Star selection rapid positioning method and system based on whale optimization algorithm

Abstract

The invention discloses a whale optimization algorithm-based satellite selection rapid positioning method and system. The method comprises the following steps of: obtaining visible satellites; sorting the visible satellites from small to large and sequentially and continuously numbering the visible satellites from 1 to m; selecting the satellite combination with the minimum GDOP value based on the WOA, and recording the serial number of the satellite combination; extracting each satellite data of the optimal combination; through satellite data, rapid positioning is carried out by using a least square method. By adopting the technical scheme of the invention, the calculation amount is greatly reduced, and the accuracy and reliability of satellite selection are further improved; even under the condition that the number of satellites is large, the satellite selection process can be completed quickly and accurately, and the real-time performance and stability of a navigation positioning system are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of global satellite navigation systems, and particularly relates to a satellite selection and rapid positioning method and system based on a whale optimization algorithm. Background Art

[0002] If the GNSS data of all visible satellites is used for navigation positioning calculation, it will lead to a huge amount of calculation, seriously affecting the real-time performance of navigation positioning solution. In addition, if only a single-system satellite selection method is adopted, it will result in waste of observation data.

[0003] Therefore, how to efficiently select satellites to ensure accuracy while improving the real-time performance and reliability of navigation positioning is the key to promoting GNSS applications. Traditional satellite selection algorithms mainly focus on single-system satellite selection methods for 4 - 6 satellites. However, with the increase in the number of navigation satellites and the improvement of GNSS chip performance, traditional algorithms can no longer meet the satellite selection requirements for multi-systems and multiple satellites (more than 6). Traditional satellite selection algorithms usually involve loop calculations. As the number of visible navigation satellites increases, the number of loops and calculation time will increase sharply, making it difficult to guarantee the real-time performance of the positioning algorithm.

[0004] The traditional rapid positioning method is to select satellites through an exhaustive method, try all combinations of all visible satellites one by one, and select the optimal satellite combination that can achieve rapid positioning according to a certain positioning accuracy evaluation criterion for positioning. Its core is to find the best solution through comprehensive search. It mainly includes the following steps:

[0005] (1) Signal reception: Use a satellite navigation receiver to receive signals from each satellite. These signals contain relevant parameters of the satellite, such as satellite number, signal strength, ephemeris data, etc.

[0006] (2) Visible satellite screening: Determine the set of visible satellites at the current moment according to factors such as the receiving ability of the receiver and the strength and quality of the satellite signal. Set an elevation angle threshold, and satellites above this threshold are considered visible satellites.

[0007] (3) Combination generation: For the determined set of visible satellites, generate all possible satellite combinations. If there are n visible satellites, the number of possible combinations ranges from all cases of selecting 1 satellite to selecting n satellites. For each satellite combination, initialize the relevant parameters for positioning calculation.

[0008] (5) Comparison and selection: After all satellite combination calculations are completed, compare their positioning accuracy indicators, and select the satellite combination with the minimum GDOP value as the final combination for rapid positioning.

[0009] (6) Storage and output: The selected optimal satellite combination information is stored and output to the subsequent modules of the positioning system for the receiver to quickly and accurately determine the position.

[0010] This method has the ability to find the optimal satellite combination in theory, thus ensuring the highest level of positioning accuracy. The design of the algorithm is concise and clear, and the operation steps are direct, making it very easy to understand and implement.

[0011] The complexity of this method for fast positioning using the traversal method is high, especially when there are a large number of visible satellites, the number of combinations will grow exponentially. This exponential growth trend will lead to a significant increase in calculation time, which is not conducive to the realization of fast real-time positioning. For receivers with limited resources, this high computational complexity may consume a lot of computing resources and memory, further increasing the burden on the receiver, resulting in the inability to quickly achieve real-time positioning.

[0012] Another fast positioning method is to use the particle swarm optimization (PSO) algorithm to intelligently select the optimal satellite combination for positioning, replacing the traditional traversal method. The PSO algorithm simulates the foraging behavior of bird flocks and finds the best solution through iterative search. It mainly includes the following steps:

[0013] (1) Signal reception: Use a satellite navigation receiver to receive signals from various satellites. These signals contain satellite-related parameters, such as satellite number, signal strength, ephemeris data, etc.

