An adaptive differential evolution algorithm for optimizing passive radar deployment.

Abstract

This invention discloses an adaptive differential evolution algorithm for optimizing passive radar station deployment, comprising the following steps: establishing a passive time difference station deployment simulation scenario; step 2: population initialization; step 3: fitness value calculation; step 4: genetic operation. On the one hand, this invention addresses the problem of numerous variable parameters and complex parameter settings in particle swarm optimization (PSO) algorithms by incorporating iteration counts, fitness values, and weights into parameter generation, making the algorithm's search and convergence more reasonable. On the other hand, this invention considers the impact of station location error, time difference error, and communication distance between observation stations on the deployment results during experimental simulation, making the modeling process more realistic.

Description

Technical Field

[0001] This invention belongs to the field of passive positioning technology, specifically relating to an adaptive differential evolution algorithm for optimizing passive radar deployment. Background Technology

[0002] In existing technologies, the impact of site location errors and time difference errors on the deployment results is not considered when establishing passive radar deployment scenarios, and the constraint of distance between observation stations is not taken into account during the optimization process. Furthermore, the network weights of the particle swarm optimization algorithm need to be manually set, involving many parameters, which complicates practical applications. While the adaptive genetic algorithm has fewer parameters than the particle swarm optimization algorithm, it does not consider the impact of fitness and iteration count on the evolutionary process. The improved differential evolution algorithm, although considering the impact of iteration count on the evolutionary process, only improves the mutation operator and does not reflect the influence of fitness and iteration count on the evolutionary process in the crossover operator.

[0003] Xi'an University of Electronic Science and Technology has studied the impact of station deployment on positioning accuracy. In its patent application, "A Passive Radar Station Deployment Method Based on an Improved Particle Swarm Optimization Algorithm" (Application No. 202110484688.5, Publication No. CN113210065A), it proposed a passive radar station deployment method based on an improved particle swarm optimization algorithm. This method optimizes the location of observation stations using an improved particle swarm optimization algorithm, using the positioning error within a certain area as an evaluation criterion, concluding that using the improved particle swarm optimization algorithm can improve the positioning accuracy of targets. However, this algorithm has many variable parameters, resulting in complex parameter settings.

[0004] In his 2021 paper "Research on Station Placement Method of MLAT System Based on Improved Differential Evolution" published in the journal *Electronic Technology Applications*, Xu Songshou used the differential evolution algorithm for station placement optimization. The main focus was on the distribution of the mean GDOP of different station placements within a specified region. His main improvements were to the mutation operation of the algorithm, incorporating the influence of the number of iterations on the mutation parameters. Furthermore, he improved the population selection by adding a second-order greedy selection. This method improved the algorithm's global convergence and local search capabilities to some extent. However, the mutation coefficients used in the former method are fixed values ​​and cannot be changed during the iteration process, still requiring parameter tuning.

[0005] In their 2022 paper, "Application of Adaptive Differential Evolutionary Algorithm in Intrusion Detection," Li Yinhuan and Lin Kaisheng used the iterative process of the differential evolutionary algorithm and the fitness value of the individual in the current generation as adaptive operators to dynamically adjust the scaling factor and crossover probability during the differencing process. They demonstrated the algorithm's superiority through experiments. However, the adaptive operator set by Li et al. assumed that the influence of the current iteration number and the current fitness value on the result was the same, assigning a weight of 0.5 to both. This allocation method fails to reflect the algorithm's requirements for convergence and diversity at different stages. Summary of the Invention

[0006] To overcome the shortcomings of the existing technologies, the present invention aims to provide an adaptive differential evolution algorithm for optimizing passive radar station deployment. On the one hand, the differential evolution algorithm can solve the problems of multiple variable parameters and complex parameter settings in the particle swarm optimization algorithm, and incorporates iteration number, fitness value and weight factors in parameter generation, making the search and convergence of the algorithm more reasonable. On the other hand, in the experimental simulation process, the present invention considers the impact of site error, time difference error and communication distance between observation stations on the deployment results, making the modeling process more realistic.

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

[0008] An adaptive differential evolution algorithm for optimizing passive radar deployment includes the following steps;

[0009] Step 1: Establish a simulation scenario for passive time-difference station deployment;

[0010] Establish the three-dimensional coordinate positions of M observation stations distributed within a certain area, where the coordinates of the M observation stations in three dimensions are S = {S0,...,S...}. M-1}, S i =(x i ,y i ,z i ), i = 0, ..., M-1, M observation stations and their coordinate positions are called an individual, and the target area to be located is the observation area x∈[x] in a certain plane in three-dimensional space. l ,x h ],y∈[y l ,y h ], z=z l The target area is discretized by dividing it into H grids, and the coordinates of the middle position of each grid are taken as the target position to be observed.

