Radar Signal Sorting Method Based on Dynamically Modified Chaotic Particle Swarm Optimization

Abstract

The present invention relates to a radar signal sorting method based on dynamically corrected chaotic particle swarm optimization, belonging to the technical fields of population evolution and signal classification. Aiming at the problems of large pulse stream density of radiation source signals and serious overlapping of characteristic parameters in a complex electromagnetic environment, a radar signal sorting method based on dynamically corrected chaotic particle swarm optimization is adopted to improve the defects that traditional clustering sorting algorithms are difficult to correctly classify and the optimization ability of particle swarm algorithms is insufficient. Chaotic search is used to increase the diversity of population iteration in the later stage; adaptively adjusted parameters are used to make the update of particles change in real time according to the state of the population; a new fitness function is used and the particle positions are dynamically corrected to make the optimization of the population more accurate. The method has great advantages over other optimization methods under several common and relatively new sorting indexes, and has better sorting effects in terms of convergence speed, stability and robustness, and can better adapt to complex electromagnetic environments.

Description

Technical Field

[0001] The present invention relates to a radar signal sorting method based on dynamically corrected chaotic particle swarm optimization, belonging to the technical fields of population evolution and signal classification. Background Art

[0002] With the increasing complexity of the electromagnetic environment, dense and variable radiation source signals enter the digital reconnaissance receiver and are intertwined into a complex pulse stream sequence. According to the characteristic parameters of the intercepted pulses, information such as the arrival time, etc., the pulse stream is sorted to accurately divide the signals belonging to the same radiation source, and then the radar model is identified according to the characteristic parameters of different radiation sources. According to the recognition results, the type, attributes, and threat level of each radar are obtained. From the above analysis, it can be seen that radiation source sorting is a key link in radar reconnaissance signal processing, which directly affects the performance of radar reconnaissance equipment and is related to subsequent combat decisions. Therefore, an efficient and accurate signal sorting method is extremely important.

[0003] Signal sorting techniques are mainly divided into two aspects: pulse repetition interval (PRI) analysis and feature clustering. Modern intercept systems often combine these two methods to achieve signal sorting. However, the widespread application of techniques such as PRI agility and low intercept has caused significant jitter and loss of the TOA of intercepted signals, thus destroying the statistical characteristics of the TOA difference. These reasons have greatly increased the sorting difficulty based on PRI analysis. Therefore, a clustering method based on radar characteristic parameters has emerged and has become an indispensable task for assisting the deinterleaving process of pulse signals.

[0004] Compared with traditional clustering sorting methods, the heuristic method is a group method that improves the sorting performance by finding the global optimum. However, although the PSO method provides the possibility of global search, it cannot guarantee convergence to the global optimum and also has disadvantages such as premature convergence and insufficient optimization ability. The main current trend to solve these problems is to increase the diversity of the population or fuse other methods, etc. For example, some scholars have proposed a method based on dynamic particle swarm optimization and K-means, which enhances the performance of the method by dynamically adjusting the inertia weight and acceleration coefficient. Some scholars improve the clustering centroid by changing the fitness function. However, they are not fully self-adaptive, and the clustering results cannot well meet the requirements of the radar system for signal sorting accuracy and real-time performance.

[0005] In order to accurately separate various radiation source signals from a dense, complex, and variable intercepted pulse stream, this application proposes a radar signal sorting method based on Dynamic Modified Chaotic Particle Swarm Optimization for Radar Signal Sorting (DMCPSO) to improve the deficiencies of difficult classification in traditional clustering sorting methods and PSO optimization, and to improve the sorting performance. The simulation results show that it has great advantages compared with several other improved particle swarm optimization methods under several common and relatively new sorting metrics, and its convergence speed, stability, and robustness also have better sorting effects. Summary of the Invention

[0006] The object of the present invention is to accurately separate various radiation source signals from a dense, complex, and variable intercepted pulse stream, improve the technical status quo of difficult correct classification in traditional clustering sorting methods and easy premature convergence and insufficient optimization ability of particle swarm optimization, and propose a radar signal sorting method based on dynamic modified chaotic particle swarm.