[0014] (2) Visible satellite screening: Determine the set of visible satellites at the current moment based on the receiver's reception capability and factors such as the strength and quality of satellite signals. For example, a signal strength threshold is set, and satellites above the threshold are considered visible satellites.

[0015] (3) Particle initialization: Each possible satellite combination is considered as a particle, and a particle swarm is initialized. Each particle represents a specific satellite combination, its position vector consists of the number of the selected satellite, and its velocity vector is used to adjust its position in the search space. During initialization, a certain number of satellite combinations are randomly selected as the initial particle swarm.

[0016] (4) Fitness evaluation: Define a fitness function to evaluate the positioning accuracy of each particle (i.e., satellite combination). The fitness value can be calculated based on indicators such as GDOP (Geometric Dilution of Precision). The smaller the GDOP value, the higher the positioning accuracy.

[0017] (5) Particle update: According to the fitness value, the speed update formula and position update formula in the PSO algorithm are used to adjust the speed and position of each particle. Through iterative updates, the particles gradually move toward the optimal solution (i.e., the optimal satellite combination).

[0018] (6) Global optimal selection: In each iteration, compare the fitness values of all particles, and select the particle with the minimum GDOP value as the current global optimal solution.

[0019] (7) Iteration termination and selection: Repeat steps (4) to (6) until the preset number of iterations is reached or the fitness value no longer improves significantly. Finally, select the global optimal solution found during the iteration as the satellite combination finally used for rapid positioning.

[0020] (8) Storage and output: Store the information of the selected optimal satellite combination and output it to the subsequent module of the positioning system for the rapid and accurate determination of the receiver's position.

[0021] This method utilizes the global search ability and fast convergence of the PSO algorithm, and can efficiently find the optimal satellite combination in a complex and changing satellite signal environment, thus ensuring that the positioning accuracy reaches a high level. Compared with the traversal method, the PSO algorithm has significant advantages in search efficiency and computational cost.

[0022] Due to the complexity and diversity of the solution space, rapid positioning based on the particle swarm optimization method often faces some challenges in satellite selection for rapid positioning. The particles in this method are easily trapped in the trap of a local optimal solution during the search process, resulting in their stagnation near the local optimal solution. This phenomenon makes it difficult for the rapid positioning method based on the particle swarm optimization method to continue exploring other potentially better solutions in the solution space, thus unable to further improve the quality of the solution. When using the particle swarm optimization method for rapid positioning, it may fall into a local optimal solution and fail to find the best satellite combination, resulting in low and unstable positioning accuracy.

[0023] In summary, due to the complex star selection calculation and long time consumption of traditional rapid positioning methods, it is often difficult to achieve a balance between global search and local optimization. Especially in the case of multi-system and high-dimensional combination star selection tasks, they are easily trapped in local optimal solutions, which limits the efficiency and robustness of rapid positioning methods in real-time applications and is difficult to meet the requirements of real-time navigation systems. Summary of the Invention

[0024] The technical problem to be solved by the present invention is to provide a star selection rapid positioning method and system for multi-system and multi-satellite GNSS data based on the Whale Optimization Algorithm (WOA), which is used to screen out the best satellite combination, thereby while ensuring the positioning accuracy, significantly reducing the amount of calculation, further improving the accuracy and reliability of star selection; even in the case of a large number of satellites, it can quickly and accurately complete the star selection process, significantly improving the real-time performance and stability of the navigation positioning system.

[0025] To achieve the above object, the present invention adopts the following technical solutions:

[0026] A star selection and rapid positioning method based on the whale optimization algorithm, comprising:

[0027] Step S1, obtaining visible satellites;

[0028] Step S2, sorting the visible satellites from small to large and continuously numbering the visible satellites from 1 to m in sequence;

[0029] Step S3, setting the population number as j, randomly selecting n from m visible stars for combination, generating j different whales to form a population, and initializing the parameter a to balance the global search and local search capabilities of the algorithm, initializing the vector A to control the moving direction and step size of the whales during the search process, and initializing the vector C to adjust the distance between the whales and the current optimal solution;

[0030] Step S4, substituting the satellite combinations in the initial population into the fitness function in turn to obtain the fitness of each satellite combination; wherein, the fitness function is the GDOP value of the satellite combination;

[0031] Step S5, continuously updating a, A and C, calculating the fitness of the satellite combination, updating the fitness and position of the optimal whale individual, judging whether the maximum number of iterations is reached, if so, terminating the iteration, obtaining the satellite combination with the smallest GDOP value, and recording the satellite combination number;

[0032] Step S6, extracting the satellite data of each satellite in the optimal combination;

[0033] Step S7, performing rapid positioning by using the least squares method through the satellite data.