[0011] Step 2: Population initialization;

[0012] N individuals, i, are randomly generated within the distribution area of ​​the observation station. Using x... i =(x i1 ,...,x ij ) represents S in step 1;

[0013] Step 3: Fitness value calculation;

[0014] Calculate the mean GDOP within the observation area. The fitness value is the mean of the geometric dilution of precision (GDOP) of the positioning error within the observation area, denoted by f. That is, calculate the sum of the GDOP values ​​of H target locations under the current observation station distribution and then calculate the average.

[0015] Step 4: Genetic manipulation;

[0016] The optimal site layout is obtained by substituting the adaptive weight coefficients into the perturbation parameters and crossover probabilities of the differential evolution algorithm.

[0017] In step 1, the target location, taking the k-th target location to be located as an example, has the following coordinates: T k =(x k ,y k ,z k ),k=1,...,H, z k =z l .

[0018] In step 2, each individual has a set of four observation stations positioned in a three-dimensional coordinate system, with a total of 12 components, using x... i =(x i1 ,...,x ij Let i = 1, ..., N, j = 1, ..., 12 to represent S in step 1; since there are four observation stations, M = 3 in step 1, where j = 1, 2, 3 refers to the three-dimensional coordinate position of the first observation station of the i-th individual, which corresponds to S0 = (x i1 ,x i2 ,x i3 ), and so on, j = 4, 5, 6 correspond to S1 = (x) in step 1. i4 ,x i5 ,x i6 Similarly, the 12-dimensional components of individual i represent the positions of the four observation stations S0, S1, S2, and S3, respectively. N individuals refer to N sets of four observation station positions.

[0019] The calculation method for f in step 3 is as follows:

[0020] Given the site error variance and time difference error variance of the system, and based on the station deployment requirements, the communication distance between observation stations is set. With these three parameters determined, the fitness value f under the current station deployment is calculated, and each individual x obtained after population initialization is... i =(x i1 ,...,x ij Substituting i = 1, ..., N j = 1, ..., 12 into the fitness function f, we obtain the specific fitness value. The smaller f is, the smaller the average positioning error accuracy within the region, that is, the better the deployment effect in the target region. The formula for calculating f is as follows:

[0021]

[0022] After obtaining the initialized population and its fitness values, the next iteration process begins, which involves mutation, crossover, and selection of N individuals. The following example illustrates the process of g iterations, where individuals i = 1, ..., N.

[0023] The genetic operation in step 4 specifically includes:

[0024] a) Population variation

[0025] In the g-th iteration of mutation, individual i is mutated. Three individuals are randomly selected from the population to serve as parents in the g+1-th iteration. These three individuals are then sorted according to their fitness values ​​from best to worst, resulting in... The i-th individual after mutation is represented as in

[0026] From this formula, we can obtain F i The value of will directly affect the individual. In the early stages of the algorithm iteration, we hope that F will take a certain value. i A larger F value can improve population diversity. In later iterations, it is hoped that F will... i A smaller value can guide a good population to converge to a dominant solution, therefore, for F... i The fitness value and the number of iterations have an impact.

[0027] The perturbation parameter F of the difference vector is generated by using a set of weights. i Adjust the relationship between the number of iterations and the fitness value.

[0028] b) Population crossover;

[0029] The individual i that underwent the mutation process described above is... Let the individual i after the crossover be... Generate a random number (0,1) using rand(0,1), and then combine it with the current crossover probability CR. i Comparison, and then analysis of the mutated individuals and individuals that have not undergone mutation By crossing, we get The calculation formula is as follows:

[0030]

[0031]

[0032] CR min The minimum value of the disturbance coefficient, CR max It is the maximum value of the disturbance coefficient, f i Individual i that has not undergone crossover and mutation fitness value, f min and f max These are the minimum and maximum fitness values ​​among all individuals. This operation allows the population to retain the dominant genes from the parents, ensuring genetic diversity.

[0033] c) Population selection

[0034] In the g-th iteration selection, the new individual i is generated as shown in the following formula.