[0007] To achieve the above object, the present invention adopts the following technical solutions.

[0008] The radar signal sorting method includes the following steps:

[0009] Step 1: Preprocess the radar pulse PDW stream data, construct a radar data set, and generate revised data to be sorted.

[0010] Among them, preprocessing the radar pulse PDW stream data includes constructing a radar data set, collecting data to be sorted, and revising the data to be sorted.

[0011] Step 1 specifically includes the following sub-steps:

[0012] Step 1.1 Construct a radar data set;

[0013] Among them, the dimension of the constructed radar data set is D;

[0014] The radar data set includes generating different types of radar signals to form data to be sorted, recording the number of classes as M, and each type of radar signal is a group of PDW stream data;

[0015] Step 1.2 Collect data to be sorted from the radar data set constructed in Step 1.1, and record the total number of data to be sorted as S;

[0016] Step 1.3 Revise the data to be sorted, that is, change the different pulse signal data in the data to be sorted into the same scale range to generate the revised data to be sorted;

[0017] Among them, the maximum value of the data to be sorted is denoted as Mmax, and the minimum value of the data to be sorted is denoted as Mmin;

[0018] Step 2: Sort the radar signals and generate the clustering center of the sorted radar signals, that is, the sorted result. Specifically: Use the chaotic particle swarm optimization method based on dynamic correction to find the global optimal solution for the revised data to be sorted generated in Step 1.3. This global optimal solution is the clustering center of the sorted data, including the following sub-steps:

[0019] Step 2.1 Initialize the parameters of the particle swarm optimization method;

[0020] Among them, each parameter includes the population size, the maximum number of iterations, the particle velocity, the maximum movement velocity of the particle, and the historical highest fitness function value of the particle;

[0021] Among them, the population size is denoted as N, and the value range of N is from 10 to 20; the value range of the maximum number of iterations is from 50 to 200, denoted as Tmax; the particle velocity is an M×D×N-dimensional velocity matrix, and each element in this velocity matrix is a random number with a value in the range of 0 to 1, and the maximum value in this velocity matrix is between 0.5 and 1.0; the historical highest fitness function value of the particle is initialized to 0;

[0022] Step 2.2 Initialize the positions of the M×D-dimensional particles using the Maxmin distance principle to obtain the initial clustering center of the population, including the following sub-steps:

[0023] Step 2.2A Randomly select a sample from the constructed radar dataset as the first clustering center;

[0024] Step 2.2B Select the sample farthest from the first clustering center as the second clustering center;

[0025] Step 2.2C Select the point with the largest minimum distance from the first and the second clustering centers as the center point of the third initial cluster, and so on, until M initial cluster center points are selected and used as the initial clustering center of the population;

[0026] Step 2.3 Set the iteration loop variable t, and the initial loop variable is set to t = 1;

[0027] Among them, the iteration loop variable t represents the t-th moment;

[0028] Step 2.4 Calculate the clustering partition of the dataset at the t-th moment and calculate the particle positions. Specifically: Divide all samples in the dataset according to the principle of the minimum Euclidean distance from the particle positions, and calculate the average value of the samples in each cluster as the new particle positions according to the divided results;

[0029] Step 2.5 Calculate the fitness function value for each particle, specifically as follows:

[0030] Step 2.5A Calculate the sum of the distances between all data samples and their cluster centroids when there is only one cluster, denoted as E1;

[0031] Step 2.5B Calculate the sum of the within-cluster distances between samples and their cluster centroids, denoted as E;

[0032] Step 2.5C Calculate the maximum value of the distances between samples, denoted as D;

[0033] Step 2.5D Divide E1 by M, E, and D to obtain the fitness function value at time t;

