Design method of heterogeneous multi-agent positioning tracking network based on niche grey wolf algorithm

Abstract

The present application relates to a heterogeneous photoelectric equipment positioning tracking network design method, in particular to a heterogeneous multi-agent positioning tracking network design method based on a niche grey wolf algorithm, which solves the technical problem that the existing multi-agent positioning tracking network station layout optimization method cannot be directly applied to the heterogeneous multi-agent positioning tracking network. The present application proposes a niche grey wolf algorithm, which adds a niche algorithm to the grey wolf algorithm, can maintain the diversity of the population, and significantly improves the global exploration ability of the grey wolf algorithm in the complex solution space; at the same time, the heterogeneous multi-agent positioning tracking network is modeled, and a theoretical framework of model-algorithm-scheme is constructed, the theoretical accuracy model and the optimization algorithm are combined, and the solution from the accuracy index to the deployment scheme is realized; in addition, the positioning accuracy model established based on the observation characteristics of different types of equipment quantifies the measurement performance of the heterogeneous multi-agent positioning tracking network.

Description

Technical Field

[0001] This invention relates to a design method for heterogeneous optoelectronic equipment positioning and tracking networks, specifically a design method for heterogeneous multi-agent positioning and tracking networks based on the niche gray wolf algorithm. Background Technology

[0002] An optoelectronic theodolite is a precision measuring instrument capable of precise measurement and real-time tracking of moving targets in space. As an important component of the field of precision measuring instruments, the heterogeneous multi-agent positioning and tracking network composed of optoelectronic theodolites and radar has been widely used in aerospace, industry, atmospheric monitoring and other fields, greatly improving the precision measurement capability of target pose information, providing reliable scientific data for the identification of moving targets in space, and has high industrial and economic value.

[0003] To achieve precise measurement of moving targets in space, radar and electro-optical theodolite work together. After the heterogeneous multi-agent positioning and tracking network is deployed, the electro-optical theodolite provides the radar with pitch and azimuth data, while the radar provides the electro-optical theodolite with target distance and radial guidance. The two work together to achieve precise measurement and tracking of the attitude of flying targets in space.

[0004] With the expansion of the measurement environment and the increasing requirements for the accuracy of measurement data, the deployment strategy of heterogeneous multi-agent positioning and tracking networks, as an important influencing factor in the construction of precision measurement networks, greatly affects the positioning accuracy of the system and plays a key role in its equipment configuration.

[0005] In the field of heterogeneous multi-agent localization and tracking network design, scholars and experts focus on optimizing the station deployment problem, using heuristic algorithms to solve it. Current research mainly concentrates on the station deployment optimization of multi-agent localization and tracking networks in scenarios such as aerospace and industrial applications, especially for the networking deployment of multiple photoelectric theodolites. However, in many large-scale precision measurement scenarios, heterogeneous multi-agent localization and tracking networks are more widely used, and the station deployment optimization methods of multi-agent localization and tracking networks are difficult to directly apply to heterogeneous multi-agent localization and tracking networks. Summary of the Invention

[0006] The purpose of this invention is to solve the technical problem that the existing site deployment optimization methods for multi-agent localization and tracking networks are difficult to apply directly to heterogeneous multi-agent localization and tracking networks, and to provide a design method for heterogeneous multi-agent localization and tracking networks based on the niche gray wolf algorithm.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A design method for a heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm, characterized by the following steps:

[0009] Step 1: Based on the measurement and control area, design a heterogeneous multi-agent positioning and tracking network, obtain the equipment type and quantity, and construct a positioning accuracy model for the heterogeneous multi-agent positioning and tracking network;

[0010] Step 2: According to the design requirements, set the population size, upper and lower bounds of the search space, initial niche radius and minimum niche size, and use the positioning accuracy model as the optimization objective function, the value of the optimization objective function as the fitness, the minimization of fitness as the optimization objective, and reset the current iteration number to zero.

[0011] Step 3: Based on the population size and the upper and lower bounds of the search space, randomly generate a set of candidate solutions in the solution space of the Grey Wolf Algorithm, wherein the candidate solutions are the location coordinates of the device;

[0012] Step 4: Calculate the fitness of each candidate solution, and then use the Grey Wolf algorithm to generate the next candidate solution based on the fitness of the candidate solutions, and increment the current iteration number by 1;

[0013] Step 5: Treat each candidate solution as a wolf individual, define the neighborhood radius of each wolf individual based on the candidate solutions of the next step, and determine the neighborhood of each wolf individual and the wolves within it with the wolf individual as the center and the neighborhood radius as the radius. Then, use the multi-neighborhood learning algorithm to generate neighborhood candidate solutions for each wolf individual.

[0014] Step 6: Calculate the fitness of the next candidate solution and the neighboring candidate solutions of each wolf individual. Determine whether the current iteration number is an integer multiple of S. If so, use the niche algorithm to obtain the current optimal solution based on the fitness under the constraints of the initial niche radius and the minimum niche size. Otherwise, take the candidate solution with the smallest fitness as the current optimal solution. Where S is an integer and 0 < S < 10.

[0015] Step 7: Update the positions of all individual wolves based on the current optimal solution, regenerate a set of candidate solutions, and then return to step 4 until the maximum number of iterations is reached. Output the current optimal solution as the global optimal solution to obtain the position coordinates of the device and complete the design of the heterogeneous optoelectronic equipment positioning and tracking network.