[0035]

[0036] in yes After mutation and crossover, the fitness values ​​of the individuals obtained are compared, and the one with the smaller fitness value is selected as the i-th individual in the g+1-th iteration.

[0037] After G iterations, the individual with the best fitness value is selected from the remaining population. The solution corresponding to the selected individual is the optimal placement result.

[0038] The weights in step a) are generated as follows:

[0039] Generate N sets of weights (the same as the total number of individuals), meaning each individual corresponds to a different weight. The weight vector of the i-th set is... in And starting from the first weight vector, to the last weight vector, It increases uniformly, and vice versa. The weights decrease uniformly. After obtaining the weights, in the g-th iteration, the perturbation parameter in the formula for generating new mutated individuals is used. Through the method of generating this perturbation parameter, the influence of the fitness value and the number of iterations on the final result during the iteration process is distributed with different weights, ensuring the diversity and convergence of solutions. Fi The calculation formula is as follows:

[0040]

[0041] Among them, F min The minimum value of the disturbance coefficient, F. max It is the maximum value of the disturbance coefficient, f p1 ,f p2 ,f p3 These are the fitness values ​​of the three selected individuals, already sorted in order of superiority, where f p1 It has the best fitness value, f p3 It is the one with the worst fitness value. g represents the current iteration number, and G represents the total number of iterations. This mutation process can increase the diversity of the population.

[0042] The optimization method is applied in both dynamic and static cases;

[0043] Dynamic Situation: In the field of radar countermeasures, when the enemy is known to be in a certain area, this algorithm can be used to demonstrate passive positioning and station deployment in that area. It can obtain better deployment results in advance, and then use aircraft or mobile carriers to carry passive equipment for deployment, saving battlefield resources. In addition, multi-aircraft deployment: This method plays a role in subsequent swarm deployment, not limited by the number of aircraft. It compares the positioning accuracy of aircraft with different combinations of numbers and selects the optimal deployment result.

[0044] Static scenario: Used for setting up fixed base stations, deploying stations across a fixed key monitoring area to achieve good positioning accuracy over a large area.

[0045] The beneficial effects of this invention are:

[0046] This invention selects the differential evolution algorithm, which has better convergence, for improvement.

[0047] This invention takes into account the influence of the number of iterations and the fitness function on the algorithm search process, optimizes the mutation operator and crossover operator to improve the convergence of the algorithm, and adds adaptive weights to increase the globality of the search.

[0048] In the simulation process, the target area of ​​this algorithm is larger and more detailed. It takes into account factors such as site error, distance error and constraint communication distance, and is closer to the real scene.

[0049] This invention uses a set of varying weights to dynamically adjust the scaling factor and crossover probability during the difference process, and experiments demonstrate that the algorithm has certain advantages.

[0050] The improved adaptive differential evolution algorithm of this invention uses significantly fewer parameters, eliminating the need to set complex parameters.

[0051] The weight perturbation term added in this invention makes the change trend of crossover and mutation parameters conform to the actual needs of the algorithm operation process. In the search process, it not only has a fast convergence speed but also a good convergence effect, which enhances the robustness and can be well applied to the optimization of four-station time difference deployment, greatly improving the feasibility of the experiment. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0053] Figure 2 The figure shows the iterative results of optimizing the four-station passive time difference layout under the traditional differential evolution algorithm.

[0054] Figure 3 This is the iterative result of the four-station passive time difference layout optimization under the adaptive differential evolution algorithm without weight perturbation.

[0055] Figure 4 The results represent the iterative optimization of the passive time difference station layout of four stations under the adaptive differential evolution algorithm with weighted perturbations.

[0056] Figure 5 This is a map showing the distribution of GDOP on the target plane from the observation station. Figure 5 The four red triangles represent the GDOP distribution map of the optimal station placement result in the 5KM plane under this algorithm iteration. Detailed Implementation

[0057] The present invention will now be described in further detail with reference to the accompanying drawings.

[0058] The implementation process of this invention is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0059] Step 1. Establish a simulation scenario for four-station passive time-difference deployment.

[0060] A model of four observation stations distributed in three-dimensional space is established, with the coordinates of the stations as shown below: S={S0,...,S3}, S i =(x i ,y i ,z i ), i = 0,...,3. The target area is an observation area distributed on a plane in three-dimensional space. This plane area is divided into H grids, and the coordinates of the middle point of each grid are taken as one of the targets that the observation station needs to monitor. Taking the k-th target to be located as an example, its coordinate position is as follows: T k =(x k ,yk ,z k ),k=1,...,H, The larger the value of H, the denser the mesh, the greater the computational cost, and the more accurate the results.