[0034] Step 2.6 For each particle, based on the fitness function value at time t obtained in Step 2.5, compare the size of this fitness function value with the fitness function value of its optimal position at time t-1 that it has experienced. If it is better, that is, the fitness function value is larger, then update the optimal position of the particle, and correct the particle position according to the centroid index to obtain the corrected particle position; if the fitness function value at time t is not greater than the fitness function value at time t-1, then do not update the optimal position of the particle, and continue to maintain the optimal position experienced at the previous time, that is, time t-1;

[0035] Among them, correcting the particle position according to the centroid index includes the following sub-steps:

[0036] Step 2.6A Calculate the total sum of the distances between all sample points, denoted as d;

[0037] Step 2.6B Calculate the neighborhood radius of the sample, denoted as r, specifically: divide the total sum of distances d obtained in Step 2.6A by the a-th power of S and the a-th power of S-1;

[0038] Among them, the value range of a is from 0 to 1;

[0039] Step 2.6C Calculate the set of neighbors of the sample that are at a distance of r from it, that is, obtain the centroid index of each within-class sample;

[0040] Step 2.6D Compare the centroid index values of the within-class samples including the particle position, and select the one with the largest centroid index as the corrected particle position;

[0041] Step 2.6E Perform class separation within each clustering cluster, specifically: if the distance between two samples is greater than a certain threshold, denoted as g, and their centroid indices are among the top h, then use these two as new clustering centers, that is, new particle positions;

[0042] Among them, the value range of g is 2 to 4 times that of r, and the value range of h is 20% to 40%;

[0043] Step 2.6F merges all the clustering centers found in Step 2.6E, specifically: if the two closest clustering centers are merged, the new clustering center after merging is the mean of the two; repeat Step 2.6F until M clustering centers are reached, which is the corrected particle position.

[0044] Step 2.7 divides all the samples in the dataset according to the principle of the smallest Euclidean distance from the obtained corrected particle position.

[0045] Step 2.8 executes Step 2.5 to recalculate the fitness function value of each corrected particle.

[0046] Step 2.9 calculates the global optimal value gbest of the particle swarm at the current time t, specifically: selects the global optimal particle with the largest fitness function value, and its corresponding position is the global optimal value gbest.

[0047] Step 2.10 uses Tent chaos search to randomly perturb the particle positions, generates a chaos sequence, and generates new particles based on the generated chaos sequence, which specifically includes the following sub-steps:

[0048] Step 2.10A normalizes the global optimal value gbest obtained in Step 2.9 from the optimization variable value range [Mmin, Mmax] to the chaos variable value range [0, 1].

[0049] Step 2.10B performs J times of chaos perturbations on the global optimal value gbest to generate a chaos sequence, specifically: when the value of the chaos variable is less than y, the generated chaos sequence is twice the original chaos variable, and when the value of the chaos variable is greater than y, the generated chaos sequence is 2 minus twice the original chaos variable.

[0050] Step 2.10C generates new particles based on the generated chaos sequence, and the particle is equal to the global optimal value gbest plus k times the chaos variable, where the value of k ranges from 1% to 10%.

[0051] Step 2.11 calculates the fitness function value of the new particles generated based on the chaos sequence, and selects the chaos sequence with the largest fitness function value to replace the particle individuals in the current particle swarm whose individual optimal remains unchanged and is not the global optimal.

[0052] Step 2.12 updates the acceleration coefficients c1 and c2 of the particle swarm, specifically: calculates the ratio between the current iteration time t and the maximum iteration number Tmax, takes the inverse exponent of this ratio and performs a double operation to obtain the acceleration coefficient c1, and takes the exponent operation of this ratio to obtain the acceleration coefficient c2.