[0034] Preferably, in step S1, according to the navigation message, all visible satellites with an elevation angle greater than 5° at the current epoch are obtained.

[0035] Preferably, in step S2, according to the pseudo-random noise code, the obtained visible satellites are sorted from small to large and continuously numbered from 1 to m in sequence.

[0036] Preferably, the satellite data includes: the navigation message and pseudo-range data transmitted by the satellite.

[0037] Preferably, in step S6, taking the specific numbers of the satellites in the best satellite combination as the key index information, the satellite data of each satellite in the recorded satellite combination is extracted.

[0038] Preferably, the calculation formula of GDOP is as follows:

[0039]

[0040] where: tr(*) represents taking the trace of a matrix, and H is the observation matrix;

[0041] In multi-GNSS, multiple satellites of multiple systems composed of BDS, Galileo, GLONASS, and GPS are simultaneously observed, and the observation matrix H is expressed as:

[0042]

[0043] where the subscripts represent the corresponding satellite systems. Suppose there are n satellites in a certain system participating in positioning. At this time, H is expressed as an n-row and 3-column matrix. The 3 columns are the direction cosines of the lines connecting each satellite in the satellite system to the observation station on the (x, y, z) axes. 1 and 0 represent a pure 1 vector of n rows and 1 column and a pure 0 vector of n rows and 1 column, respectively.

[0044] Preferably, in step S7, based on the least squares method, the pseudorange observations from multiple satellite systems and the navigation messages transmitted by the satellites are used as inputs for joint positioning calculation to achieve fast positioning.

[0045] The present invention also provides a star selection fast positioning system based on the whale optimization algorithm, including: a memory and a processor. A computer program is stored on the memory and run by the processor. When the computer program is run by the processor, it executes the star selection fast positioning method based on the whale optimization algorithm.

[0046] The fast positioning based on the whale optimization algorithm of the present invention effectively solves complex optimization problems by simulating the process of whales searching for prey in the ocean, enabling fast positioning to perform satellite selection and optimization more efficiently and accurately, thereby significantly improving the performance and reliability of the entire system. The fast positioning based on the whale optimization algorithm can quickly find the optimal solution in large-scale satellite data, avoid falling into local optima, and improve the accuracy and efficiency of fast positioning. In addition, this method also exhibits strong robustness and adaptability, and can maintain stable performance under different environments and conditions. Therefore, applying the whale optimization algorithm to fast positioning can not only improve the accuracy and speed of star selection, but also enhance the stability and reliability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0048] Figure 1This is the flowchart of the star selection and rapid positioning method based on the whale optimization algorithm in the embodiments of the present invention. Specific embodiments

[0049] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0050] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the drawings and specific embodiments.

[0051] Embodiment 1:

[0052] As Figure 1 shown, the embodiments of the present invention provide a star selection and rapid positioning method based on the whale optimization algorithm, including:

[0053] Step S1: According to the navigation message, obtain all visible satellites with an elevation angle greater than 5° at the current epoch;

[0054] Step S2: According to the pseudo-random noise code, sort the visible satellites from small to large and continuously number the visible satellites from 1 to m in sequence;

[0055] Step S3: Set the population number as j, randomly select n from m visible stars for combination, generate j different whales to form a population, and initialize the parameter a to balance the global search and local search capabilities of the algorithm, initialize the vector A to control the moving direction and step size of the whales during the search process, and initialize the vector C to adjust the distance between the whales and the current optimal solution;

[0056] Step S4: Substitute the satellite combinations in the initial population into the fitness function in sequence to obtain the fitness of each satellite combination; among them, the fitness function is the GDOP value of the satellite combination;