[0016] Furthermore, step 5 specifically includes:

[0017] Step 5.1: Treat each candidate solution as a wolf individual, and define the neighborhood radius of each wolf individual according to the candidate solutions in the next step using the following formula:

[0018]

[0019] in, Let be the radius of the neighborhood of the i-th wolf individual, where i is an integer and 1 ≤ i ≤ pop. size pop size Population size; For the i-th wolf individual, This is a candidate solution for the next step;

[0020] Step 5.2: Using the individual wolf as the center and the radius of its neighborhood as the radius, determine the neighborhood and the individual wolves within it for each wolf using the following formula:

[0021]

[0022] in, Let i be the neighborhood of the i-th wolf. Let J be the number of wolves in the neighborhood of the i-th wolf, where j is an integer and 1 ≤ j ≤ J, and J is the number of wolves in the neighborhood of the i-th wolf. express and The Euclidean distance between them For the domain;

[0023] Step 5.3: Using a multi-neighborhood learning algorithm, generate candidate neighborhood solutions for each individual wolf using the following formula:

[0024]

[0025] in, Let be the candidate solution in the neighborhood of the i-th wolf individual. , These represent random wolf individuals within the neighborhood of the i-th wolf individual and globally random wolf individuals, respectively. This is a function for generating random numbers.

[0026] Furthermore, step 6 specifically includes:

[0027] Step 6.1: Calculate the fitness of the next candidate solution and the neighborhood candidate solutions of each wolf individual. Determine whether the current iteration number is an integer multiple of S. If so, treat the next candidate solution and the neighborhood candidate solutions of each wolf individual as individuals, select the individual with the smallest fitness as the best elite, and then execute Step 6.2; otherwise, take the candidate solution with the smallest fitness as the current optimal solution and execute Step 7.

[0028] Step 6.2: Centered on the best elite and with the initial niche radius as the radius, under the constraint of the minimum niche size, determine a niche and the individuals within it from all individuals according to the distance between the individual and the best elite;

[0029] Step 6.3: Among the remaining individuals not assigned to a niche, select the individual with the lowest fitness as the best elite, and then return to step 6.2 until all individuals are assigned to the corresponding niches, resulting in multiple niches;

[0030] Step 6.4: Set the elite retention ratio. According to the elite retention ratio, retain the candidate solutions with low fitness in each student's territory to obtain the elites.

[0031] Step 6.5: Use the iterative density clustering method to make elites learn from the best elites and obtain the optimal solution of each niche. The optimal solution of the niche with the smallest fitness is taken as the current optimal solution. Then calculate the radius of the current niche and take it as the initial niche radius.

[0032] Furthermore, in step 6.5, the optimal solution for the niche is obtained using the following formula:

[0033]

[0034] in, This is the optimal solution for the niche. For the elite, For learning rate, For the best elite, For disturbance terms;

[0035] In step 6.5, the radius of the current microhabitat is calculated using the following formula:

[0036]

[0037] in, For the current microhabitat radius, The initial niche radius, This represents the current iteration number. This represents the maximum number of iterations.

[0038] Furthermore, step 1 specifically includes:

[0039] Step 1.1: Based on the measurement and control area, design a heterogeneous multi-agent positioning and tracking network, including one radar and N photoelectric theodolites, where N is an integer and N≥2;

[0040] Step 1.2: Establish the observation equations for radar and photoelectric theodolite respectively, and then establish a joint observation equation based on the observation equations of radar and photoelectric theodolite;

[0041] Step 1.3: Perform a first-order Taylor expansion on the joint observation equation to obtain the matrix relationship of error propagation, and then derive the measurement Jacobian matrix;

[0042] Step 1.4: Define the inverse matrix of the covariance matrix of the random noise error of the heterogeneous multi-agent localization and tracking network as the weight matrix. Then, using the least squares estimation theory, based on the measurement Jacobian matrix and the weight matrix, obtain the covariance matrix of the position estimation localization error.

[0043] Step 1.5: Based on the covariance matrix of the positioning error, establish a positioning accuracy model.

[0044] Further, in step 1.2, the radar's observation equation is:

[0045]

[0046]

[0047]

[0048] in, , , These are the observed values ​​of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively. , , These are the theoretical values ​​of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively. , , These are the X, Y, and Z coordinates of the target location, respectively. , , These are the X, Y, and Z coordinates of the radar location, respectively. , , These are the zero-mean Gaussian random noise errors of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively, all of which follow a normal distribution;

[0049] In step 1.2, the observation equations for the photoelectric theodolite are established using dual-station intersection measurement. The observation equations for the photoelectric theodolite are as follows:

[0050]

[0051]

[0052] in, , These are the azimuth and elevation angle observations of the target relative to the photoelectric theodolite, respectively. , These are the theoretical values ​​of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively. , , These are the X, Y, and Z axis coordinates of the position of the photoelectric theodolite; , These are the zero-mean Gaussian random noise errors of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively, both of which follow a normal distribution;

[0053] In step 1.2, the joint observation equation is:

[0054]

[0055]

[0056]

[0057] in, , , These are the observed values ​​for the target's azimuth, elevation, and radial distance, respectively.

[0058] Further, in step 1.3, the matrix relationship of the error propagation is as follows:

[0059]

[0060] in, , is the measurement error vector. For the radial distance measurement error between the target and the radar, , These are the measurement errors of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively. , where is the position error vector. , , These represent the errors of the target position along the X, Y, and Z axes, respectively; H is the measurement Jacobian matrix. This is due to random noise error;

[0061] In step 1.3, the measurement Jacobian matrix is:

[0062]

[0063] in, , These are the measurement Jacobian matrices for photoelectric theodolites and radar, respectively. The horizontal projection of the line connecting the photoelectric theodolite and the target. ; The distance between the photoelectric theodolite and the target. .

