poor solution are generated. A new scheme matrix is calculated in combination with the basis vector, the decay factor and the like, and if the fitness of the new scheme matrix is better, the current optimal solution is replaced. The satellite weight in the historical evolution matrix is adjusted by using a dynamic weight distribution strategy, and the scheme matrix is further optimized. Iteration comparison is continuously carried out, the scheme matrix with the optimal fitness is taken as the current iteration result, and the maximum number of iterations is reached until the optimal satellite selection scheme is finally output. The method can improve the satellite selection efficiency and accuracy.

Description

Technical Field

[0001] This application relates to the field of satellite navigation technology, and in particular to a method, apparatus, equipment and medium for low-Earth orbit satellite positioning. Background Technology

[0002] Given the challenges of low-Earth orbit (LEO) satellite dynamic satellite selection, including high computational complexity, difficulties in final satellite selection due to dense distribution of candidate satellites, and the waste of computing resources and increased receiver power consumption caused by drastic changes in constellation spatial configuration and rapid replacement of visible satellites, research is currently underway both domestically and internationally on optimizing satellite selection strategies for navigation constellations. In recent years, LEO satellite construction has been in a phase of rapid deployment. In large-scale LEO constellation scenarios, ground receivers face a massive number of satellites; tracking all of them would not only result in redundant observations but also significantly increase computational costs. Therefore, satellite selection is not only the primary step in positioning calculations but also crucial for constructing good observational data for subsequent calculations. Consequently, satellite selection technology based on LEO satellite positioning has become a research hotspot in navigation technology.

[0003] Currently, some researchers have proposed an efficient LEO satellite selection algorithm that significantly reduces computational complexity through matrix factorization and recursive update rules, while ensuring that GDOP converges to the suboptimal interval. Other researchers have proposed a Doppler Geometric Dilution of Precision (DGDOP) model suitable for LEO satellites and a clustering-based fast star selection method. Experiments using Starlink measured signals show that this method can stably reduce positioning errors by over 45%, meeting the requirement of low computational complexity while maintaining accuracy. Star selection refers to selecting the combination of stars with the optimal geometric distribution and shortest measurement operation period from the star catalog according to the requirements of astronomical measurement specifications, forming an observation star sequence with measurement timelines.

[0004] However, traditional satellite selection algorithms suffer from inefficiency and inconsistent selection schemes between adjacent epochs. This increases the computational load on the receiver, posing a challenge to real-time positioning. Currently, accurate, stable, and efficient satellite selection algorithms are lacking. Therefore, systematically analyzing and researching satellite selection strategies and algorithms, and deeply analyzing the impact mechanism of satellite configuration and motion on positioning accuracy, in order to design high-quality, stable, and accurate satellite selection strategies for GNSS and LEO navigation constellations, has become a key problem that positioning algorithms in scenarios with massive LEO satellites must solve. Summary of the Invention

[0005] Therefore, it is necessary to provide a satellite selection method, device, equipment, and medium for low-Earth orbit satellite positioning that can improve the efficiency and accuracy of satellite selection, in order to address the aforementioned technical problems.

[0006] A satellite selection method for low-Earth orbit satellite positioning, the method comprising:

[0007] Obtain the adaptive parameters for satellite selection; the adaptive parameters include the population dimension of the candidate schemes, the number of selected satellites, the maximum number of iterations, and the number of visible satellites at the current epoch; design the candidate scheme matrix and the random step size matrix based on the population dimension of the candidate schemes and the number of visible satellites at the current epoch;

[0008] The candidate scheme matrix is ​​sampled with replacement to obtain the evolution matrix; the decay factor is calculated based on the maximum number of iterations and the number of fitness evaluations.

[0009] The basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix; the fitness values ​​of the evolution matrix are calculated, and dominant and inferior solutions are generated according to the pre-set fitness relationships; a new solution matrix is ​​calculated based on the basis vectors, decay factors, random step size matrix, and dominant solutions.

[0010] If the fitness of the new scheme matrix is ​​better than that of the evolution matrix of the historical epoch, it is taken as the current optimal scheme matrix. The weights of each satellite in the evolution matrix of the historical epoch are dynamically adjusted using a dynamic weight allocation strategy to obtain the optimized scheme matrix. The optimized scheme matrix is ​​compared with the current optimal scheme matrix, and the scheme matrix with better fitness is taken as the optimal solution for the current iteration. This process continues until the maximum number of iterations is reached, at which point the optimal solution is output as the best satellite selection scheme.