[0057] Step S5: Iterative update. Update a, A, and C such that a linearly decreases from its initial value to 0. At the beginning of the calculation, the value of a is large, and the calculation tends to perform global search, capable of widely exploring possible solutions in the entire search space; as the number of iterations increases, the value of a gradually decreases, and the calculation gradually focuses on local areas for more refined search to find better solutions. The absolute value of A determines whether the whale performs global search or local search. When |A| ≥ 1, the whale will explore more widely in the search space, tending to global search, that is, the whale may move away from the current optimal solution to find a better solution; when |A| ≤ 1, the whale will approach the current optimal solution for local search to further optimize the current solution. Through C, the whale can flexibly approach or move away from the current optimal solution during the search process, increasing the randomness and diversity of the search, enabling the whale search to jump out of local optima. By continuously updating a, A, and C, calculate the fitness of the satellite combination, update the fitness and position of the optimal whale individual, and determine whether the maximum number of iterations is reached. If so, terminate the iteration to obtain the satellite combination with the minimum GDOP value, and record the satellite combination number;

[0058] Step S6: Extract data of each satellite in the optimal combination, which includes: navigation message and pseudorange data transmitted by the satellite;

[0059] Step S7: Perform rapid positioning using the least squares method based on satellite data. Establish a pseudorange observation equation according to the error, linearize it, and set the approximate values of the receiver's initial coordinates and clock offset to obtain the coordinates and clock offset corrections to be solved. Write the linearized error equation in matrix form to form the matrix form of the error equation. Solve the parameters by the least squares method to minimize the sum of the squares of the observation residuals, solve the parameter vector to be determined, and update the receiver's coordinates and clock offset with the obtained parameter correction vector. Judge whether the coordinate and clock offset corrections meet the convergence condition through iteration. If not, repeat the above steps until convergence. The receiver coordinates and clock offset obtained after convergence are the positioning solution results.

[0060] Adopt a rapid positioning strategy based on WOA to accurately calculate the geometric dilution of precision GDOP for all monitorable satellite combinations. During this process, various possible satellite combinations are deeply explored, and the best satellite combination is identified through accurate calculation methods. Among numerous combinations, the present invention applies the WOA satellite selection strategy to screen out the combination with the minimum GDOP value, which represents the optimal satellite configuration and can achieve a high level of positioning accuracy. After determining the satellite combination with the minimum GDOP value, specifically record the satellite numbers in the best satellite combination. Using the number as the key index information, extract the detailed information of each satellite in the recorded satellite combination, and perform positioning on these detailed information using the least squares method to achieve rapid positioning.

[0061] The core content of the WOA rapid positioning method is rapid satellite selection. Inspired by the hunting behavior of humpback whales in nature, in this method, the position of each humpback whale represents a feasible solution, and the global optimal solution is obtained by continuously updating the positions of the whales in the solution space. The satellite spatial position combination of satellite positioning directly affects the positioning accuracy and the realization of rapid positioning. The main search process of this method can be divided into three stages: ①Surrounding the prey ②Bubble hunting ③Searching for the prey.

[0062] The selection of the fitness function in the WOA rapid positioning method directly affects the convergence speed of this method and whether the optimal solution can be found. Aiming at the problem of rapid satellite selection and positioning in a multi-satellite navigation and positioning system, the GDOP value will be selected as the fitness function to evaluate the geometric configuration quality of the selected satellite combination.

[0063] The calculation formula of GDOP is as follows:

[0064]

[0065] In the formula: tr(*) represents taking the trace of the matrix, and H is the observation matrix. In multi-GNSS, multiple satellites of multiple systems including BDS, Galileo, GLONASS, and GPS can be observed simultaneously. At this time, the observation matrix H can be expressed as:

[0066]

[0067] In the formula: the subscripts represent the corresponding satellite systems. Assuming that n satellites in a certain system participate in positioning, then H at this time is expressed as an n×3 matrix. The three columns are the direction cosines of the lines connecting each satellite in the satellite system to the observation station on the (x, y, z) axes. 1 and 0 represent a pure 1 vector of n×1 and a pure 0 vector of n×1 respectively.

[0068] The satellite selection principle is: at a certain moment, m satellites with an elevation angle greater than 5° are available for positioning, and n satellites need to be selected so that the GDOP value formed by the combination of these n satellites is the smallest. In the WOA rapid positioning method, a whale is randomly generated by any combination of n satellites, denoted as X i =[x i,1 ,x i,2 ,x i,3 L,x i,n , the subscript i represents the i-th whale, and the number of whales in the whale group is j, where

[0069] For the WOA rapid positioning method, the parameters that mainly affect the satellite selection performance include the population size (i.e., the number of whales) and the number of iterations (i.e., the number of searches). Different settings of these parameters significantly affect the satellite selection error and the calculation time.

