Generalized second-order delay inequality model positioning node optimization method and device based on genetic algorithm

Abstract

The invention discloses a generalized second-order delay inequality model positioning node optimization method and device based on a genetic algorithm, and relates to the field of underwater acoustic positioning. The problems that positioning nodes need to be selected at equal intervals in an existing positioning model, but when an underwater vehicle executing a positioning task sails in water, due to the fact that the navigational speed and other conditions cannot be guaranteed, distribution of the selected positioning nodes at equal intervals in the space is not beneficial to positioning are solved. The method comprises the following steps: calculating horizontal precision factors of four selected positioning nodes; the horizontal precision factor is used as an evaluation index, calculation of a genetic algorithm is carried out, and node distribution of a generalized second-order delay inequality positioning model for positioning is determined; and establishing a positioning solution equation by applying node distribution, solving the established positioning solution equation by utilizing a Newton iteration method, and realizing high-precision positioning by applying the determined node position of the generalized second-order delay inequality positioning model. The method is also suitable for the field of optimizing the spatial distribution of the positioning nodes by the genetic algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic positioning, and particularly relates to an optimization method and device for positioning nodes of a generalized second-order time-delay difference model based on a genetic algorithm. Background Art

[0002] The transmission period of a signal transmitter submerged underwater will show a deviation in the signal period during the use process. In this case, the transmission period of the underwater signal cannot be completely determined. The positioning model based on the second-order time-delay difference can improve the accuracy of underwater positioning when the signal period is unknown. This model requires equally spaced positioning nodes to be selected. However, when an underwater vehicle performing a positioning task is navigating in water, due to conditions such as the speed not being guaranteed, the equally spaced positioning nodes selected may not be conducive to positioning in space. On this basis, the proposed generalized second-order time-delay difference positioning model can select positioning nodes without equal time intervals, but the distribution of the optimal positioning nodes for the generalized second-order time-delay difference positioning model is not yet clear, and the positioning accuracy cannot reach the optimal value. It is necessary to find the optimal position of the positioning nodes to further improve the positioning accuracy. Summary of the Invention

[0003] The present invention aims to solve the problems in the prior art that the positioning model based on the second-order time-delay difference requires equally spaced positioning nodes to be selected. However, when an underwater vehicle performing a positioning task is navigating in water, due to conditions such as the speed not being guaranteed, the equally spaced positioning nodes selected may not be conducive to positioning in space.

[0004] To solve the above technical problems, the present invention is realized through the following technical solutions:

[0005] Solution 1: The present invention proposes an optimization method for positioning nodes of a generalized second-order time-delay difference model based on a genetic algorithm. The method includes the following steps:

[0006] Step 1: Calculate the horizontal dilution of precision of four selected positioning nodes;

[0007] Step 2: Use the horizontal dilution of precision described in Step 1 as an evaluation index to perform genetic algorithm calculations to determine the node distribution for positioning using the generalized second-order time-delay difference positioning model;

[0008] Step 3: Apply the node distribution described in Step 2 to establish a positioning solution equation, use the Newton iteration method to solve the established positioning solution equation, and use the node positions of the generalized second-order time-delay difference positioning model determined in Step 2 to achieve high-precision positioning.

[0009] Furthermore, a preferred implementation is provided. The method for calculating the horizontal dilution of precision of four selected positioning nodes in Step 1 is:

[0010] Step 1.1: Calculate the partial derivative matrices of the target position, signal arrival time, underwater sound speed, underwater depth, and node position according to the positioning solution equation;

[0011] Step 1.2: Set the covariance matrix D of the position error of the acoustic beacon according to the actual situation x , the covariance matrix D of the signal arrival time error received by the underwater positioning platform t , the covariance matrix D of the underwater sound speed error c , the covariance matrix D of the measured underwater depth error z , the covariance matrix D of the coordinate error of the position of the underwater positioning platform INS ;

[0012] Step 1.3: Calculate the covariance matrix D according to the partial derivative matrix and error matrix described in Step 1.2 x ;

[0013] Step 1.4: Calculate the horizontal dilution of precision of the four selected positioning nodes according to Steps 1.1 to 1.3.