[0011] A satellite selection device for low-Earth orbit positioning, the device comprising:

[0012] The parameter acquisition and alternative scheme matrix design module is used to acquire the adaptive parameters for satellite selection. The adaptive parameters include the population dimension of alternative schemes, the number of satellites selected, the maximum number of iterations, and the number of visible satellites at the current epoch. The alternative scheme matrix and the random step size matrix are designed based on the population dimension of alternative schemes and the number of visible satellites at the current epoch.

[0013] The evolution matrix and decay factor calculation module is used to perform sampling with replacement on the candidate scheme matrix to obtain the evolution matrix; and to calculate the decay factor based on the maximum number of iterations and the number of fitness evaluations.

[0014] The scheme matrix update module is used to calculate the basis vectors based on the maximum number of iterations, the number of fitness evaluations, and the candidate scheme matrix; calculate the fitness values ​​of the evolution matrix and generate dominant and inferior solutions based on the pre-set fitness relationships; and calculate the new scheme matrix based on the basis vectors, decay factors, random step size matrix, and dominant solutions.

[0015] The optimal satellite selection scheme calculation module is used to select the current optimal scheme matrix if the fitness of the new scheme matrix is ​​better than that of the evolution matrix of the historical epochs. It dynamically adjusts the weights of each satellite in the evolution matrix of the historical epochs using a dynamic weight allocation strategy to obtain an optimized scheme matrix. The optimized scheme matrix is ​​compared with the current optimal scheme matrix, and the scheme matrix with better fitness is selected as the optimal solution for the current iteration. This process continues until the maximum number of iterations is reached, at which point the optimal solution output is taken as the optimal satellite selection scheme.

[0016] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0017] Obtain the adaptive parameters for satellite selection; the adaptive parameters include the population dimension of the candidate schemes, the number of selected satellites, the maximum number of iterations, and the number of visible satellites at the current epoch; design the candidate scheme matrix and the random step size matrix based on the population dimension of the candidate schemes and the number of visible satellites at the current epoch;

[0018] The candidate scheme matrix is ​​sampled with replacement to obtain the evolution matrix; the decay factor is calculated based on the maximum number of iterations and the number of fitness evaluations.

[0019] The basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix; the fitness values ​​of the evolution matrix are calculated, and dominant and inferior solutions are generated according to the pre-set fitness relationships; a new solution matrix is ​​calculated based on the basis vectors, decay factors, random step size matrix, and dominant solutions.

[0020] If the fitness of the new scheme matrix is ​​better than that of the evolution matrix of the historical epoch, it is taken as the current optimal scheme matrix. The weights of each satellite in the evolution matrix of the historical epoch are dynamically adjusted using a dynamic weight allocation strategy to obtain the optimized scheme matrix. The optimized scheme matrix is ​​compared with the current optimal scheme matrix, and the scheme matrix with better fitness is taken as the optimal solution for the current iteration. This process continues until the maximum number of iterations is reached, at which point the optimal solution is output as the best satellite selection scheme.

[0021] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0022] Obtain the adaptive parameters for satellite selection; the adaptive parameters include the population dimension of the candidate schemes, the number of selected satellites, the maximum number of iterations, and the number of visible satellites at the current epoch; design the candidate scheme matrix and the random step size matrix based on the population dimension of the candidate schemes and the number of visible satellites at the current epoch;

[0023] The candidate scheme matrix is ​​sampled with replacement to obtain the evolution matrix; the decay factor is calculated based on the maximum number of iterations and the number of fitness evaluations.

[0024] The basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix; the fitness values ​​of the evolution matrix are calculated, and dominant and inferior solutions are generated according to the pre-set fitness relationships; a new solution matrix is ​​calculated based on the basis vectors, decay factors, random step size matrix, and dominant solutions.

[0025] If the fitness of the new scheme matrix is ​​better than that of the evolution matrix of the historical epoch, it is taken as the current optimal scheme matrix. The weights of each satellite in the evolution matrix of the historical epoch are dynamically adjusted using a dynamic weight allocation strategy to obtain the optimized scheme matrix. The optimized scheme matrix is ​​compared with the current optimal scheme matrix, and the scheme matrix with better fitness is taken as the optimal solution for the current iteration. This process continues until the maximum number of iterations is reached, at which point the optimal solution is output as the best satellite selection scheme.