[0064] Further, in step 1.4, the weight matrix is:

[0065]

[0066] in, For the weight matrix, Let be the covariance matrix of the random noise error in the heterogeneous multi-agent localization and tracking network. , , These represent the measurement noise of the target's azimuth and elevation angle observations relative to the photoelectric theodolite, respectively. The measurement noise for the radial distance observation between the target and the radar. , , ;

[0067] In step 1.4, the covariance matrix of the location estimation positioning error is calculated using the following formula:

[0068]

[0069] in, This is the covariance matrix of the location estimation positioning error.

[0070] Further, in step 1.5, the positioning accuracy model is:

[0071]

[0072] in, This is the positioning accuracy factor. This indicates finding the trace of a matrix.

[0073] Further, in step 3, the candidate solution is generated using the following formula:

[0074]

[0075] in, As a candidate solution, , These are the upper and lower bounds of the search space, respectively. For population size, For the number of devices, This is a function for generating random numbers.

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] 1. The present invention provides a design method for heterogeneous multi-agent localization and tracking networks based on the niche gray wolf algorithm. The invention proposes the niche gray wolf algorithm, which adds the niche algorithm to the gray wolf algorithm to maintain the diversity of the population and significantly improves the global exploration capability of the gray wolf algorithm in complex solution space.

[0078] 2. The heterogeneous multi-agent localization and tracking network design method based on the niche gray wolf algorithm provided by this invention models the heterogeneous multi-agent localization and tracking network, constructs a theoretical framework of model-algorithm-solution, and combines the theoretical accuracy model with the optimization algorithm to realize the solution from accuracy index to deployment scheme.

[0079] 3. The heterogeneous multi-agent positioning and tracking network design method based on the niche gray wolf algorithm provided by this invention establishes a positioning accuracy model based on the observation characteristics of different types of equipment and error propagation theory, thereby realizing the quantification of measurement errors and geometric accuracy analysis of different types of equipment and quantifying the measurement performance of the heterogeneous multi-agent positioning and tracking network. Attached Figure Description

[0080] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0081] Figure 2 This is a scene diagram of the measurement and control area in step 1.1 of this embodiment of the invention;

[0082] Figure 3 This is a schematic diagram of the geometric relationship of radar measurement in step 1.2 of an embodiment of the present invention;

[0083] Figure 4 This is a schematic diagram of the geometric relationship of the photoelectric theodolite bi-station intersection measurement in step 1.2 of the embodiment of the present invention;

[0084] Figure 5 This is a schematic diagram of the measurement model of the heterogeneous multi-agent localization and tracking network in step 1.2 of an embodiment of the present invention;

[0085] Figure 6 The diagram shows a comparison of optimization simulation experiments between the Nigwolf Algorithm (NIGWO), APSO Algorithm, and AGA Algorithm in this embodiment of the invention. (a) is a comparison of convergence curves, and (b) is a comparison of the final solution quality.

[0086] Figure 7 The diagram shows the Rastrigin function used in the convergence simulation experiment, where (a) is a three-dimensional curve and (b) is a contour plot.

[0087] Figure 8 The following are simulation comparison diagrams of the convergence of the Nigwolf Algorithm (NIGWO) with the IGWO, GWO, APSO and AGA algorithms in the embodiments of the present invention. Among them, (a) is a comparison diagram of convergence curves and (b) is a comparison diagram of the final solution quality. Detailed Implementation

[0088] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further detailed explanation of the design method for a heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm proposed in this invention. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of this invention and are not intended to limit the scope of protection of this invention.

[0089] A design method for heterogeneous multi-agent localization and tracking networks based on the niche gray wolf algorithm, such as Figure 1 As shown, it includes the following steps:

[0090] Step 1: Based on the measurement and control area, design a heterogeneous multi-agent positioning and tracking network, obtain the equipment types and quantities, and construct a positioning accuracy model for the heterogeneous multi-agent positioning and tracking network. Specifically:

[0091] Step 1.1: Based on the measurement and control area, design a heterogeneous multi-agent positioning and tracking network, including one radar and four photoelectric theodolites. In this embodiment, as shown... Figure 2 As shown, the measurement and control area is A two-dimensional planar station area of ​​a certain size is used. Within this measurement and control area, a heterogeneous multi-agent positioning and tracking network consisting of one radar and four electro-optical theodolites is employed to complete the positioning and tracking task of a high-speed flight trajectory. The target's path is set as an aerial curved segment to simulate the target's autonomous flight path. This high-speed flight trajectory is discretized into 10 key trajectory measurement points, which are used as observation points. The optimization objective is to improve the overall positioning accuracy of the heterogeneous multi-agent positioning and tracking network for these 10 observation points. The radar position is fixed behind the starting point of the high-speed flight trajectory, and only the position optimization problem of the electro-optical theodolites is considered.

[0092] Step 1.2: Use dual-station intersection measurement, with two photoelectric theodolites as a group, establish the observation equations for the radar and the two photoelectric theodolites respectively, and then establish the joint observation equations based on the observation equations of the radar and the two photoelectric theodolites.