[0070] The swarm intelligence optimization algorithm aims to gradually approach the true value through iterative optimization. However, due to the randomness of this method and the differences in the selection of initial values, the results of each run may not fully converge to the true value. To evaluate the star selection performance of the algorithm, the present invention conducts multiple repeated experiments to statistically obtain the maximum, minimum, and average values of GDOP (Geometric Dilution of Precision), and uses these to determine the maximum value of the algorithm performance parameter GDOP, which reflects the worst case of the satellite configuration, the minimum value corresponding to the optimal configuration, and the average value representing the average star selection performance of the algorithm.

[0071] To more precisely evaluate the star selection effect of the WOA fast positioning method, the present invention also uses the result of the traversal method as a reference solution, and quantifies the actual performance of the WOA fast positioning method in the star selection process by comparing the two results.

[0072] The experimental results show that the maximum difference in GDOP between the traversal method and the WOA fast positioning method for different numbers of selected stars is only 0.0221, indicating that the WOA fast positioning method can search for an optimal satellite combination with better quality. However, the calculation time of the traversal method is significantly higher than that of the WOA fast positioning method, and the gap gradually expands as the number of selected stars increases. When the number of selected stars is 7, the calculation time of the traversal method is 18.5864 seconds, while the WOA fast positioning method is only 0.4132 seconds, that is, on the premise of maintaining a small GDOP difference, the calculation time of the WOA fast positioning method is greatly shortened compared to the traversal method.

[0073] Calculate the GDOP values of the observable satellite combinations through the above method. This process covers in-depth analysis and precise calculation of possible satellite combinations, and can accurately identify the optimal satellite combination. Among many combinations, the combination with the smallest GDOP value is selected by the WOA star selection method, and this value represents the optimal satellite configuration and can achieve the highest precision positioning result.

[0074] After determining the satellite combination with the minimum GDOP value, record the satellite numbers in these combinations in detail. These numbers serve as important index information, facilitating quick locking of the best satellite combination when rapid positioning is required. Thus, obtain the numbers of the satellite combinations and acquire the navigation messages transmitted by each satellite and their corresponding pseudorange data. Based on the orbital parameters and time information extracted from the satellite ephemeris data, construct a detailed visible satellite catalog. Provide accurate position and status information, providing crucial data support for positioning and navigation services. Based on the least squares method, take the pseudorange observations from multiple satellite systems and the navigation messages transmitted by the satellites as inputs, establish a pseudorange observation equation according to the error, linearize it, and set the approximate values of the receiver's initial coordinates and clock offset to obtain the coordinates and clock offset corrections to be solved. Write the linearized error equation in matrix form to form the matrix form of the error equation. Solve the parameters by least squares to minimize the sum of the squares of the observation residuals, solve the vector of the parameters to be determined, and update the receiver's coordinates and clock offset with the obtained parameter correction vector. Iteratively determine whether the coordinate and clock offset corrections meet the convergence condition. If not, repeat the above steps until convergence. The receiver coordinates and clock offset obtained after convergence are the positioning solution results to achieve rapid positioning.

[0075] The present invention applies a rapid positioning strategy based on the whale optimization method, accurately calculates the geometric dilution of precision (GDOP) of the monitorable satellite combinations. Studies and screens out the satellite combinations with the minimum GDOP value and records the specific numbers of the satellites in these combinations. Extracts the detailed information of each satellite in these satellite combinations and uses it in the positioning process. By acquiring the navigation messages and pseudorange data transmitted by the satellites, constructs a detailed visible satellite catalog, providing crucial data support for positioning and navigation services. Uses the least squares method to perform joint positioning calculations in combination with the pseudorange observations and the navigation messages transmitted by the satellites to achieve rapid positioning.