[0014] Further, a preferred implementation is provided. The method for calculating the horizontal dilution of precision in Step 1.4 is as follows:

[0015]

[0016] Further, a preferred implementation is provided. The method for using the horizontal dilution of precision described in Step 1 as an evaluation index to perform genetic algorithm calculations in Step 2 is as follows:

[0017] Step 2.1: Encode the four selected positioning nodes in Step 1;

[0018] Step 2.2: Initialize the four encoded positioning nodes in Step 2.1;

[0019] Step 2.3: Evaluate the fitness of the positioning nodes in Step 2.2 using the horizontal dilution of precision;

[0020] Step 2.4: Sort according to the magnitude of the fitness and determine the individuals with large fitness as the parents for crossover operation;

[0021] Step 2.5: Arbitrarily select two for crossover operation in Step 2.4;

[0022] Step 2.6: Perform mutation operation based on the crossover operation. During the mutation operation, mutate any one of the four positioning nodes and replace it with any point within the entire spatial region;

[0023] Step 2.7: Determine whether the number of iterations is satisfied. If not, return to Step 2.3; if satisfied, output the result.

[0024] Further, a preferred implementation is provided. The method for establishing a positioning solution equation by applying the node distribution described in Step 2 in Step 3 is as follows:

[0025]

[0026] where, is the arrival time of each received pulsed acoustic signal, and n i is the cycle number of the signal received by the positioning system at this position, is the distance between the positioning system and the acoustic beacon at this position, and c is the speed of sound in water.

[0027] Further, a preferred implementation is provided. The method for solving the established positioning solution equation by using the Newton iteration method in Step 3 is as follows: Set the magnitude of the initial value x1, calculate the Jacobian matrix of the equation, and perform iterative calculations to obtain the coordinates of the position where the acoustic beacon is located.

[0028] Further, a preferred implementation is provided. The method for iterative calculation is as follows:

[0029]

[0030] where F is the positioning solution equation and F' is its Jacobian matrix.

[0031] Solution 2: A positioning node optimization device based on a genetic algorithm for a generalized second-order time delay difference model. The device includes:

[0032] A horizontal dilution of precision calculation module, which is used to calculate the horizontal dilution of precision of four selected positioning nodes;

[0033] An optimization module, which is used to perform genetic algorithm calculations by using the horizontal dilution of precision calculated by the horizontal dilution of precision calculation module as an evaluation index, and is used to determine the node distribution for positioning by the generalized second-order time delay difference positioning model;

[0034] A positioning module, which is used to establish a positioning solution equation by applying the node distribution of the optimization module, solve the established positioning solution equation by using the Newton iteration method, and implement high-precision positioning by applying the node positions of the generalized second-order time delay difference positioning model determined by the optimization module.

[0035] Solution 3: A computer device, including a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the method described in any one of Solution 1.

[0036] Solution 4: A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method described in any one of Solution 1 are implemented.

[0037] The advantages of the present invention are as follows:

[0038] The method and device for optimizing positioning nodes of a generalized second-order time-delay difference model based on a genetic algorithm according to the present invention effectively improve the positioning accuracy of the generalized second-order time-delay difference positioning model. First, a genetic algorithm search is performed. During the application of the genetic algorithm, four positioning nodes are used as a potential solution to a problem, and the horizontal dilution of precision is used as the evaluation criterion for the potential solution. The node distribution conducive to positioning by the generalized second-order time-delay difference positioning model is calculated. Using this spatial distribution, a positioning solution equation is established, and the traditional Newton iteration method is used to solve the equation, and a high-precision positioning result can be obtained with higher efficiency.