[0061] Step 2. Population Initialization

[0062] N individuals are randomly generated within the distribution area of ​​the observation stations. Each individual has four observation stations at their coordinate positions in three-dimensional space, so each individual has a dimension of 12. A population is randomly generated based on the range of maximum and minimum values ​​for each dimension of the individual. Taking individual i as an example, x... i =(x i1 ,...,x ij i = 1, ..., N j = 1, ..., 12. Using binary encoding, specifically the Binary Differential Evolution (BDE) algorithm, for each gene x... ij Encode it. Let gene x be... ij The real number range of i = 1, ..., N, j = 1, ..., 12 is [a, b] KM. This application aims for precision down to the meter, so x needs to be... ij The partitioning of i = 1, ..., N, j = 1, ..., 12 into (ba) * 10 3 Divide into equal parts, and from this, obtain the length L of the gene encoding, such that 2 L-1 <(ba)·10 3 ≤2 L Then, randomly generate a binary string of length L containing only 0s and 1s, <l1,...,l>. L If >, then the corresponding variables converted from this binary string are:

[0063]

[0064] Step 3. Fitness value calculation

[0065] Given the site location error and time difference error, the communication distance between observation stations is determined. With these three parameters fixed, the mean GDOP within the observation area is calculated. Each individual is then substituted into the fitness function f to obtain a specific fitness value. A smaller f indicates better station placement effectiveness. The formula for calculating f is as follows:

[0066]

[0067] Taking individual i as an example x i =(x i1 ,...,x ijGiven that i = 1, ..., N, j = 1, ..., 12, the coordinates of the four observation stations corresponding to individual i are S0 = (x i1 ,x i2 ,x i3 ),S1=(x i4 ,x i5 ,x i6 ),S2=(x i7 ,x i8 ,x i9 ),S3=(x i10 ,x i11 ,x i12 This paper employs this method in operations such as crossover and mutation. Furthermore, the coordinate positions of the four observation stations corresponding to an individual can be represented as S0 = (x0, y0, z0), S1 = (x1, y1, z1), S2 = (x2, y2, z2), and S3 = (x3, y3, z3). The following calculates the target location T under the station layout of the i-th individual. k =(x k ,y k ,z k The derivation of the GDOP formula at k = 1, ..., H is presented using the second representation method for ease of understanding; the first representation method is used when performing operations such as crossover and mutation selection.

[0068] Let S0 = (x0, y0, z0) be the main station among the four observation stations, and the other stations S1, S2, and S3 be the secondary stations. Then let Δr... i This is the distance difference between the target location and the main station, and the target location and the secondary station.

[0069]

[0070] Taking the total differential of this equation, we get dR = [dΔr1, dΔr2, dΔr3] T Expressing dR in matrix form, we get dR = QdX + dS, where the target localization error dX = [dx, dy, dz]. T

[0071]

[0072] make in Let dS represent the distances from the four observation stations to the target. Then, the station location error is: dS = [k1-k0, k2-k0, k3-k0]. T Let K = (Q) T Q) -1 Q T Then the target positioning error is: dX = Q -1If (dR-dS)=K(dR-dS), then the covariance matrix of the target positioning error can be expressed as:

[0073] P = Cov(dX) = E(dXdX) T )

[0074] =K[Cov(dR)+Cov(dS)]K T

[0075] Assume that the time difference error follows a mean of 0 and a variance of . If the distribution is Gaussian, then the correlation coefficient between time difference errors is... Suppose that the site location error is independently distributed in the three directions (x, y, z), and the distribution function is N(0, σ). s ), then we have

[0076]

[0077] From this, the noise covariance matrix [F] can be obtained. ij ] N*N =Cov(dR)+Cov(dS), where each element can be written as:

[0078]

[0079] The total covariance of the location can then be written as P = Cov(dX) = K[F ij ] N*N K T

[0080]

[0081] Step 4. Genetic manipulation

[0082] a) Variation

[0083] The main improvement is to incorporate adaptive weight coefficients into the perturbation parameters and crossover probabilities of the differential evolution algorithm.