[0053] Step 2.13 Update the inertia weight w of the particle swarm, specifically: calculate the ratio of the fitness function value of the particle at the current time t to the global optimal fitness function value, and perform an inverse exponential operation on this ratio to obtain the inertia weight w;

[0054] Step 2.14 Update the velocity and position of the particle swarm to generate a new particle population; the update method is specifically as follows:

[0055] Step 2.14A Update the velocity of the particle swarm, specifically: add the inertia memory term, self-cognition term, and swarm cognition term of the particle;

[0056] Among them, the inertia memory term is obtained by multiplying the inertia weight w by the velocity of the particle at time t - 1; the self-cognition term is a vector calculated from the particle position point at time t - 1 pointing to the particle's own best position point pbest, and is multiplied by the acceleration coefficient and a random number within the range of 0 to 1; the swarm cognition term is a vector calculated from the particle position point at time t - 1 pointing to the best position point of the population, that is, the global optimal value gbest, and is multiplied by the acceleration coefficient and a random number within the range of 0 to 1;

[0057] Among them, if the updated velocity of the particle is greater than the maximum velocity of the particle obtained in Step 2.1, then the updated velocity at the current time t is taken as the maximum velocity value; if the updated velocity of the particle is less than the negative value of the maximum velocity of the particle obtained in Step 2.1, then the updated velocity at the current time t is taken as the negative value of the maximum velocity value;

[0058] Step 2.14B Update the position of the particle swarm. The update method is specifically: add the position of the particle at time t - 1 to the velocity of the particle at the current time t to obtain the position of the particle at time t; judge whether the position of the particle at this time t is greater than the maximum value Mmax of the position. If so, take the maximum value Mmax as the position of the particle at time t; otherwise, if the position of the particle at time t is less than the minimum value Mmin of the position, then take the minimum value Mmin as the position of the particle at time t;

[0059] Step 2.15 Calculate the variance of the population fitness function value;

[0060] Step 2.16 Judge whether the iteration termination condition is reached, specifically: compare whether the variance is less than a certain threshold v, or compare whether the time t is greater than the maximum number of iterations Tmax;

[0061] Among them, the value range of the threshold v is 0.2 to 0.8 times the fitness variance of the population at time t = 1;

[0062] If one or both of these two conditions are satisfied, the position of the particle at time t is taken as the clustering center for radar signal sorting; if neither of them is satisfied, update t: t = t + 1, and jump to step 2.4;

[0063] Step 3: Evaluate the clustering results obtained in step 2 based on evaluation metrics;

[0064] Among them, the evaluation metrics include clustering quality, adjusted Rand index, normalized mutual information, centroid index, Davies-Bouldin index, and silhouette index;

[0065] So far, from step 1 to step 3, the radar signal sorting method based on dynamically corrected chaotic particle swarm optimization is completed.

[0066] Beneficial effects

[0067] The radar signal sorting method based on dynamically corrected chaotic particle swarm optimization described in the present invention has the following beneficial effects compared with the existing large signal sorting methods:

[0068] 1. To address the problem that the population diversity is lost in the later stage of the particle swarm method iteration and it is easy to fall into local optimum, Tent chaotic search is added; and in view of the small cycle and unstable cycle point phenomena that are not conducive to optimization in Tent, the chaotic mapping is improved;

[0069] 2. To address the problem that the particle swarm method uses fixed parameters and cannot be adaptively adjusted, adaptive adjustment parameters (inertia weight and acceleration coefficient) related to the fitness value are used to sense the changes in the population in real time, so that the global search and local search capabilities of the particles are better combined;

[0070] 3. To address the problems of the fitness function form being single, containing less information, and being greatly affected by discrete points and feature distributions due to the particle swarm method only using internal distances for parameters, a new fitness function is proposed to improve the sorting accuracy;

[0071] 4. To address the problem that the particle swarm method is sensitive to discrete points and cannot accurately sort, the positions of the particles are adjusted through clustering analysis, and then the centroid index is introduced to make a final position correction for the particles that meet the conditions, making them closer to the true clustering center;