[0026] The aforementioned method, apparatus, equipment, and medium for low-Earth orbit satellite positioning utilizes adaptive parameters, encompassing key information such as the population dimension of candidate schemes, to lay the foundation for satellite selection based on its design matrix. Through sampling with replacement, calculation of attenuation factors and basis vectors, and combining advantageous and disadvantageous solutions, a new scheme matrix is ​​generated, refining the iterative process. Historical satellite selection schemes are introduced, employing strategies such as initializing "high-value" satellite selection, adding switching penalties, and assigning more weight to historical satellites during evolution. Combined with dynamic weight allocation to optimize the matrix, this approach leverages historical experience to ensure satellite selection stability while enhancing directionality through heuristic search. It continuously filters for schemes with better fitness during iteration, enabling the satellite selection results to efficiently converge to high-quality solutions under low Doppler geometric precision factor constraints. This improves satellite selection efficiency and positioning accuracy, mitigating the drawbacks of traditional algorithms. While ensuring a low Doppler geometric precision factor and a low satellite switching frequency, it significantly enhances satellite selection efficiency and positioning accuracy. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating a satellite selection method for low-Earth orbit positioning in one embodiment.

[0028] Figure 2 This is a flowchart of a satellite selection method for low-Earth orbit positioning in one embodiment;

[0029] Figure 3 This is a schematic diagram of the algebraic sum of the projected areas of a triangle formed by unit observation vectors onto three orthogonal coordinate planes in one embodiment;

[0030] Figure 4 This is a structural block diagram of a satellite selection device for low-Earth orbit positioning in one embodiment;

[0031] Figure 5 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0033] In one embodiment, such as Figure 1 and Figure 2 As shown, a satellite selection method for low-Earth orbit satellite positioning is provided, including the following steps:

[0034] Step 102: Obtain the adaptive parameters for satellite selection; the adaptive parameters include the population dimension of the candidate scheme, the number of selected satellites, the maximum number of iterations, and the number of visible satellites at the current epoch; design the candidate scheme matrix and the random step size matrix based on the population dimension of the candidate scheme and the number of visible satellites at the current epoch.

[0035] Before data acquisition, a dual-objective optimization model is established, considering both the number of satellite switching attempts between fusion satellite selection schemes and DGDOP (Discretionary Gain of Opportunity). This model defines discretized time-varying satellite selection... The plan is as follows:

[0036] ;

[0037] in This represents the set of visible satellites at epoch k. Number of visible satellites To constrain the number of stars selected, a multi-objective optimization problem is constructed:

[0038] ;

[0039] In the formula: For the DGDOP index during the observation period Time average ; To measure the frequency of satellite switching between selection schemes by using the cardinality of the symmetric difference between the selection sets of satellites in previous and subsequent epochs. The sign for the difference of sets is symmetric. express Pseudo-norm. The DGDOP indicator is:

[0040] ;

[0041] Wherein, the benchmark scaling factor is set. Define the normalized scaling factor . The volume of the triangular pyramid spanned by three unit observation vectors i, j, and k. For example... Figure 3 As shown, For unit observation vector and The algebraic sum of the projected areas of the triangle formed onto the three orthogonal coordinate planes.

[0042] Constructing an aggregate objective function based on Pareto optimality theory:

[0043] ;

[0044] in , These are the theoretical lower and lower bounds for single-objective optimization, respectively. A dynamically adjusted set of preference weights. This represents the set of preference weights in the 0-1 interval. Given the NP-hard nature of the global optimization above, a recursive optimization framework based on epoch decomposition is designed. In the... Establishing local optimization problems based on epochs:

[0045] (1)

[0046] ;

[0047] in For the historical solution of the previous epoch, the weight coefficients satisfy It can be dynamically adjusted according to the spatial distribution of satellites. To suppress jumps in satellite selection schemes between adjacent epochs, a temporal coupling constraint is introduced:

[0048] ;

[0049] in This constraint, set as the maximum replacement ratio threshold, limits the maximum number of replacements per epoch. To ensure the temporal smoothness of the satellite selection scheme, the above local optimization problem is solved. The satellites are ranked according to their fitness values, and the top N satellites are selected to generate an initial satellite selection scheme. The initial satellite selection scheme is then used as a candidate scheme for iterative optimization to generate the optimal satellite selection scheme.

[0050] The initialization process requires inputting parameters such as the base station position, satellite position and velocity, candidate population dimension L, maximum number of iterations PMax, number of selected satellites N, and various fitness parameters, as shown in Table 1.