[0039] The underwater acoustic positioning model based on the generalized second-order time-delay difference according to the present invention can more freely select positioning nodes. By introducing the generalized second-order time-delay difference, the model can better adapt to the complexity of the underwater environment and improve the positioning accuracy.

[0040] The present invention introduces a genetic algorithm to optimize the spatial distribution of positioning nodes. As a search algorithm that simulates natural selection and genetic mechanisms, the genetic algorithm shows superiority in solving complex optimization problems due to its strong global search ability, high adaptability, and good robustness. Through the genetic algorithm, the optimal node distribution can be found in a vast search space, thereby improving the positioning accuracy and efficiency of the positioning system.

[0041] The present invention is also applicable to the field of optimizing the spatial distribution of positioning nodes by a genetic algorithm. Description of the Drawings

[0042] Figure 1 It is a spatial schematic diagram of the node distribution for positioning using the generalized second-order time-delay difference positioning model described in Embodiment 1.

[0043] Figure 2 It is a flowchart of the genetic algorithm in the method for optimizing positioning nodes of a generalized second-order time-delay difference model based on a genetic algorithm described in Embodiment 1.

[0044] Figure 3 It is a situation diagram of an autonomous underwater vehicle (AUV) in Embodiment 11 for positioning a fixed sound source located at the bottom of a lake.

[0045] Figure 4 It is a schematic diagram of the precise positioning result of the route described in Embodiment 11. Detailed Embodiments

[0046] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, rather than all of them.

[0047] Embodiment 1. This embodiment proposes an optimization method for positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm. The method includes the following steps:

[0048] Step 1. Calculate the horizontal dilution of precision of the four selected positioning nodes.

[0049] Step 2. Use the horizontal dilution of precision described in Step 1 as an evaluation index to perform genetic algorithm calculations to determine the node distribution for positioning using the generalized second-order time delay difference positioning model.

[0050] Step 3. Apply the node distribution described in Step 2 to establish a positioning solution equation, use the Newton iteration method to solve the established positioning solution equation, and use the node positions of the generalized second-order time delay difference positioning model determined in Step 2 to achieve high-precision positioning.

[0051] Embodiment 2. This embodiment further limits the optimization method for positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm described in Embodiment 1. The method for calculating the horizontal dilution of precision of the four selected positioning nodes in Step 1 is as follows:

[0052] Step 1.1. Calculate the partial derivative matrix of the target position, signal arrival time, underwater sound speed, underwater depth, and node position according to the positioning solution equation.

[0053] Step 1.2. Respectively set the covariance matrix D of the position error of the acoustic beacon according to the actual situation x , the covariance matrix D of the signal arrival time error received by the underwater positioning platform t , the covariance matrix D of the underwater sound speed error c , the covariance matrix D of the measured underwater depth error z , and the covariance matrix D of the coordinate error of the position of the underwater positioning platform INS ;

[0054] Step 1.3. Calculate the covariance matrix D according to the partial derivative matrix and error matrix described in Step 1.2 x ;

[0055] Step 1.4. Calculate the horizontal dilution of precision of the four selected positioning nodes according to Steps 1.1 to 1.3.

[0056] Embodiment 3. This embodiment further limits the optimization method for positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm described in Embodiment 2. The method for calculating the horizontal dilution of precision in step 1.4 is as follows:

[0057]

[0058] Embodiment 4. This embodiment further limits the optimization method for positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm described in Embodiment 1. The method for using the horizontal dilution of precision described in step 1 as an evaluation index for genetic algorithm calculation in step 2 is as follows:

[0059] Step 2.1: Encode the four positioning nodes selected in step 1;

[0060] Step 2.2: Initialize the four encoded positioning nodes in step 2.1;

[0061] Step 2.3: Evaluate the fitness of the positioning nodes in step 2.2 using the horizontal dilution of precision;

[0062] Step 2.4: Sort according to the magnitude of the fitness, and determine the individual with a large fitness as the parent for crossover operation;

[0063] Step 2.5: Arbitrarily select two for crossover operation in step 2.4;

[0064] Step 2.6: Perform a mutation operation based on the crossover operation. During the mutation operation, mutate any one of the four positioning nodes and replace it with any point within the entire spatial region;

[0065] Step 2.7: Determine whether the iteration times are satisfied. If not, return to step 2.3; if satisfied, output the result.