[0093] Radar is an active device that obtains the target's radial range, azimuth, and elevation angles through the propagation of electromagnetic fields and by calculation, thereby determining the target's spatial position and orientation. For example... Figure 3 As shown, the radial distance, azimuth angle, and elevation angle of the target relative to the radar can be expressed as follows:

[0094]

[0095]

[0096]

[0097] in, , , These are the theoretical values ​​of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively. , , These are the X, Y, and Z coordinates of the target location, respectively. , , These are the X, Y, and Z coordinates of the radar position, respectively.

[0098] During the measurement process, radar measurements are subject to random noise errors. Therefore, the radar observation equation is:

[0099]

[0100]

[0101]

[0102] in, , , These are the observed values ​​of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively. , , These are the zero-mean Gaussian random noise errors of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively, all of which follow a normal distribution.

[0103] When using an electro-optical theodolite to locate and track a moving target in space, there are various measurement methods, including two-station intersection measurement, three-station measurement, and four-station measurement. Among these, two-station intersection measurement is the most commonly used method for electro-optical theodolites. In this embodiment, two-station intersection measurement is selected, such as... Figure 4 As shown, based on the positioning principle of the photoelectric theodolite in dual-station intersection surveying, the theoretical observation equation for each photoelectric theodolite can be obtained as follows:

[0104]

[0105]

[0106] in, , These are the theoretical values ​​of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively. , , These are the X, Y, and Z axis coordinates of the position of the photoelectric theodolite.

[0107] In other embodiments, the theoretical azimuth observation equation relative to the photoelectric theodolite varies depending on the target's location, as shown in the following formula:

[0108]

[0109] Electro-optical theodolites, through optical imaging and signal processing, can obtain high-precision target azimuth and elevation angles. By solving data from two-station intersection measurements, they can accurately acquire target pose information. However, during the measurement process, electro-optical theodolites also suffer from random noise errors; therefore, their observation equation is:

[0110]

[0111]

[0112] in, , These are the azimuth and elevation angle observations of the target relative to the photoelectric theodolite, respectively. , These are the zero-mean Gaussian random noise errors of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively, both of which follow a normal distribution.

[0113] Heterogeneous multi-agent positioning and tracking networks offer numerous advantages in large-scale, long-distance measurement and control areas. By combining radar and photoelectric theodolites, precise target positioning and tracking can be achieved. A single photoelectric theodolite provides high-precision angle information but lacks distance information; a single radar device provides both distance and angle information, but with low angle accuracy. The ranging error of the radar itself and the angle measurement error of the photoelectric theodolite are independent of each other. Combining the two into a heterogeneous multi-agent positioning and tracking network enables information fusion, improving robustness and measurement accuracy.

[0114] In a heterogeneous multi-agent positioning and tracking network, the position coordinates of two photoelectric theodolites are grouped together for optimization. Figure 5 As shown, based on the principle of positioning and tracking target T by combining radar R with two photoelectric theodolites P, the joint observation equation can be obtained:

[0115]

[0116]

[0117]

[0118] in, , , These are the observed values ​​for the target's azimuth, elevation, and radial distance, respectively.

[0119] Step 1.3: Perform first-order Taylor expansions on the two joint observation equations to obtain the corresponding error propagation matrix relationships, and then derive the two measurement Jacobian matrices. The error propagation matrix relationship is as follows:

[0120]

[0121] in, , is the measurement error vector. For the radial distance measurement error between the target and the radar, , These are the measurement errors of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively. , where is the position error vector. , , These represent the errors of the target position along the X, Y, and Z axes, respectively; H is the measurement Jacobian matrix. This is random noise error.

[0122] After error calibration of the photoelectric theodolite and radar, random noise error It can be considered to have zero mean, that is , , Then the joint observation equation can be regarded as an unbiased estimate:

[0123]

[0124]

[0125]

[0126] For unbiased estimation, there exists a lower bound. In subsequent steps, the positioning accuracy factor is calculated by solving the measurement Jacobian matrix and the covariance matrix of the position estimation positioning error.

[0127] Calculate the radar's measurement partial derivatives, and then obtain the radar's measurement Jacobian matrix. :

[0128]

[0129] Calculate the measurement partial derivatives of the photoelectric theodolite, and then obtain the measurement Jacobian matrix of the photoelectric theodolite. :

[0130]

[0131] in, The horizontal projection of the line connecting the photoelectric theodolite and the target. ; The distance between the photoelectric theodolite and the target. .

[0132] The measurement Jacobian matrix of the radar and the two photoelectric theodolites can be obtained from the above formula. :

[0133]

[0134] Step 1.4: Define the inverse matrix of the covariance matrix of the random noise error of the heterogeneous multi-agent localization and tracking network as the weight matrix. Then, using the least squares estimation theory, based on the measurement Jacobian matrix and the weight matrix, obtain the covariance matrix of the position estimation localization error.

[0135] Heterogeneous equipment includes photoelectric theodolites and radar. The standard deviations of the observations from these two types of equipment are different. Therefore, unlike the photoelectric theodolites used in bi-station intersection measurements, a weighting matrix needs to be added to reflect the impact of equipment type on measurement accuracy. In this embodiment, the weighting matrix is ​​defined as the inverse of the covariance matrix of the random noise error of the heterogeneous multi-agent positioning and tracking network, i.e.:

[0136]

[0137] in, For the weight matrix, Let be the covariance matrix of the random noise error in the heterogeneous multi-agent localization and tracking network. , , These represent the measurement noise of the target's azimuth and elevation angle observations relative to the photoelectric theodolite, respectively. The measurement noise for the radial distance observation between the target and the radar. , , .