[0051] Table 1

[0052]

[0053] The size of the alternative matrix depends on L and the number of visible satellites at epoch k, i.e. The initial weights of each satellite are calculated using a formula, and K is set to 0. If K = 0, the L-dimensional candidate matrix X is directly initialized based on the weights; if K ≠ 0, the historical schemes of epoch k-1 are first obtained, and then the L-dimensional candidate matrix X is initialized based on the weights. When initializing the parameters of the satellite selection scheme, since this application requires the solution space to be continuous, while the selection of a satellite is usually represented by discrete Boolean values, the weights are used to measure the contribution of a satellite to the optimization objective when designing the algorithm. This makes the solution space continuous. When the algorithm outputs, the satellites are arranged in descending order of weight, and the top N satellites are taken as the satellite selection scheme.

[0054] During the initialization phase, a multi-factor fusion satellite prior weighting strategy is adopted, as follows:

[0055] ;

[0056] in, This represents the initial satellite weight vector for the k-th epoch. This represents the total number of visible satellites in the k-th epoch. This is the satellite residency factor vector; This is a scale factor vector; express Vie Uniformly distributed random vectors. This initialization design, by introducing prior information for guidance, can eliminate interference from transient satellites and effectively reduce the risk of blind searching during the optimization process. Its mechanism is similar to setting up directional signs in a maze, significantly improving search efficiency. By dynamically adjusting the weight coefficients a1, a2, and a3, a balance can be achieved between low DGDOP, low satellite switching frequency, and random exploration capability. , , The range of values ​​is ,and .

[0057] Step 104: Sample the candidate scheme matrix with replacement to obtain the evolution matrix; calculate the decay factor based on the maximum number of iterations and the number of fitness evaluations.

[0058] The number of fitness evaluations (P) must be greater than the maximum number of iterations. If the condition is met, the process ends; otherwise, it proceeds to the iterative optimization phase for calculation. LThe evolutionary matrix E is calculated, and the fitness of the candidate solutions in E is solved. Then, a random number rand(0,1) is generated. If it is less than 0.5, a basis vector F is generated based on the fitness-weighted sampling matrix B; otherwise, a basis vector F is generated based on the diagonalized sampling matrix A. Afterwards, the _th_ evolutionary matrix E is calculated. i The dominant solution, the disadvantaged solution, and the difference step size θ are then used to obtain the th dominant solution, the th disadvantaged solution, and the difference step size θ. i A new interpretation, Enew, specifically includes:

[0059] The evolution matrix E is obtained by performing a sampling with replacement operation on the candidate matrix X, i.e. , Among the symbols This indicates that L sampling operations with replacement are performed. This step is to generate a matrix for evolution from the candidate solution set to explore new solution spaces. Decay factor The ability to explore and develop control algorithms is calculated using the following formula:

[0060] ;

[0061] Where P represents the number of fitness assessments. As the number of fitness assessments P increases, It exhibits a non-linear decreasing trend, thereby enabling the algorithm to transition from global exploration to local development. Let be a random step size matrix, where the elements take random values ​​between 0 and 1. Fitness is calculated using formula (1).

[0062] Step 106: Calculate the basis vectors based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix; calculate the fitness value of the evolution matrix and generate dominant and inferior solutions based on the pre-set fitness relationship; calculate the new solution matrix based on the basis vectors, decay factor, random step size matrix, and dominant solutions.

[0063] The formula for calculating the basis vector F is as follows:

[0064] ;

[0065] in, and All by Calculated; express The learning rate This indicates the iteration situation when rand(0,1)<0.5. express The learning rate This indicates the iteration situation when rand(0,1)≥0.5. This represents the iteration case when rand(0,1)<0.5. iThe basis vectors of the nth iteration. This represents the iteration case where rand(0,1)≥0.5. i The basis vectors of the nth iteration. Indicates the weighting coefficient; A is A square matrix of order X, which is sampled with replacement from the matrix of alternative solutions X. This is obtained in the following way. B is a matrix with J rows and D columns. B is obtained by sampling J times without replacement from the alternative matrix X. It is the first in B. j The weight of the i-th solution in a row is calculated using the following formula:

[0066] ;

[0067] in, Representing the j Line 1 i One solution. Function The function for calculating fitness, i.e. return The objective function value of the star selection scheme. If the loop has just started, the initial basis vectors... It will be randomly generated based on the effective search space.

[0068] Based on the pre-set fitness relationship Generate the i-th advantageous solution Disadvantage solution A stochastic solution to the relation. Difference step size. For one A dimensional random vector.

[0069] Calculate the new solution for the i-th iteration. The calculation formula is as follows:

[0070] ;

[0071] in, express The i-th row vector in the array.