[0066] Embodiment 5. This embodiment further limits the optimization method for positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm described in Embodiment 1. The method for applying the node distribution described in step 2 to establish a positioning solution equation in step 3 is as follows:

[0067]

[0068] Among them, is the arrival time of each received pulse acoustic signal, and n i is the cycle number of the signal received by the positioning system at this position, is the distance between the positioning system at this position and the acoustic beacon, and c is the speed of sound in water.

[0069] Embodiment 6. This embodiment further limits a method for optimizing positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm described in Embodiment 5. The method for solving the established positioning calculation equation using the Newton iteration method in step 3 is as follows: Set the magnitude of the initial value x1, find the Jacobian matrix of the equation, and perform iterative calculations to obtain the coordinates of the position where the acoustic beacon is located.

[0070] Embodiment 7. This embodiment further limits a method for optimizing positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm described in Embodiment 6. The method for iterative calculation is as follows:

[0071]

[0072] where F is the positioning calculation equation and F' is its Jacobian matrix.

[0073] Embodiment 8. This embodiment proposes an apparatus for optimizing positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm. The apparatus includes:

[0074] A horizontal dilution of precision calculation module, configured to calculate the horizontal dilution of precision of four selected positioning nodes;

[0075] An optimization module, configured to use the horizontal dilution of precision calculated by the horizontal dilution of precision calculation module as an evaluation index to perform genetic algorithm calculations to determine the node distribution for positioning using the generalized second-order time delay difference positioning model;

[0076] A positioning module, configured to establish a positioning calculation equation using the node distribution described by the optimization module, solve the established positioning calculation equation using the Newton iteration method, and implement high-precision positioning using the node positions of the generalized second-order time delay difference positioning model determined by the optimization module.

[0077] Embodiment 9. This embodiment proposes a computer device, including a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the method described in any one of Embodiments 1 to 7.

[0078] Embodiment 10. This embodiment proposes a computer-readable storage medium. The computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps of the method described in any one of Embodiments 1 to 7 are implemented.

[0079] Embodiment 11. This embodiment proposes an example, which is used to explain the above Embodiments 1 to 8. The specific example is as follows:

[0080] See Figures 1 to 4This embodiment is an optimization method for positioning nodes of a generalized second-order time-delay difference model based on a genetic algorithm, mainly including three main steps: calculating the horizontal dilution of precision, optimizing nodes by the genetic algorithm, and positioning and solving by the generalized second-order time-delay difference model.

[0081] Step 1: Calculate the horizontal dilution of precision. Calculate the horizontal dilution of precision of the four selected positioning nodes for subsequent evaluation of the positioning accuracy of the positioning nodes.

[0082] Step 2: Optimize nodes by the genetic algorithm. Using the horizontal dilution of precision as an evaluation index, perform iterative calculations to search for the node positions that are most suitable for applying the generalized second-order time-delay difference positioning model in a body of water.

[0083] Step 3: Positioning and solving by the generalized second-order time-delay difference model. According to the spatial distribution obtained in Step 1, establish a positioning and solving equation, and use the Newton iteration method to solve it to achieve high-precision positioning by applying the generalized second-order time-delay difference model.

[0084] Specific Step 1: Calculate the horizontal dilution of precision.

[0085] To perform subsequent calculations using the genetic algorithm, the horizontal dilution of precision (HDOP) is introduced as an evaluation index for positioning accuracy.