[0084] In the g-th iteration of mutation, three randomly selected parent individuals are sorted from best to worst based on their fitness value; a smaller fitness value indicates a better solution. The sorted individuals are as follows. in If the i-th individual has the best fitness value, then the i-th individual after mutation is represented as: in From this formula, we can obtain F i The value of will directly affect the individual. The value of F. In the early stages of the algorithm iteration, it is hoped that F will... i A larger F value can improve population diversity. In later iterations, it is hoped that F will... iA smaller value can guide a good population to converge to a dominant solution. Therefore, for F... i The fitness value and the number of iterations have an impact. This invention proposes generating a set of weights to adjust the relationship between the number of iterations and the fitness value. The weights are generated as follows: N sets of weights are generated. The weight vector of the i-th group is The relationship between them is And starting from the first weight vector, to the last weight vector, It increases uniformly, and similarly, It decreases uniformly. After obtaining the weights, in the g-th iteration, the perturbation parameter F in the formula for generating new mutated individuals... i Obtained from the following formula.

[0085]

[0086] Among them, F min The minimum value of the disturbance coefficient, F. max It is the maximum value of the disturbance coefficient, f p1 ,f p2 ,f p3 These are the fitness values ​​of the three selected individuals, already sorted in order of superiority, where f p1 It has the best fitness value, f p3 It has the worst fitness value. g represents the current iteration number, and G represents the total number of iterations.

[0087] This invention uses the Hamming distance between two genes to represent the difference vector. set up and Hamming distance between For d 23 Then after F i Scaling, d * =F i ×d 23 d * When d is a real number, it is necessary to adjust d. * Round up or down. The probabilities of rounding up and down are as follows:

[0088] Table 1 and binary encoding

[0089]

[0090] but The number of positions that need to be mutated is rand(1) generates a random number between 0 and 1. Taking Table 1 as an example, d... 23Equal to 5, assume F i =0.5, then d * ＝2.5 If rand(1) < 0.5, then Three positions need to be mutated, and vice versa. Let's assume there are three positions here. Invert the bits of three random positions, positions 1, 4, and 6, to obtain... By repeating this operation for j = 1, ..., 12, we obtain the individual.

[0091] b) Cross

[0092] In the g-th iteration, the individual The calculation formula is as follows:

[0093]

[0094] Since the crossover probability affects the proportion of mutated individuals in the population, increasing the crossover probability is beneficial to population diversity. However, it is desirable that in the later stages of evolution, the crossover probability can guide the population to converge to a dominant solution. Therefore, the crossover probability is related to the perturbation parameter F. i Similarly, CR i It is also affected by the fitness value and the number of iterations. In the g-th iteration, In the calculation formula, CR i The calculation formula is as follows:

[0095]

[0096] c) Population selection

[0097] In the g-th iteration, new individuals are generated as shown in the following formula. Individuals with good fitness values ​​will be directly selected for the next iteration. Here, f is the fitness function obtained in step three. It is the individual after crossover, the individual and Calculate the fitness value of each individual, and select the individual with the smaller fitness value as the new individual for the next iteration.

[0098]

[0099] After all iterations are completed, the individual with the best fitness value is selected from the remaining population. The coordinates of the four observation stations corresponding to the selected individual are the optimal station layout obtained by this algorithm.

[0100] This invention employs an improved adaptive differential evolution algorithm for optimizing the deployment of four-station passive time difference localization. The invention refines the parameters of the adaptive differential evolution algorithm during crossover and mutation, proposing the generation of a set of weights to adjust the relationship between the number of iterations and the fitness value. Specifically, it innovatively introduces adaptive weights in the generation of the perturbation coefficient F and the crossover probability CR. The experimental modeling process considered error factors and constraints comprehensively, closely approximating real-world conditions.

[0101] The effects of this invention are illustrated below in conjunction with the simulation conditions of the experiment:

[0102] 1. Experimental conditions

[0103] Device: Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz 2.59GHz, Windows 10

[0104] Software: MATLAB R2020a

[0105] 2. Experiment Content

[0106] Three sets of experiments were set up: one set used a differential evolution algorithm with fixed mutation difference coefficients; the second set used an adaptive differential evolution algorithm without weight perturbation; and the third set used the differential evolution algorithm with weight perturbation proposed in this paper. The three algorithms were applied to the site optimization of four-station passive positioning based on time difference. The experimental results of the three sets of experiments are shown in the figure below. Figure 2 , Figure 3 , Figure 4 As shown in the figure, the horizontal axis of these three graphs represents the number of iterations of the algorithm, and the vertical axis represents the fitness value. The graphs show the curves of how the convergence rate of the fitness value changes as the number of iterations increases. Figure 4 This is a graph showing the results of the algorithm proposed in this invention. The vertical axis represents the fitness value, i.e., the value of the fitness function mentioned earlier. The smaller the fitness, the better the experimental results and the better the station placement effect.