[0072] Step 108: If the fitness of the new scheme matrix is ​​better than that of the evolution matrix of the historical epoch, then it is taken as the current optimal scheme matrix; the weights of each satellite in the evolution matrix of the historical epoch are dynamically adjusted using a dynamic weight allocation strategy to obtain the optimized scheme matrix; the optimized scheme matrix is ​​compared with the current optimal scheme matrix, and the scheme matrix with better fitness is taken as the optimal solution for the current iteration, until the optimal solution output when the maximum number of iterations is reached is taken as the optimal satellite selection scheme.

[0073] like If the fitness is better, then update the optimal solution. To enhance the algorithm's preference for stable satellite selection strategies, a historical selection enhancement mechanism is designed. During the iterative optimization process, a dynamic weight allocation strategy is used to assign priority weights to satellites in historical selections, mathematically expressed as:

[0074] ;

[0075] In the formula, This is the weight vector of the optimal scheme in the previous epoch, representing the weight distribution of N satellites in the historical scheme; This is the weight vector of the new scheme generated in the i-th iteration of the current epoch; for Epichronous satellite selection set; This refers to the inheritance coefficient of historical schemes. This mechanism maintains the inheritance of high-quality historical schemes while reducing the frequency of satellite handover by dynamically adjusting the ratio of historical weights to newly added weights.

[0076] Adjusted according to historical plans The weights of each satellite are then combined with the optimal satellite selection scheme for this large-scale cycle. Perform fitness comparisons and update the optimal solution. Finally, determine... i>L If the condition is met, return to the step of "initializing the L-dimensional alternative matrix X according to the weights" to start a new round of iteration; if not, continue the current iteration process to generate a new solution, and so on, repeating this process to continuously iterate and optimize until P > 0. The termination condition is to output the first N satellites in the optimal solution as the star selection scheme for epoch k.

[0077] The aforementioned satellite selection method for low-Earth orbit (LEO) positioning, as described in this application, accurately acquires adaptive parameters, encompassing key information such as the population dimension of candidate schemes, and lays the foundation for satellite selection based on its design matrix. Through sampling with replacement, calculation of attenuation factors and basis vectors, and combining advantageous and disadvantageous solutions, a new scheme matrix is ​​generated, refining the iterative process. Historical satellite selection schemes are introduced, and strategies such as initializing "high-value" satellite selection, adding switching penalties, and assigning more weight to historical satellites during evolution are employed. Combined with dynamic weight allocation to optimize the matrix, this approach leverages historical experience to ensure satellite selection stability while enhancing directionality through heuristic search. It continuously filters for schemes with better fitness during iteration, enabling the satellite selection results to efficiently converge to high-quality solutions under the constraint of a low Doppler geometric precision factor. This improves satellite selection efficiency and positioning accuracy, mitigating the drawbacks of traditional algorithms. While ensuring a low Doppler geometric precision factor and a low satellite switching frequency, it significantly improves satellite selection efficiency and positioning accuracy.

[0078] In one embodiment, the decay factor is calculated based on the maximum number of iterations and the number of fitness evaluations, including:

[0079] The decay factor is calculated based on the maximum number of iterations and the number of fitness evaluations:

[0080] ;

[0081] in, Indicates the number of fitness assessments. This indicates the maximum number of iterations.

[0082] In one embodiment, the basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix, including:

[0083] The basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the matrix of alternative solutions:

[0084] ;

[0085] in, and All by Calculations show that express The learning rate This indicates the iteration situation when rand(0,1)<0.5. express The learning rate This indicates the iteration situation when rand(0,1)≥0.5. This represents the iteration case when rand(0,1)<0.5. i The basis vectors of the nth iteration. This represents the iteration case where rand(0,1)≥0.5. i The basis vectors of the nth iteration. A represents the weighting coefficient. A square matrix of order X, which is sampled with replacement from the matrix of alternative solutions X. This yields B, which is a matrix with J rows and D columns. B is obtained by sampling J times without replacement from the alternative matrix X. It is the first in B. j The first line i The weight of each solution.

[0086] In one embodiment, generating dominant and disadvantageous solutions based on a pre-set fitness relationship includes:

[0087] Based on the pre-set fitness relationship Generate the first i One advantageous solution and disadvantage solution ,in, This represents the fitness value of the evolutionary matrix.