[0138] The covariance matrix of the location estimation error is calculated using the following formula:

[0139]

[0140] in, This is the covariance matrix of the location estimation positioning error.

[0141] Step 1.5: Based on the covariance matrix of the location estimation error, establish a positioning accuracy model as shown in the following formula:

[0142]

[0143] in, This is the positioning accuracy factor. This indicates finding the trace of a matrix.

[0144] In the above process, it is necessary to transform the observed and theoretical values ​​to the same coordinate system. The most commonly used coordinate system in practical engineering is the launch coordinate system, which uses the launch point of the target as the origin. This point has a defined geodetic coordinate system, with the vertical axis perpendicular to the ground and pointing towards the sky, and the horizontal axis pointing towards the horizontal component of the flight direction. The normal axis, vertical axis, and horizontal axis form a complete rectangular coordinate system, which is convenient for describing velocity and attitude states, and also facilitates the acceleration calculation of the inertial navigation system. Therefore, in this embodiment, the observed and theoretical values ​​are transformed to the launch coordinate system.

[0145] It should be noted that, since this embodiment uses bi-station intersection measurement, in steps 2-7, the position coordinates of two of the photoelectric theodolites are optimized as a group. Then, steps 2-7 are repeated once to optimize the position coordinates of the remaining two photoelectric theodolites, thereby completing the design of the heterogeneous multi-agent positioning and tracking network. In other embodiments, if three-station or four-station measurement is used, the position coordinates are optimized by grouping any three or all four photoelectric theodolites.

[0146] Step 2: According to the design requirements, set the population size, upper and lower bounds of the search space, initial niche radius, and minimum niche size. Use the positioning accuracy model as the optimization objective function, the objective function value as the fitness, and minimizing the fitness as the optimization objective. Set the current iteration count to zero. The design requirements include the baseline length between any two devices. In this embodiment, the initial niche radius is... The smallest microhabitat size is 13, of which, , These are the upper and lower bounds of the search space, respectively. These parameters were obtained through preliminary experiments and can achieve a good balance between exploring existing areas and developing new areas.

[0147] In this embodiment, the decision variable of the optimization problem is the position coordinates of the photoelectric theodolite, and its solution space is highly nonlinear. To ensure the rationality of the heterogeneous multi-agent positioning and tracking network in practical problems, a design requirement is introduced: the baseline length between any two devices must be greater than 8 km. The design optimization problem of the heterogeneous multi-agent positioning and tracking network in this scenario is a highly complex nonlinear programming problem. To solve this problem, in this embodiment, the penalty function method is used to set the constrained optimization problem as an unconstrained optimization problem. The specific form of the penalty function is that the baseline length between the two photoelectric theodolites is greater than 8 km, the solution space of the problem is the position coordinates of the two photoelectric theodolites, the fitness is defined as the positioning accuracy factor of all observation points, and the optimization objective is to minimize the fitness.

[0148] Step 3: Based on the population size and the upper and lower bounds of the search space, randomly generate a set of candidate solutions in the solution space using the following formula, where the candidate solutions are the device's location coordinates:

[0149]

[0150] in, As a candidate solution, For population size, For the number of devices, This is a function for generating random numbers.

[0151] Step 4: Calculate the fitness of each candidate solution, and then use the Grey Wolf algorithm to generate the next candidate solution based on the fitness of the candidate solutions, and increment the current iteration number by 1.

[0152] Step 5: Treat each candidate solution as a wolf individual. Define the neighborhood radius of each wolf individual based on the candidate solutions in the next step. Using the wolf individual as the center and the neighborhood radius as the radius, determine the neighborhood of each wolf individual and the wolves within it. Then, use a multi-neighborhood learning algorithm to generate neighborhood candidate solutions for each wolf individual. Specifically:

[0153] Step 5.1: Treat each candidate solution as a wolf individual. Based on the candidate solutions for the next step, define the neighborhood radius of each wolf individual using the following formula:

[0154]

[0155] in, Let be the radius of the neighborhood of the i-th wolf individual, where i is an integer and 1 ≤ i ≤ pop. size ; For the i-th wolf individual, This is a candidate solution for the next step;

[0156] Step 5.2: Using the individual wolf as the center and the radius of its neighborhood as the radius, determine the neighborhood and the individual wolves within it for each wolf using the following formula:

[0157]

[0158] in, Let i be the neighborhood of the i-th wolf. Let J be the number of wolves in the neighborhood of the i-th wolf, where j is an integer and 1 ≤ j ≤ J, and J is the number of wolves in the neighborhood of the i-th wolf. express and The Euclidean distance between them For the domain;

[0159] Step 5.3: Using a multi-neighborhood learning algorithm, generate candidate neighborhood solutions for each individual wolf using the following formula:

[0160]

[0161] in, Let be the candidate solution in the neighborhood of the i-th wolf individual. , These represent random wolf individuals within the neighborhood of the i-th wolf individual and globally random wolf individuals, respectively.

[0162] In this embodiment, the gray wolf algorithm and the multi-neighborhood learning algorithm are used to guide the population towards the optimal region under the guidance of high-quality individuals. The advantages are obvious: fast convergence speed and strong ability to detect the optimal solution. However, this also causes the population to prematurely gather at a local optimum and ignore global exploration when solving nonlinear multimodal problems. Therefore, a niche algorithm is added in subsequent steps.