[0086] The specific process of solving HDOP is as follows:

[0087] Calculate the partial derivative matrix of the target position, signal arrival time, underwater sound speed, underwater depth, and node position according to the solving equation:

[0088]

[0089] Among them, [x s , y s , z s is the target position coordinate, [x1, y1, z1] is the coordinate of positioning node 1, [x2, y2, z2] is the coordinate of positioning node 2, [x3, y3, z3] is the coordinate of positioning node 3, [x4, y4, z4] is the coordinate of positioning node 4, and δ i is the cycle number between positioning nodes, that is, n i+1 - n i .

[0090] According to the actual situation, respectively set the covariance matrix D x of the position error of the acoustic beacon, the covariance matrix D t of the signal arrival time error received by the underwater positioning platform, and the covariance matrix D c of the underwater sound speed error., the covariance matrix D of the underwater depth measurement error z , the covariance matrix D of the coordinate error of the underwater positioning platform INS .

[0091] Calculate the covariance matrix D according to the above partial derivative matrix and error matrix x

[0092]

[0093] (4) Calculate the size of HDOP according to the following formula:

[0094]

[0095] Specific step two: Optimize nodes using genetic algorithm

[0096] Use the above horizontal dilution of precision to perform calculations of the genetic algorithm. The flowchart of the genetic algorithm is as Figure 1 , and the specific algorithm process is as follows:

[0097] (1) Encode the solution to the problem

[0098] If the coordinates of the four points in an individual are [x1, y1], [x2, y2], [x3, y3] and [x4, y4] respectively, then the encoding of this individual is a vector in the form of [x1 y1 x2 y2 x3 y3 x4 y4]

[0099] (2) Initialize the population

[0100] This process mainly randomly selects the coordinates of four points as an individual within the entire spatial region to provide positioning points for subsequent calculation of positioning accuracy, and repeats this operation to generate 100 individuals encoded as follows

[0101] [x1 y1 x2 y2 x3 y3 x4 y4]

[0102] ...

[0104]

[0105] (3) Evaluate the fitness of individuals

[0106] Introduce HDOP as an index to measure positioning accuracy, and evaluate the fitness of individuals using the following formula

[0107]

[0108] Among them, f is the fitness function and r is a constant parameter. When the size of the space is relatively large, a larger value of r can be selected, which is beneficial to distinguishing individuals with different magnitudes of fitness.

[0109] (4) Selection operation: The population needs to be sorted according to the fitness size, and individuals with relatively large fitness should be selected as the parents for the crossover operation as much as possible. The specific selection operation uses the roulette wheel method. Individuals with higher fitness will have a higher probability of being selected as parents for subsequent operations. The algorithm steps are as follows:

[0110] Total fitness = sum(fitness);

[0111]

[0112] Fitness rate = cumsum(fitness rate);

[0113] Generate an array A sorted from small to large;

[0114]

[0115] (5) Crossover operation. To perform the crossover operation, any two of the parents selected in the previous selection operation need to be randomly selected for crossover. The specific crossover operation algorithm is as follows:

[0116] Parent(1, :) = Population(randi([1, size]), :);

[0117] Parent(2, :) = Population(randi([1, size]), :);

[0118] Crossover point = randi([1, 3]);

[0119] Offspring 1 = [Parent(1, 1:2 * Crossover point), Parent(2, 2 * Crossover point + 1:end)];

[0120] Offspring 2 = [Parent(2, 1:2 * Crossover point), Parent(1, 2 * Crossover point + 1:end)];

[0121] The above operations can be used to obtain new offspring individuals.

[0122] (6) Mutation operation. When performing the mutation operation, any one of the four points in the individual will be selected for mutation and replaced with any point within the entire space region.

[0123] Judge whether the iteration times are satisfied. If not, return to the third step; if satisfied, output the result.

[0124] The above is the basic process of the entire genetic algorithm to find the optimal positioning point. The entire genetic process will make the population move in the direction of greater fitness, that is, in the direction of higher positioning accuracy.

[0125] Specific step three: Positioning solution calculation of the generalized second-order time-delay difference model.