[0072] 5. The method has fewer parameters, does not require operations such as crossover and mutation, and has no internal and external loops, and the number of loops can be controlled within a small range; therefore, compared with other optimization methods, it has the advantages of fast convergence, fewer iteration times, and higher sorting recognition rate. Description of the drawings

[0073] Figure 1Schematic flow chart of the radar signal sorting method based on dynamically modified chaotic particle swarm optimization according to the present invention;

[0074] Figure 2 Spatial distribution diagram of radar parameters of the radar signal sorting method based on dynamically modified chaotic particle swarm optimization according to the present invention;

[0075] Figure 3 Signal sorting result of the radar signal sorting method based on dynamically modified chaotic particle swarm optimization according to the present invention;

[0076] Figure 4 Curve graph of fitness variance of different methods of the radar signal sorting method based on dynamically modified chaotic particle swarm optimization according to the present invention. Detailed implementation manners

[0077] To better illustrate the purpose and advantages of the present method, the specific implementation content of the present application will be further described in detail in combination with the accompanying drawings and specific embodiments.

[0078] Embodiment 1

[0079] Modern radar signal sorting methods increasingly emphasize joint sorting using multiple parameters. Generally, the more parameters are used, the higher the accuracy of the signal sorting result. Commonly used signal sorting parameters include pulse arrival angle DOA, pulse width PW, and pulse frequency RF. Due to the performance of radar receiver equipment and external environmental factors, measurement errors occur in radar pulse parameters. Therefore, the PDW stream data of the radar will vary within a certain range, resulting in different degrees of overlap in sorting parameters to a certain extent, which will reduce the accuracy of radar signal sorting.

[0080] This embodiment elaborates on the specific implementation of the radar signal sorting method based on dynamically modified chaotic particle swarm optimization described in the present application when sorting radar signals with overlapping parameters. The implementation flowchart of the present application is as Figure 1 shown.

[0081] The characteristic parameters of the radar, namely the pulse description word PDW, are composed of six parameters: pulse arrival angle DOA, pulse width PW, pulse frequency RF, pulse amplitude PA, pulse repetition frequency PRT, and pulse arrival time DOA. In this example, three characteristic parameters, DOA, PW, and RF, are used for radar signal sorting;

[0082] In this example, 8 groups of radar characteristic mixed sequences with different degrees of overlap in characteristic parameters generated by a PDW radar signal generator are used. The sorting parameters and signal forms are shown in Table 1 below:

[0083] Table 1 Constructed radar data

[0084]

[0085] When performing method processing, we select 1000 groups of radar pulse signals from the total generated PDW stream for signal sorting, and obtain parameters such as the final signal sorting running time and various sorting evaluation indicators. The distribution of signal parameters in three-dimensional space is shown in Figure 2 .

[0086] The radar signal sorting proposed in this application is divided into 2 steps, mainly including: the preprocessing of radar pulse PDW stream data and the radar signal sorting based on dynamically modified chaotic particle swarm, these two processes.

[0087] The specific implementation process of radar signal sorting is as follows:

[0088] Step 1: Perform data preprocessing on the radar pulse stream;

[0089] Step 1.1: Construct a radar data set;

[0090] Among them, this data set includes generating different types of radar signals to form the data to be sorted, and each type of radar signal is a group of PDW stream data; the dimension of the constructed radar data set is D, and the number of classes is M; each radar signal with different parameters represents a data sample;

[0091] Step 1.2: Collect the data to be sorted from the radar data set in Step 1.1; specifically: select S data samples from the generated mixed radar signal data set to form the radar data sample set to be sorted, and S takes the value of 1000;

[0092] Step 1.3: Make the different pulse signal data in the data to be sorted into the same scale range to generate the revised data to be sorted; the processing method is as follows:

[0093]

[0094] Among them, x represents each data sample; xmax represents the maximum value of the data sample to be sorted, and xmin represents the minimum value of the data sample to be sorted;