[0163] Niche algorithms simulate the natural phenomenon of niches in the wild. Their core principle is to divide the population into multiple sub-living spaces, maintaining the diversity of candidate solutions and thus avoiding getting trapped in local optima. By designing crowding control rules, individuals from different niches are prevented from clustering together. Niche algorithms can maintain population diversity and prevent premature clustering in localized areas. This characteristic can be well combined with the Grey Wolf algorithm, achieving population diversity through dynamic learning strategies and niche clustering techniques, thereby enhancing global exploration capabilities.

[0164] Step 6: Calculate the fitness of the next candidate solution and the neighboring candidate solutions for each wolf individual. Determine if the current iteration number is a multiple of 5. If so, use the niche algorithm to obtain the current optimal solution based on fitness, under the constraints of the initial niche radius and minimum niche size. Otherwise, take the candidate solution with the lowest fitness as the current optimal solution. Specifically:

[0165] Step 6.1: Calculate the fitness of the next candidate solution and the neighboring candidate solutions of each wolf individual. Determine if the current iteration number is an integer multiple of 5. If so, treat the next candidate solution and the neighboring candidate solutions of each wolf individual as individuals, select the individual with the smallest fitness as the best elite, and then execute Step 6.2; otherwise, take the candidate solution with the smallest fitness as the current optimal solution and execute Step 7.

[0166] Step 6.2: Centered on the best elite and with the initial niche radius as the radius, under the constraint of the minimum niche size, determine a niche and the individuals within it from all individuals according to the distance between the individual and the best elite;

[0167] Step 6.3: Among the remaining individuals not assigned to a niche, select the individual with the lowest fitness as the best elite, and then return to step 6.2 until all individuals are assigned to the corresponding niches, resulting in multiple niches;

[0168] Step 6.4: Set the elite retention ratio to 5%. According to the elite retention ratio, retain the candidate solutions with low fitness in each student's territory to obtain the elites.

[0169] Step 6.5: Employ iterative density clustering to allow elites to learn from the best elites. The optimal solution for each niche is obtained using the following formula:

[0170]

[0171] in, This is the optimal solution for the niche. For the elite, For learning rate, For the best elite, For disturbance terms;

[0172] The optimal solution of the niche with the lowest fitness is taken as the current optimal solution. Then, the radius of the current niche is calculated using the following formula, and this radius is used as the initial niche radius:

[0173]

[0174] in, For the current microhabitat radius, The initial niche radius, This represents the current iteration number. This represents the maximum number of iterations.

[0175] The niche algorithm employs an iterative density clustering method. In the initial stage, all individuals are in an unassigned state. In each round, the individual with the lowest fitness among the unassigned individuals is selected as the best elite. With the best elite as the center, neighboring individuals are searched within the niche radius to form a niche. If the niche size is smaller than the preset minimum niche size, the nearest individual is selected from other unassigned individuals to supplement it, ensuring that the niches have sufficient diversity. This operation is repeated until the niche division is complete.

[0176] This embodiment incorporates a niche algorithm into the Gray Wolf algorithm, effectively solving the premature convergence problem of the Gray Wolf algorithm framework. The niche algorithm maintains population diversity through iterative density clustering and elite learning.

[0177] Step 7: Update the positions of all individual wolves based on the current optimal solution, regenerate a set of candidate solutions, and then return to step 4 until the maximum number of iterations is reached. Output the current optimal solution as the global optimal solution to obtain the position coordinates of the device and complete the design of the heterogeneous optoelectronic equipment positioning and tracking network.

[0178] The heterogeneous optoelectronic equipment positioning and tracking network obtained in this embodiment was simulated, and the random measurement error is shown in Table 1. It can be seen that the measurement error of the heterogeneous multi-agent positioning and tracking network obtained by using the heterogeneous multi-agent positioning and tracking network design method based on the niche gray wolf algorithm provided in this embodiment is very small.

[0179] Table 1

[0180]

[0181] The optimization processes of the Niche Improved Grey Wolf Optimizer (NIGWO) algorithm provided in this embodiment are compared with those of the APSO (Adaptive Particle Swarm Optimization) and AGA (Adaptive Genetic Algorithm) algorithms. All algorithms use real-number encoding to represent the device's position coordinates, and the maximum number of iterations is uniformly set to 200. To eliminate the randomness of the simulation—that is, the problem that the degree of exploration in the solution space by the optimization algorithm is not completely consistent in each run—multiple experiments are conducted by running the algorithm for 30 rounds and taking the average value. The results are as follows: Figure 6 The comparison chart of the optimized simulation experiments is shown below. Figure 6 As shown in (a), the convergence curve of the AGA algorithm exhibits significant oscillations during the iteration process, with large fluctuations in fitness, indicating that the algorithm struggles to effectively focus in complex solution spaces and becomes trapped in local oscillations. The APSO algorithm shows a rapid decline in the early stages, but the decline rate slows significantly in the later stages of iteration, indicating insufficient exploration. In contrast, the NIGWO algorithm proposed in this embodiment demonstrates the best convergence performance, with the curve declining steadily and rapidly throughout the entire iteration period, ultimately converging to a fitness value superior to the comparative algorithms, indicating that the introduced niche algorithm effectively maintains population diversity. Figure 6 As shown in Figure (b), the NIGWO algorithm has the highest midpoint position in the box plot, the smallest average GDOP value, and the most concentrated and compact quality distribution of the solution. This indicates that the NIGWO algorithm has good robustness and can stably output high-quality, repeatable deployment schemes.