[0126] Use the positioning node optimization results in the previous step to establish a positioning solution equation:

[0127]

[0128] Among them, is the arrival time of each received pulsed acoustic signal, and n i is the cycle number of the signal received by the positioning system at this position, is the distance between the positioning system at this position and the acoustic beacon, and c is the speed of sound in water.

[0129] Finally, solve the Jacobian matrix of the equation, and use the Newton iteration method to find the coordinates of the position where the acoustic beacon is located. The specific steps are as follows:

[0130] (1) Set the magnitude of the initial value x1 and find the Jacobian matrix of the equation.

[0131] (2) Use the following formula for iterative calculation:

[0132]

[0133] Among them, F is the positioning solution equation, and F' is its Jacobian matrix.

[0134] The specific implementation example is as follows:

[0135] Use an autonomous underwater vehicle (AUV) to locate a fixed sound source at the bottom of a lake. The AUV adopts a circumferential route and sails around the acoustic beacon for two weeks. The test situation is as Figure 2 shown. The specific solution process is as follows:

[0136] The method for solving HDOP is as follows:

[0137] (1) Calculate the partial derivative matrix of the target position, signal arrival time, underwater sound speed, and underwater depth, as well as the partial derivative matrix of the node positions in the route;

[0138] (2) According to the actual situation, respectively set the covariance matrix D x of the position error of the acoustic beacon, the covariance matrix D t of the signal arrival time error received by the underwater positioning platform, the covariance matrix D c of the underwater sound speed error, and the covariance matrix D z of the measured underwater depth error., covariance matrix D of the coordinate error of the underwater positioning platform's location INS

[0139] (3) Calculate covariance matrix D based on the above partial derivative matrix and error matrix x

[0140] (4) Calculate the HDOP values at the positions of each group of positioning nodes;

[0141] Genetic algorithm optimization of nodes

[0142] According to the results of the genetic algorithm operation, select the intervals between every four positioning nodes. Here, the selected positioning node intervals are m, m - 500, m - 750, m - 500;

[0143] Generalized second - order time - delay difference model for positioning solution

[0144] First, establish the positioning solution equation:

[0145]

[0146] Finally, solve the Jacobian matrix of the equation, use the Newton - Raphson method to find the coordinates of the acoustic beacon's location, and finally take the average of each positioning result to obtain the coordinates of the target as [38.36m, - 72.93m];

[0147] Use the RELAX node optimization method in the original generalized second - order time - delay difference positioning model and the genetic search algorithm described in the present invention for positioning respectively. The obtained positioning results are as Figure 3 shown. Through calculation, it can be known that the average positioning error of the original generalized second - order time - delay difference method is 3.91m, and the average positioning error after optimization by the method proposed in the present invention is 3.12m. Through the analysis of the positioning error, the original generalized second - order time - delay difference method already has a relatively high positioning accuracy, but it also further verifies that the method proposed in this paper can still improve the positioning accuracy. From the perspective of the operation time, the average operation time of the original generalized second - order time - delay difference method is 15.2ms, while the optimized method proposed in the present invention reduces the average operation time to 1.15ms. Therefore, the method described in the present invention has higher operation efficiency.

[0148] Those skilled in the art can understand that the above is only the preferred embodiment of the present invention. The features described in each embodiment and / or claim of the present disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly recorded in the present disclosure. It is not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or equivalently replace some of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0149] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they know the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present invention. Obviously, those skilled in the art can make various changes and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. An optimization method for positioning nodes of a generalized second-order time delay difference model based on a genetic algorithm, characterized in that The method includes the following steps: Step 1, calculate the horizontal dilution of precision of the four selected positioning nodes; Step 2, use the horizontal dilution of precision described in Step 1 as an evaluation index to perform genetic algorithm calculations for determining the node distribution for positioning using the generalized second-order time-delay difference positioning model; Step 3, apply the node distribution described in Step 2 to establish a positioning solution equation, use the Newton iteration method to solve the established positioning solution equation, and achieve high-precision positioning using the node positions of the generalized second-order time-delay difference positioning model determined in Step 2.