[0095] Step 2: Sort the radar signals and generate the sorted results, specifically: use the dynamically modified chaotic particle swarm optimization method to find the global optimal solution for the revised data to be sorted generated in Step 1.3, and this global optimal solution is the data clustering center after sorting; it includes the following sub-steps:

[0096] Step 2.1: Initialize the parameters of the particle swarm optimization method. Among them, the parameters include the population size, the maximum number of iterations, the particle velocity, the maximum movement velocity of the particle, and the historical highest fitness function value of the particle, specifically:

[0097] The number of the particle population is set to 10, i.e., N = 10; the maximum number of iterations of the particle is set to 50 times, i.e., Tmax = 50. The initial velocity of the particle is a matrix of M×D×N dimensions. M is determined by the number of classes of the dataset constructed in Step 1.1, and D is determined by the dimension of the dataset constructed in Step 1.1. Here, D is 3-dimensional, referring to the direction of arrival (DOA), pulse width (PW), and pulse carrier frequency (RF) respectively. Each element in the velocity matrix is a random number whose value is between the maximum and minimum values of the data samples obtained in Step 1.3; the maximum velocity of the particle is set to 0.8; the historical highest fitness function value of the particle is initialized to 0;

[0098] In Step 2.2, the particle position is initialized using the Maxmin distance principle. The particle position is M×D-dimensional and is divided into the following sub-steps;

[0099] In Step 2.2A, randomly select a sample from the constructed radar dataset as the first cluster center;

[0100] In Step 2.2B, select the sample farthest from the first cluster center as the second cluster center, where the distance is the Euclidean distance, and its calculation method is:

[0101]

[0102] where x and y represent different data samples, and n represents the dimension of the data samples;

[0103] In Step 2.2C, select the point with the largest minimum distance from the first and second cluster centers as the center point of the third initial cluster, and so on, until M initial cluster center points are selected and used as the initial cluster centers of the population;

[0104] In Step 2.3, set the iteration loop variable t, i.e., the t-th moment. The initial loop variable is set to t = 1;

[0105] In Step 2.4, calculate the clustering partition of the dataset at the t-th moment and calculate the particle position. Specifically: all samples in the dataset are partitioned according to the principle of the minimum Euclidean distance from the particle position, and the average value of the samples in each cluster is calculated as the new particle position according to the partition result;

[0106] In Step 2.5, calculate the fitness function value IPBM of each particle. Specifically: calculate the sum of the distances between all data samples and their cluster centroids in only one cluster, denoted as E1. Calculate the sum of the within-cluster distances between the samples and their cluster centroids, denoted as E. Calculate the maximum value of the distances between the samples, denoted as D. The calculation method of the fitness function value IPBM is as follows:

[0107]

[0108] Step 2.6 For each particle, according to the fitness function value of the particle at time t obtained in Step 2.5, compare this value with the fitness function value of the optimal position experienced by the particle at time t - 1. If it is better, that is, the fitness function value is larger, then update the position of the particle, and correct the position according to the barycenter index; if the fitness function value is not better than before, then do not update the optimal position of the particle, and continue to maintain the optimal position experienced at the previous moment, i.e., the optimal position experienced at time t - 1. Among them, the correction of the particle position according to the barycenter index is divided into the following sub-steps:

[0109] Step 2.6A Calculate the sum of the distances between all sample points, denoted as d;

[0110] Step 2.6B Calculate the neighborhood radius of the sample, denoted as r. Specifically: divide the total distance d obtained in Step 2.6A by the a-th power of S and the a-th power of S - 1, where the value of a is 0.3, and the calculation method is shown in formula (4);

[0111] Step 2.6C Calculate the set of neighbors of the sample that are at a distance r from it, that is, obtain the barycenter index GCI of each sample within the class. The calculation method is as follows:

[0112]

[0113] Step 2.6D Compare the barycenter indices of the samples within the class including the particle position, and select the one with the largest barycenter index as the corrected particle position;