[0088] In one embodiment, a new filing scheme matrix is ​​calculated based on the basis vectors, attenuation factor, random step size matrix, and dominant solution, including:

[0089] Based on the basis vectors, attenuation factor, random step size matrix, and dominant solution, the new filing scheme matrix is ​​calculated as follows:

[0090] ;

[0091] in, express The first in i row vectors Represents basis vectors. Indicates the attenuation factor. Represents the random step size matrix, Indicates the first i A superior solution, Indicates the first i An evolutionary matrix.

[0092] In one embodiment, a dynamic weight allocation strategy is used to dynamically adjust the weights of each satellite in the evolution matrix of historical epochs to obtain an optimized scheme matrix, including:

[0093] By dynamically adjusting the weights of each satellite in the evolution matrix of historical epochs using a dynamic weight allocation strategy, the optimized scheme matrix is ​​obtained as follows:

[0094] ;

[0095] in, This is the weight vector of the optimal solution in the previous epoch, representing the historical solutions. N The weight distribution of each satellite; This is the weight vector of the new scheme generated in the i-th iteration of the current epoch; for Epichronous satellite selection set; This represents the inheritance coefficient of historical schemes.

[0096] In one embodiment, the total time complexity of the optimal solution calculation process is calculated, and the value of the fitness parameter is selected based on the calculation result; the process of calculating the total time complexity of the optimal solution calculation process is as follows:

[0097] ;

[0098] in, This represents the total time complexity of the initialization phase. This represents the initialization scheme vector. This indicates that there were sampling times with replacement. This represents the total time complexity of computing the basis vector F. Indicates the number of samples without replacement. This represents the total time complexity of updating the optimal solution. This indicates the number of times the optimal solution has been updated. This represents the total time complexity of fitness calculation. This indicates the maximum number of iterations.

[0099] In a specific embodiment, during the initialization phase, each initialization scheme vector is calculated. When vector addition and multiplication are involved, the time complexity is O(n log n). Because M such initialization scheme vectors need to be generated, the total time complexity of the initialization phase is O(M). .

[0100] When calculating the basis vectors F, the generating matrix A needs to be calculated from the candidate matrix X. Since sampling with replacement occurs twice, each sampling operation requires iterating through the elements of X, so the time complexity of each sampling operation is O(n log n). Therefore, the time complexity of generating A is . When generating matrix B, the candidate matrix X needs to be sampled J times without replacement. Each sampling also requires traversing X, and the time complexity of each sampling operation is O(M(K)). Therefore, the time complexity of generating B is O(M(K)). Calculate the weights. At that time, it is necessary to calculate The fitness of each solution is calculated and summed, among other operations. The time complexity of calculating the fitness is O(n log n). (Calculating DGDOP requires matrix multiplication and inversion operations), so the time complexity of calculating the weights is O(n log n). In summary, the total time complexity for calculating the basis vector F is:

[0101] .

[0102] In the solution update step, the new solution is calculated. This involves vector addition and multiplication operations, with a time complexity of O(n log n). Since each iteration requires updating L solutions, the total time complexity of the solution update step is O(L). .

[0103] Furthermore, fitness calculation is performed multiple times within the algorithm. Assuming the maximum number of iterations is PMax, and the number of fitness calculations in each iteration is related to the population size (let the population size be L), then the total time complexity of fitness calculation is... .

[0104] Combining the above steps, the total time complexity of the star selection algorithm based on AE is:

[0105] ;

[0106] In practical application scenarios, , , , The values ​​of these parameters will vary depending on the specific problem and the size of the data. As the problem size increases, if... (representing the total number of visible satellites at epoch k) and A significant increase in the maximum number of iterations leads to a substantial rise in the algorithm's time complexity, which in turn increases computational costs significantly. Conversely, when the number of visible satellites is small, the algorithm's computational efficiency is relatively high. Meanwhile, the time complexity of calculating fitness also decreases. The impact on overall time complexity should not be underestimated. In conclusion, when applying the method of this application, these parameters need to be selected reasonably according to the characteristics of the specific problem and actual needs in order to balance the performance and computational cost of the algorithm.

[0107] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order in which these steps are executed, and they can be performed in other orders. Furthermore, Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0108] In one embodiment, such as Figure 4 As shown, a satellite selection device for low-Earth orbit satellite positioning is provided, including: a parameter acquisition and alternative scheme matrix design module 402, an evolution matrix and attenuation factor calculation module 404, a scheme matrix update module 406, and an optimal satellite selection scheme calculation module 408, wherein:

[0109] The parameter acquisition and alternative scheme matrix design module 402 is used to acquire the adaptive parameters for satellite selection. The adaptive parameters include the population dimension of alternative schemes, the number of satellites selected, the maximum number of iterations, and the number of visible satellites in the current epoch. The alternative scheme matrix and the random step size matrix are designed based on the population dimension of alternative schemes and the number of visible satellites in the current epoch.