[0076] Compared with the traditional traversal method, the WOA fast positioning method demonstrates excellent computational efficiency in dealing with the satellite selection problem of multi-GNSS integrated navigation systems. Specifically, when performing joint positioning of BDS / GPS / Galileo / GLONASS, compared with the traversal method, the error of the Geometric Dilution of Precision (GDOP) is 0.37%, and the efficiency of the WOA fast positioning method is greatly improved. The fast positioning method proposed by the present invention can obtain an approximately optimal satellite combination with a small GDOP error and a small computational time consumption, effectively reducing the computational amount, being applicable to the research of real-time satellite navigation fast positioning data processing, and can be extended to scenarios of efficient satellite selection and fast positioning. Implementing fast positioning with the selected satellite combination can quickly obtain the optimal satellite configuration, thereby ensuring the high precision of the positioning result. This method not only improves the positioning efficiency but also guarantees the positioning accuracy. With the WOA fast positioning method, the present invention effectively screens out the optimal satellite combination and achieves fast and high-precision positioning in practical applications.

[0077] Embodiment 2:

[0078] The embodiment of the present invention also provides a satellite selection fast positioning system based on the whale optimization algorithm, including: a memory and a processor, where a computer program run by the processor is stored on the memory, and the computer program executes the satellite selection fast positioning method based on the whale optimization algorithm when run by the processor.

[0079] The above-described embodiments are only descriptions of the preferred embodiments of the present invention and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for rapid star selection and positioning based on a whale optimization algorithm, characterized in that: include: Step S1, obtaining visible satellites; Step S2, sort the visible satellites from small to large and number the visible satellites consecutively from 1 to m; Step S3, assuming that the number of populations is j, randomly select n stars from the m visible stars for combination, generate j different whales to form a population, and initialize the parameters a to balance the global search and local search capabilities of the algorithm, the initialization vector A to control the movement direction and step size of the whale during the search process, and the initialization vector C to adjust the distance between the whale and the current optimal solution; Step S4, substituting the satellite combinations in the initial population into the fitness function in turn to obtain the fitness of each satellite combination; wherein the fitness function is the GDOP value of the satellite combination; Step S5, continuously update a, A and C, calculate the fitness of the satellite combination, update the fitness and position of the optimal whale individual, determine whether the maximum number of iterations has been reached, if so, terminate the iteration, obtain the optimal satellite combination, and record the satellite combination number; Step S6, extracting the best combination of satellite data; Step S7: Using satellite data, use the least squares method to perform rapid positioning.

2. The method for rapid star selection and positioning based on the whale optimization algorithm according to claim 1, characterized in that: In step S1, all visible satellites with elevation angles greater than 5° in the current epoch are obtained according to the navigation message.

3. The method for rapid star selection and positioning based on the whale optimization algorithm according to claim 2, characterized in that: In step S2, the obtained visible satellites are sorted from small to large according to the pseudo-random noise and the visible satellites are numbered consecutively from 1 to m.

4. The method for rapid star selection and positioning based on the whale optimization algorithm according to claim 3, characterized in that: Satellite data includes: navigation messages and pseudo-range data transmitted by satellites.

5. The method for rapid star selection and positioning based on the whale optimization algorithm according to claim 4, characterized in that: In step S6, the satellite data of each satellite in the recorded satellite combination is extracted using the specific number of the satellite in the best satellite combination as key index information.

6. The method for rapid star selection and positioning based on the whale optimization algorithm according to claim 5, characterized in that: The calculation formula of GDOP is as follows: Where: tr(*) represents the trace of the matrix, H is the observation matrix; In multi-GNSS, multiple satellites of multiple systems consisting of BDS, Galileo, GLONASS and GPS are observed at the same time, and the observation matrix H is expressed as: Among them, the subscripts represent the corresponding satellite systems. Suppose there are n satellites participating in positioning in a system, then H is represented by a matrix of n rows and 3 columns. The 3 columns are the direction cosines of the lines connecting each satellite and the observation station in the satellite system on the (x, y, z) axis. 1 and 0 represent pure 1 vectors of n rows and 1 column and pure 0 vectors of n rows and 1 column, respectively.

7. The method for rapid star selection and positioning based on the whale optimization algorithm according to claim 6, characterized in that: In step S7, based on the least square method, pseudo-range observations from multiple satellite systems and navigation messages transmitted by satellites are used as input to perform joint positioning solution to achieve rapid positioning.

8. A star selection and rapid positioning system based on the whale optimization algorithm, characterized in that: include: A memory and a processor, wherein the memory stores a computer program executed by the processor, and when the computer program is executed by the processor, the method for rapid star selection and positioning based on the whale optimization algorithm according to any one of claims 1 to 7 is executed.

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