[0107] 3. Experimental parameters

[0108] Common parameters: Population size N = 100, number of iterations G = 500, observation target area x: [0, 100] KM, y: [0, 100] KM, z: 0.01 KM, observation station distribution area x: [0, 100] KM, y: [0, 100] KM, z = 5 KM, given station location error: 0.005 KM, time difference error: 5 ns; maximum communication distance between observation stations: 100 KM, minimum communication distance: 5 KM;

[0109] In one set of experiments, the perturbation parameter F was set to 0.5, and the crossover probability was 0.8.

[0110] The second set of experiments used an adaptive differential evolution algorithm without weight perturbation, so the weight coefficients... All are set to 0.5;

[0111] The minimum value of the perturbation coefficient F in the three sets of experiments min The maximum value of the disturbance coefficient F is 0.1. max The minimum crossover probability CR is 0.9. min The maximum crossover probability CR is 0.1. max It is 0.9.

[0112] 4. Simulation Analysis

[0113] from Figure 2 As can be seen, the experimental group containing the differential evolution algorithm converges faster than the experimental group containing the adaptive differential evolution algorithm. The fitness value stabilizes after 80 iterations. However, the results show poor diversity throughout the search process, with the fitness value only decreasing in a few iterations. The overall search performance is also worse than the experimental group containing the differential evolution algorithm. Therefore, when applying the differential evolution algorithm to passive station deployment, relying on fixed parameters cannot achieve good deployment results, but it can obtain a relatively optimal solution in a short time. Comparing the experimental group containing the differential evolution algorithm with the experimental group containing the adaptive differential evolution algorithm, i.e. Figure 3 and Figure 4 contrast, Figure 3 The downward trend of the curve and Figure 4 Similar. But Figure 3 The convergence trend tends to plateau around the 100th and 300th iterations, while Figure 4 There is a clear convergence trend around the 20, 200, and 300 iterations. Furthermore, Figure 4 The final convergence effect is better than Figure 3 Good. It is evident that adding weight perturbations to the differential evolution algorithm better aligns with the search patterns of the station deployment process, resulting in excellent convergence speed and performance. This demonstrates that using this algorithm for station deployment optimization in passive time-of-flight systems will improve average positioning accuracy. To better illustrate the GDOP distribution of irregular station deployments, Figure 5 The image shows the GDOP distribution under the optimal station layout, where the red triangles represent the locations of the four observation stations. It can be seen that when the objective function requires a good mean GDOP value for a specified area, the GDOP distribution is relatively uniform, without excessively large GDOP values ​​at lower angles.