[0110] The evolution matrix and decay factor calculation module 404 is used to perform sampling with replacement on the candidate scheme matrix to obtain the evolution matrix; and to calculate the decay factor based on the maximum number of iterations and the number of fitness evaluations.

[0111] The scheme matrix update module 406 is used to calculate the basis vector based on the maximum number of iterations, the number of fitness evaluations, and the candidate scheme matrix; calculate the fitness value of the evolution matrix and generate dominant and inferior solutions according to the pre-set fitness relationship; and calculate the new scheme matrix based on the basis vector, decay factor, random step size matrix, and dominant solution.

[0112] The optimal satellite selection scheme calculation module 408 is used to select the current optimal scheme matrix if the fitness of the new scheme matrix is ​​better than that of the evolution matrix of the historical epochs; dynamically adjust the weights of each satellite in the evolution matrix of the historical epochs using a dynamic weight allocation strategy to obtain the optimized scheme matrix; compare the optimized scheme matrix with the current optimal scheme matrix, and select the scheme matrix with better fitness as the optimal solution for the current iteration, until the optimal solution is output when the preset maximum number of iterations is reached, which is then taken as the optimal satellite selection scheme.

[0113] Specific limitations regarding the satellite selection device for low-Earth orbit (LEO) positioning can be found in the limitations regarding the satellite selection method for LEO positioning described above, and will not be repeated here. Each module in the aforementioned LEO satellite selection device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0114] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 5 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a satellite selection method for low-Earth orbit satellite positioning. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0115] Those skilled in the art will understand that Figure 5 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0116] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0117] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0118] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

Claims

1. A satellite selection method for low-Earth orbit satellite positioning, characterized in that, The method includes: Obtain the adaptive parameters for satellite selection; the adaptive parameters include the population dimension of the candidate schemes, the number of selected satellites, the maximum number of iterations, and the number of visible satellites at the current epoch; design the candidate scheme matrix and the random step size matrix based on the population dimension of the candidate schemes and the number of visible satellites at the current epoch; The candidate scheme matrix is ​​sampled with replacement to obtain the evolution matrix; the decay factor is calculated based on the maximum number of iterations and the number of fitness evaluations. The basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix; the fitness values ​​of the evolution matrix are calculated, and dominant and inferior solutions are generated according to the pre-set fitness relationships; a new solution matrix is ​​calculated based on the basis vectors, the decay factor, the random step size matrix, and the dominant solution. If the fitness of the new scheme matrix is ​​better than that of the evolution matrix of the historical epoch, it is taken as the current optimal scheme matrix. The weights of each satellite in the evolution matrix of the historical epoch are dynamically adjusted using a dynamic weight allocation strategy to obtain an optimized scheme matrix. The optimized scheme matrix is ​​compared with the current optimal scheme matrix, and the scheme matrix with better fitness is taken as the optimal solution for the current iteration. This process continues until the maximum number of iterations is reached, at which point the optimal solution is output as the optimal satellite selection scheme. The basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix, including: The basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix. in, and All by Calculations show that express F a The learning rate This indicates the iteration situation when rand(0,1)<0.

5. express F b The learning rate This indicates the iteration situation when rand(0,1)≥0.

5. This represents the iteration case when rand(0,1)<0.

5. i The basis vectors of the nth iteration. This represents the iteration case where rand(0,1)≥0.

5. i The basis vectors of the nth iteration. A represents the weighting coefficient. A square matrix of order X, which is sampled with replacement from the candidate matrix X. This yields B, which is a matrix with J rows and D columns. B is obtained by sampling J times without replacement from the alternative matrix X. It is the first in B. j The first line i The weights of each solution; By dynamically adjusting the weights of each satellite in the evolution matrix of historical epochs using a dynamic weight allocation strategy, an optimized scheme matrix is ​​obtained, including: By dynamically adjusting the weights of each satellite in the evolution matrix of historical epochs using a dynamic weight allocation strategy, the optimized scheme matrix is ​​obtained as follows: in, This is the weight vector of the optimal solution in the previous epoch, representing the historical solutions. N The weight distribution of each satellite; For the current epoch k The weight vector of the new scheme generated in the i-th iteration; for Epichronous satellite selection set; This represents the inheritance coefficient of historical schemes.