[0114] Step 2.6E Separate the classes within each clustering cluster. Specifically: if the distance between two samples is greater than a certain threshold, denoted as g, and their barycenter indices are within the top h, then both of them can be used as new clustering centers, that is, new particle positions; where the value of g is 3r, and the value of h is 30%;

[0115] Step 2.6F Merge all the clustering centers found in Step 2.6E. Specifically: if the two closest clustering centers are merged, the new clustering center after merging is the average of the two, and so on until M clustering centers are reached, which is the corrected particle position;

[0116] Step 2.7 Divide all the samples in the dataset according to the principle of the smallest Euclidean distance from the obtained corrected particle position;

[0117] Step 2.8 Recalculate the fitness function value of the corrected particle according to Step 2.5;

[0118] Step 2.9 Calculate the global optimal value gbest of the particle swarm at the current time t. Specifically: select the global optimal particle with the largest fitness function value, and its corresponding position is the global optimal particle position;

[0119] Step 2.10 uses Tent chaos search to randomly perturb the particle positions, generate a chaos sequence, and generate new particles based on the generated chaos sequence. The specific steps are as follows:

[0120] Step 2.10A normalizes the current global optimal value gbest from the optimization variable value range [Mmin, Mmax] to the chaos variable Zn value range [0, 1];

[0121] Step 2.10B performs J times of chaos perturbation on the global optimal value to generate a chaos sequence. The calculation method is as follows:

[0122]

[0123] Step 2.10C generates a new particle according to the generated chaos sequence. This particle is equal to the global optimal value gbest plus k times the chaos variable, where the value of k is 0.05, that is, X = X gbest + k * z;

[0124] Step 2.11 calculates the fitness function value for the chaos sequence according to Step 2.5, and selects the chaos sequence with the largest fitness function value to replace the particle individual in the current particle swarm whose individual optimal remains unchanged and is not the global optimal;

[0125] Step 2.12 updates the acceleration coefficients c1 and c2 of the particle swarm. The calculation method is:

[0126]

[0127]

[0128] where t is the iteration number, that is, at time t, t max is the maximum iteration number;

[0129] Step 2.13 updates the inertia weight w of the particle swarm. Specifically: calculate the ratio of the fitness function value of the particle at the current time t to the global optimal fitness function value, and perform the inverse exponential operation on this ratio to obtain the inertia weight w;

[0130] Step 2.14 updates the velocity and position of the particle swarm to generate a new particle swarm; the update method is as follows:

[0131] Step 2.14A updates the velocity of the particle swarm. The update method is as follows:

[0132] V i (k + 1) = w * V i (k) + c1 * rand * (X pbest,i - X i ) + c2 * rand * (Xgbest,i -X i ) (7)

[0133] where X pbest and X gbest represent the better value of the k-th generation individual and the best value in the solution group respectively; c and w are the values of the acceleration coefficient and the inertia weight obtained in the above steps 2.12 and 2.13; rand represents a random number in the range of 0 - 1. The first part of this formula is the memory term, representing the influence of the previous velocity magnitude and direction; the second part is the self-cognition term, which is a vector pointing from the particle position at time t - 1 to the particle's own best position pbest, indicating the part of the particle's action derived from its own experience; the third part is the swarm-cognition term, which is a vector calculated by pointing from the particle position at time t - 1 to the best position of the population, i.e., the global optimal value gbest, reflecting the cooperation and knowledge sharing among particles;

[0134] where, if the updated velocity of the particle is greater than the maximum velocity of the particle obtained in step 2.1, then the updated velocity at the current time t is taken as the maximum velocity value; if the updated velocity of the particle is less than the negative value of the maximum velocity of the particle obtained in step 2.1, then the updated velocity at the current time t is taken as the negative value of the maximum velocity value;

[0135] Step 2.14B updates the positions of the particle swarm, and the update method is as follows:

[0136] X i (k + 1) = X i (k) + V i (k + 1) (8)

[0137] This formula indicates that the update of the particle's position at the current time t is related to the position at the previous time, i.e., t - 1, and the velocity at the current time t.