Claims

1. A method for optimizing passive radar station using adaptive differential evolution algorithm, characterized in that, Includes the following steps; Step 1: Establish a simulation scenario for passive time-difference station deployment; Establish the three-dimensional coordinate positions of M observation stations distributed in a certain area, the coordinates of the M observation stations in three dimensions , , M observation stations and their coordinate positions are called an individual, and the target area to be positioned is an observation area distributed in a certain plane in three-dimensional space , discretize the target area, that is, uniformly divide it into H grids, and take the coordinates of the middle position of each grid as the target position to be observed; Step 2: Population initialization; N individuals are randomly generated within the distribution area of ​​the observation station. ,use In step 1 ; Step 3: Fitness value calculation; Calculate the mean GDOP within the observation area. The fitness value is the mean of the geometrically diluted positioning error within the observation area. This means calculating the sum of the GDOP values ​​of H target locations under the current observation station distribution, and then averaging them. Step 4: Genetic manipulation; The optimal station placement is obtained by substituting the adaptive weight coefficients into the perturbation parameters and crossover probabilities of the differential evolution algorithm. The genetic operation in step 4 specifically includes: a) Population variation In the g-th iteration mutation, for individuals Mutation is performed, and three individuals are randomly selected from the population as parents in the g+1 iterations. These three individuals are then sorted according to their fitness values ​​from best to worst, resulting in... , , , Then the mutated first Each individual is represented as ,in , ; From this formula, we can obtain that The value of will directly affect the individual. The desired value of is to be determined in the early stages of the algorithm iteration. A larger size can improve population diversity, and in the later stages of iteration, it is hoped that... Smaller values ​​can guide a good population to converge to a dominant solution, therefore... The fitness value and the number of iterations have an impact. The perturbation parameters of the difference vector are generated using a set of weights. Adjusting the relationship between the number of iterations and the fitness value; b) Population crossover; Individuals that have undergone mutations during the aforementioned mutation process for Then let the individuals after the crossover for ,pass produce A random number, and its relationship to the current crossover probability. Comparison, and then analysis of the mutated individuals and individuals that have not undergone mutation By crossing, we get The calculation formula is as follows: ， This refers to the minimum value of the disturbance coefficient. It is the maximum value of the disturbance coefficient. Individuals that have not undergone crossover and mutation Right now fitness value, and These are the minimum and maximum fitness values ​​among all individuals. This operation allows the population to retain the dominant genes from the parents, ensuring genetic diversity. c) Population selection In the g-th iteration selection, the new individual The following formula is generated. in yes After mutation and crossover, the resulting individuals are compared in fitness value, and the one with the smaller fitness value is selected as the first individual in the (g+1)th iteration. Individual; exist After each iteration, the individual with the best fitness value is selected from the remaining population, and the solution corresponding to the selected individual is the optimal placement result. The weights in step a) are generated as follows: Generate N sets of weights, meaning each individual corresponds to a different weight, the th... Group weight vector is ,in And starting from the first weight vector, to the last weight vector, It increases uniformly, and vice versa. The weights decrease uniformly. After obtaining the weights, in the g-th iteration, the perturbation parameter in the formula for generating new mutated individuals is used. By generating this perturbation parameter, the influence of the fitness value and the number of iterations on the final result during the iteration process is distributed with different weights, ensuring the diversity and convergence of solutions. The calculation formula is as follows: in, This refers to the minimum value of the disturbance coefficient. It is the maximum value of the disturbance coefficient. These are the fitness values ​​of the three selected individuals, already sorted in order of superiority. It has the best fitness value. It has the worst fitness value. Indicates the current iteration number. This represents the total number of iterations, through which the diversity of the population can be increased.

2. The adaptive differential evolution algorithm for optimizing passive radar deployment according to claim 1, characterized in that, In step 1, the coordinates of the k-th target location that needs to be located are as follows: ， 。 3. The adaptive differential evolution algorithm for optimizing passive radar deployment according to claim 1, characterized in that, In step 2, each individual has a set of four observation stations positioned in a three-dimensional coordinate system, with a total of 12 components. To represent step 1 ; Since there are four observation stations, M=3 in step 1, where It refers to the first The three-dimensional coordinates of the first observation station of each individual, corresponding to the position in step 1. And so on. This corresponds to step 1. And so on, individuals The 12-dimensional components represent respectively The locations of these four observation stations, N individuals, refer to N sets of four observation station locations.

4. The adaptive differential evolution algorithm for optimizing passive radar deployment according to claim 1, characterized in that, In step 3 The calculation method is as follows: Given the site error variance and time difference error variance of the system, and based on the station deployment requirements, the communication distance between observation stations is set. With these three parameters determined, the fitness value for the current station deployment is calculated. Each individual obtained after population initialization Substitute into the fitness function The specific fitness value is obtained through calculation, where... The smaller the value, the smaller the average positioning error accuracy within the area, meaning the better the deployment effect in that target area. The calculation formula is as follows: ； After obtaining the initialized population and its fitness values, the next iteration process begins, which involves mutation, crossover, and selection of N individuals. The following discussion focuses on the population size after g iterations. .

5. The method for optimizing passive radar deployment using an adaptive differential evolution algorithm according to claim 1, characterized in that, The optimization method is applied in both dynamic and static cases; Dynamic Situation: In the field of radar countermeasures, when the enemy is known to be in a certain area, this algorithm can be used to demonstrate passive positioning and station deployment in that area. It can obtain better deployment results in advance, and then use aircraft or mobile carriers to carry passive equipment for deployment, saving battlefield resources. In addition, multi-aircraft deployment: This method plays a role in subsequent swarm deployment, not limited by the number of aircraft. It compares the positioning accuracy of aircraft with different combinations of numbers and selects the optimal deployment result. Static scenario: Used for setting up fixed base stations, deploying stations across a fixed key monitoring area to achieve good positioning accuracy over a large area.

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