2. The method according to claim 1, characterized in that, The decay factor is calculated based on the maximum number of iterations and the number of fitness evaluations, including: The decay factor is calculated based on the maximum number of iterations and the number of fitness evaluations. in, Indicates the number of fitness assessments. This indicates the maximum number of iterations.

3. The method according to claim 1, characterized in that, Generate dominant and disadvantageous solutions based on pre-defined fitness relationships, including: Based on the pre-set fitness relationship Generate the first i One Advantage Solution and disadvantage solution ,in, This represents the fitness value of the evolutionary matrix.

4. The method according to claim 1, characterized in that, A new filing scheme matrix is ​​calculated based on the basis vectors, attenuation factors, random step size matrix, and dominant solution, including: Based on the basis vectors, attenuation factors, random step size matrix, and dominant solution, the new filing scheme matrix is ​​calculated as follows: in, express The first in i row vectors Represents basis vectors. Indicates the attenuation factor. Represents the random step size matrix, Indicates the first i A superior solution, Indicates the first i An evolutionary matrix.

5. The method according to claim 1, characterized in that, The method further includes: The total time complexity of the optimal solution calculation process is calculated, and the value of the fitness parameter is selected based on the calculation result; the process of calculating the total time complexity of the optimal solution calculation process is as follows: in, This represents the total time complexity of the initialization phase. This represents the initialization scheme vector. This indicates that there were sampling times with replacement. This represents the total time complexity of computing the basis vector F. Indicates the number of samples without replacement. This represents the total time complexity of updating the optimal solution. This indicates the number of times the optimal solution has been updated. This represents the total time complexity of fitness calculation. This indicates the maximum number of iterations.

6. A satellite selection device for low-Earth orbit satellite positioning, characterized in that, The device includes: The parameter acquisition and alternative scheme matrix design module is used to acquire the adaptive parameters for satellite selection; the adaptive parameters include the population dimension of alternative schemes, the number of satellites selected, the maximum number of iterations, and the number of visible satellites at the current epoch; the alternative scheme matrix and the random step size matrix are designed based on the population dimension of alternative schemes and the number of visible satellites at the current epoch. The evolution matrix and decay factor calculation module is used to perform sampling with replacement on the candidate scheme matrix to obtain the evolution matrix; and to calculate the decay factor based on the maximum number of iterations and the number of fitness evaluations. The scheme matrix update module is used to calculate the basis vectors based on the maximum number of iterations, the number of fitness evaluations, and the candidate scheme matrix, including: The basis vectors are calculated based on the maximum number of iterations, the number of fitness evaluations, and the candidate solution matrix. in, and All by Calculations show that express F a The learning rate This indicates the iteration situation when rand(0,1)<0.

5. express F b The learning rate This indicates the iteration situation when rand(0,1)≥0.

5. This represents the iteration case when rand(0,1)<0.

5. i The basis vectors of the nth iteration. This represents the iteration case where rand(0,1)≥0.

5. i The basis vectors of the nth iteration. A represents the weighting coefficient. A square matrix of order X, which is sampled with replacement from the candidate matrix X. This yields B, which is a matrix with J rows and D columns. B is obtained by sampling J times without replacement from the alternative matrix X. It is the first in B. j The first line i The weights of each solution are determined; the fitness values ​​of the evolution matrix are calculated, and dominant and inferior solutions are generated according to the pre-set fitness relationship; a new scheme matrix is ​​calculated based on the basis vectors, decay factors, random step size matrix, and dominant solutions. The optimal satellite selection matrix is ​​used to calculate the best satellite selection matrix if the fitness of the new matrix is ​​better than that of the evolution matrix at the historical epochs. It dynamically adjusts the weights of each satellite in the evolution matrix at the historical epochs using a dynamic weight allocation strategy to obtain the optimized matrix, including: By dynamically adjusting the weights of each satellite in the evolution matrix of historical epochs using a dynamic weight allocation strategy, the optimized scheme matrix is ​​obtained as follows: in, This is the weight vector of the optimal solution in the previous epoch, representing the historical solutions. N The weight distribution of each satellite; For the current epoch k The weight vector of the new scheme generated in the i-th iteration; for Epichronous satellite selection set; The inheritance coefficient of historical schemes is used; the optimized scheme matrix is ​​compared with the current best scheme matrix, and the scheme matrix with better fitness is taken as the optimal solution of the current iteration, until the optimal solution is output when the preset maximum number of iterations is reached, which is taken as the best selected scheme.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

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