[0182] To verify the optimization performance of the NIGWO algorithm provided in this embodiment, a convergence simulation experiment was conducted. The test function was set as the classic multimodal function Rastrigin function from the CEC2005 test set. This function is often used to test the performance of optimization algorithms due to its complex multimodal characteristics. The 3D curve and contour plot of the Rastrigin function are shown below. Figure 7As shown in (a) and (b), the function has a unique global minimum and a large number of local minima. This characteristic places extremely high demands on the global search capability of the optimization algorithm. If the optimization algorithm has poor global search performance, it is easy to get trapped in local minima and converge prematurely before finding the global minimum. The global search capability of the NIGWO algorithm is verified by comparing it with the Rastrigin function.

[0183] The comparison algorithms used were IGWO (Improved Grey Wolf Optimizer), GWO (Grey Wolf Optimizer), APSO, and AGA. All algorithms used real-number encoding, with a population size of 50, a maximum number of iterations of 200, a search dimension of 30, and a search space of [-100, 100]. After multiple comparisons and parameter tuning, the APSO algorithm had an inertia weight of 0.729, and individual and social learning factors of 1.500 and 1.400, respectively. The AGA algorithm was designed according to literature recommendations, with k2=0.5, k4=0.5, k1=1.0, and k3=1.0 to facilitate global exploration using chromosomes with lower fitness.

[0184] The test performance of the NIGWO, IGWO, GWO, APSO, and AGA algorithms on the Rastrigin function is as follows: Figure 8 As shown, Figure 8 The convergence curve comparison chart in (a) shows the optimization trajectory after 200 iterations. It is evident that the NIGWO algorithm provided in this embodiment exhibits the best global search capability, demonstrating a significant advantage in convergence performance. In the early stages of iteration, the NIGWO, IGWO, and GWO algorithms show a rapid convergence trend, with convergence speeds significantly better than the APSO and AGA algorithms, indicating that the GWO algorithm framework possesses strong global search capabilities from the initial exploration phase. In the middle stages of iteration, the convergence of the IGWO and GWO algorithms slows down, while the NIGWO algorithm effectively maintains population diversity, avoiding premature convergence, and its convergence curve steadily decreases until the iteration limit of 200. In contrast, the APSO and AGA algorithms, overall, prematurely fall into premature convergence, getting trapped in local minima. Figure 8 In the final solution quality comparison chart in (b), the solution of the NIGWO algorithm has a significantly lower fitness value than other comparison algorithms, which proves the global search capability of the NIGWO algorithm.

Claims

1. A design method for a heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm, characterized in that, Includes the following steps: Step 1: Based on the measurement and control area, design a heterogeneous multi-agent positioning and tracking network, obtain the equipment type and quantity, and construct a positioning accuracy model for the heterogeneous multi-agent positioning and tracking network; Step 2: According to the design requirements, set the population size, upper and lower bounds of the search space, initial niche radius and minimum niche size, and use the positioning accuracy model as the optimization objective function, the value of the optimization objective function as the fitness, the minimization of fitness as the optimization objective, and reset the current iteration number to zero. Step 3: Based on the population size and the upper and lower bounds of the search space, randomly generate a set of candidate solutions in the solution space of the Grey Wolf Algorithm, wherein the candidate solutions are the location coordinates of the device; Step 4: Calculate the fitness of each candidate solution, and then use the Grey Wolf algorithm to generate the next candidate solution based on the fitness of the candidate solutions, and increment the current iteration number by 1; Step 5: Treat each candidate solution as a wolf individual, define the neighborhood radius of each wolf individual based on the candidate solutions of the next step, and determine the neighborhood of each wolf individual and the wolves within it with the wolf individual as the center and the neighborhood radius as the radius. Then, use the multi-neighborhood learning algorithm to generate neighborhood candidate solutions for each wolf individual. Step 6: Calculate the fitness of the next candidate solution and the neighboring candidate solutions of each wolf individual. Determine whether the current iteration number is an integer multiple of S. If so, use the niche algorithm to obtain the current optimal solution based on the fitness under the constraints of the initial niche radius and the minimum niche size. Otherwise, take the candidate solution with the smallest fitness as the current optimal solution. Where S is an integer and 0 < S < 10. Step 7: Update the positions of all individual wolves based on the current optimal solution, regenerate a set of candidate solutions, and then return to step 4 until the maximum number of iterations is reached. Output the current optimal solution as the global optimal solution to obtain the position coordinates of the device and complete the design of the heterogeneous optoelectronic equipment positioning and tracking network.

2. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to claim 1, characterized in that, Step 5 specifically involves: Step 5.1: Treat each candidate solution as a wolf individual, and define the neighborhood radius of each wolf individual according to the candidate solutions in the next step using the following formula: ； in, Let be the radius of the neighborhood of the i-th wolf individual, where i is an integer and 1 ≤ i ≤ pop. size pop size Population size; For the i-th wolf individual, This is a candidate solution for the next step; Step 5.2: Using the individual wolf as the center and the radius of its neighborhood as the radius, determine the neighborhood and the individual wolves within it for each wolf using the following formula: ； in, Let i be the neighborhood of the i-th wolf. Let J be the number of wolves in the neighborhood of the i-th wolf, where j is an integer and 1 ≤ j ≤ J, and J is the number of wolves in the neighborhood of the i-th wolf. express and The Euclidean distance between them For the domain; Step 5.3: Using a multi-neighborhood learning algorithm, generate candidate neighborhood solutions for each individual wolf using the following formula: ； in, Let be the candidate solution in the neighborhood of the i-th wolf individual. , These represent random wolf individuals within the neighborhood of the i-th wolf individual and globally random wolf individuals, respectively. This is a function for generating random numbers.

3. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to claim 2, characterized in that, Step 6 specifically involves: Step 6.1: Calculate the fitness of the next candidate solution and the neighborhood candidate solutions of each wolf individual. Determine whether the current iteration number is an integer multiple of S. If so, treat the next candidate solution and the neighborhood candidate solutions of each wolf individual as individuals, select the individual with the smallest fitness as the best elite, and then execute Step 6.2; otherwise, take the candidate solution with the smallest fitness as the current optimal solution and execute Step 7. Step 6.2: Centered on the best elite and with the initial niche radius as the radius, under the constraint of the minimum niche size, determine a niche and the individuals within it from all individuals according to the distance between the individual and the best elite; Step 6.3: Among the remaining individuals not assigned to a niche, select the individual with the lowest fitness as the best elite, and then return to step 6.2 until all individuals are assigned to the corresponding niches, resulting in multiple niches; Step 6.4: Set the elite retention ratio. According to the elite retention ratio, retain the candidate solutions with low fitness in each student's territory to obtain the elites. Step 6.5: Use the iterative density clustering method to make elites learn from the best elites and obtain the optimal solution of each niche. The optimal solution of the niche with the smallest fitness is taken as the current optimal solution. Then calculate the radius of the current niche and take it as the initial niche radius.

4. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to claim 3, characterized in that, In step 6.5, the optimal solution for the niche is obtained using the following formula: ； in, This is the optimal solution for the niche. For the elite, For learning rate, For the best elite, For disturbance terms; In step 6.5, the radius of the current microhabitat is calculated using the following formula: ； in, For the current microhabitat radius, The initial niche radius, This represents the current iteration number. This represents the maximum number of iterations.

5. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to any one of claims 1-4, characterized in that, Step 1 is as follows: Step 1.1: Based on the measurement and control area, design a heterogeneous multi-agent positioning and tracking network, including one radar and N photoelectric theodolites, where N is an integer and N≥2; Step 1.2: Establish the observation equations for radar and photoelectric theodolite respectively, and then establish a joint observation equation based on the observation equations of radar and photoelectric theodolite; Step 1.3: Perform a first-order Taylor expansion on the joint observation equation to obtain the matrix relationship of error propagation, and then derive the measurement Jacobian matrix; Step 1.4: Define the inverse matrix of the covariance matrix of the random noise error of the heterogeneous multi-agent localization and tracking network as the weight matrix. Then, using the least squares estimation theory, based on the measurement Jacobian matrix and the weight matrix, obtain the covariance matrix of the position estimation localization error. Step 1.5: Based on the covariance matrix of the positioning error, establish a positioning accuracy model.

6. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to claim 5, characterized in that, In step 1.2, the radar's observation equation is: ； ； ； in, , , These are the observed values ​​of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively. , , These are the theoretical values ​​of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively. , , These are the X, Y, and Z coordinates of the target location, respectively. , , These are the X, Y, and Z coordinates of the radar location, respectively. , , These are the zero-mean Gaussian random noise errors of the target's radial distance, azimuth angle, and elevation angle relative to the radar, respectively, all of which follow a normal distribution; In step 1.2, the observation equations for the photoelectric theodolite are established using dual-station intersection measurement. The observation equations for the photoelectric theodolite are as follows: ； ； in, , These are the azimuth and elevation angle observations of the target relative to the photoelectric theodolite, respectively. , These are the theoretical values ​​of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively. , , These are the X, Y, and Z axis coordinates of the position of the photoelectric theodolite; , These are the zero-mean Gaussian random noise errors of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively, both of which follow a normal distribution; In step 1.2, the joint observation equation is: ； ； ； in, , , These are the observed values ​​for the target's azimuth, elevation, and radial distance, respectively.

7. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to claim 6, characterized in that, In step 1.3, the matrix relationship of error propagation is as follows: ； in, , is the measurement error vector. For the radial distance measurement error between the target and the radar, , These are the measurement errors of the azimuth and elevation angles of the target relative to the photoelectric theodolite, respectively. , where is the position error vector. , , These represent the errors of the target position along the X, Y, and Z axes, respectively; H is the measurement Jacobian matrix. This is due to random noise error; In step 1.3, the measurement Jacobian matrix is: ； in, , These are the measurement Jacobian matrices for photoelectric theodolites and radar, respectively. The horizontal projection of the line connecting the photoelectric theodolite and the target. ; The distance between the photoelectric theodolite and the target. .

8. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to claim 7, characterized in that, In step 1.4, the weight matrix is: ； in, For the weight matrix, Let be the covariance matrix of the random noise error in the heterogeneous multi-agent localization and tracking network. , , These represent the measurement noise of the target's azimuth and elevation angle observations relative to the photoelectric theodolite, respectively. The measurement noise for the radial distance observation between the target and the radar. , , ; In step 1.4, the covariance matrix of the location estimation positioning error is calculated using the following formula: ； in, This is the covariance matrix of the location estimation positioning error.

9. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to claim 8, characterized in that, In step 1.5, the positioning accuracy model is as follows: ； in, This is the positioning accuracy factor. This indicates finding the trace of a matrix.

10. The design method for heterogeneous multi-agent localization and tracking network based on the niche gray wolf algorithm according to claim 9, characterized in that, In step 3, the candidate solution is generated using the following formula: ； in, As a candidate solution, , These are the upper and lower bounds of the search space, respectively. For population size, For the number of devices, This is a function for generating random numbers.

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