2. The node positioning optimization method for the generalized second-order time delay difference model based on the genetic algorithm according to claim 1, wherein The method for calculating the horizontal dilution of precision of the four selected positioning nodes in Step 1 is: Step 1.1, calculate the partial derivative matrix of the target position, signal arrival time, underwater sound speed, underwater depth, and node position according to the positioning solution equation; Step 1.

2. Set the covariance matrix D of the position error of the acoustic beacon according to the actual situation x , the covariance matrix D of the time-of-arrival error of the signal received by the underwater positioning platform t , the covariance matrix D of the underwater sound speed error c , the covariance matrix D of the measured underwater depth error z , the covariance matrix D of the position coordinate error of the underwater positioning platform INS ; Step 1.

3. Calculate the covariance matrix D based on the partial derivative matrix and the error matrix described in Step 1.2 x ; Step 1.4, calculate the horizontal dilution of precision of the four selected positioning nodes according to Steps 1.1 to 1.

3.

3. The node positioning optimization method for the generalized second-order time delay difference model based on the genetic algorithm according to claim 2, characterized in that, The method for calculating the horizontal dilution of precision in Step 1.4 is:

4. The optimization method for locating nodes of the generalized second-order time delay difference model based on the genetic algorithm according to claim 1, characterized in that The method for using the horizontal dilution of precision described in Step 1 as an evaluation index to perform genetic algorithm calculations in Step 2 is: Step 2.1, encode the four selected positioning nodes in Step 1; Step 2.2, initialize the four encoded positioning nodes in Step 2.1; Step 2.3, use the horizontal dilution of precision to evaluate the fitness of the positioning nodes in Step 2.2; Step 2.4, sort according to the magnitude of the fitness and determine the individuals with large fitness as the parents for crossover operations; Step 2.5, randomly select two for crossover operations in Step 2.4; Step 2.6, perform mutation operations based on the crossover operations. During mutation operations, randomly mutate any one of the four positioning nodes and replace it with any point within the entire spatial region; Step 2.7, determine whether the iteration times are satisfied. If not, return to Step 2.

3. If satisfied, output the result.

5. The optimized method for locating nodes of the generalized second-order time delay difference model based on the genetic algorithm according to claim 1, wherein The method for applying the node distribution described in Step 2 to establish a positioning solution equation in Step 3 is: Among them, is the arrival time of each received pulsed sound signal, n i is the cycle number of the signal received by the positioning system at this position, is the distance between the positioning system at this position and the acoustic beacon, and c is the speed of sound in water.

6. The node positioning optimization method for the generalized second-order time delay difference model based on the genetic algorithm according to claim 5, wherein The method for using the Newton iteration method to solve the established positioning solution equation in Step 3 is: set the magnitude of the initial value x1, calculate the Jacobian matrix of the equation, and perform iterative calculations to obtain the coordinates of the position where the acoustic beacon is located.

7. The node positioning optimization method for the generalized second-order time delay difference model based on the genetic algorithm according to claim 6, characterized in that, The method for iterative calculations is: where F is the positioning solution equation and F' is its Jacobian matrix.

8. An optimization device for locating nodes of a generalized second-order time delay difference model based on a genetic algorithm, characterized in that The device includes: A horizontal dilution of precision calculation module for calculating the horizontal dilution of precision of the four selected positioning nodes; An optimization module for using the horizontal dilution of precision described by the horizontal dilution of precision calculation module as an evaluation index to perform genetic algorithm calculations for determining the node distribution for positioning using the generalized second-order time-delay difference positioning model; A positioning module for applying the node distribution described by the optimization module to establish a positioning solution equation, using the Newton iteration method to solve the established positioning solution equation, and achieving high-precision positioning using the node positions of the generalized second-order time-delay difference positioning model determined by the optimization module.

9. A computer device, comprising a memory and a processor, characterized in that, The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes the method described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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