[0138] where, if the position of the particle is greater than the maximum value Mmax of the position, then the maximum value is taken as the position of the particle at time t; if the position of the particle is less than the minimum value Mmin of the position, then the minimum value is taken as the position of the particle at time t;

[0139] Step 2.15 calculates the variance of the population fitness function value;

[0140] Step 2.16 determines whether the iteration termination condition is reached. Specifically: compare whether the variance is less than a certain threshold, which is denoted as v, and the value of v is 0.6 times the fitness variance of the population at the first iteration; or compare whether t is greater than the maximum number of iterations Tmax.

[0141] If either of these two conditions is satisfied, the position of the particle is used as the clustering center for radar signal sorting; if neither is satisfied, update t: t = t + 1, and jump to step 2.4;

[0142] Step 3. Evaluate the clustering results obtained in step 2 based on evaluation metrics. For the dataset D = {x1, x2,..., x m}, assuming the cluster partition obtained by clustering is Ω = {ω1, ω2,..., ω K}, and the cluster partition given by the reference model is C = {c1, c2,..., c K}, where K is the number of clusters;

[0143] Among them, the evaluation metrics include clustering quality, adjusted Rand index, normalized mutual information, centroid index, Davies-Bouldin index, and silhouette index;

[0144] Step 3.1 Calculate the clustering quality CQ

[0145]

[0146] Among them, N i is the number of samples in ω i that belong to the category c i , which is also the measure of homogeneity. When ω i only contains samples from the same category, CQ = 1, which indicates that the larger the clustering quality index, the better the clustering effect and the higher the accuracy rate.

[0147] Step 3.2 Calculate the adjusted Rand index ARI;

[0148] Let λ, λ * represent the cluster label vectors corresponding to Ω and C respectively. Considering the samples in pairs, define

[0149] a = |SS|, SS = {(x i , x j ) | λ i = λ j , λ * i = λ * j , i < j},

[0150] b = |SD|, SD = {(x i , x j ) | λ i = λ j , λ * i ≠ λ * j , i < j},

[0151] c = |DS|, DS = {(x i , x j ) | λ i ≠ λ j , λ * i = λ * j , i < j},

[0152] d = |DD|, DD = {(x i , x j ) | λ i ≠ λ j , λ * i ≠ λ * j , i < j},

[0153]

[0154]

[0155] Among them, the value range of ARI is [-1, 1]. Generally speaking, ARI measures the degree of coincidence between two data distributions, and the larger the value, the more consistent the clustering result is with the real situation.

[0156] Step 3.3 Calculate the Normalized Mutual Information NMI

[0157] The calculation formula of the Normalized Mutual Information NMI is as follows:

[0158]

[0159]

[0160]

[0161] Among them, I represents the increase in the class information Ω or the reduction in its uncertainty under the premise of the given cluster information C. P(w k ), P(c j ), P(w k ∩ c j ) can be regarded as the probabilities that the sample belongs to the cluster w k , belongs to the class c j , and belongs to both at the same time. The larger the value, the higher the similarity with the real class information.

[0162] Step 3.4 Calculate the Centroid Index CI

[0163] The centroid index measures the difference between two classes through the cluster centroid and is calculated as follows:

[0164]

[0165]

[0166]

[0167] CI = max{CI(Ω, C), CI(C, Ω)} (12)

[0168] Among them, CI = 0 indicates that the two clusters have the same structure. The larger the value, the more the number of clusters is differently assigned, and the worse the clustering effect is.

[0169] Step 3.5 Calculate the Davies-Bouldin index DBI

[0170] This index considers the average ratio of compactness and separation in all clusters, and the calculation formula is as follows:

[0171]

[0172] Among them, e i and e j are the average Euclidean distances from all samples i and j to their respective centroids, and d i,j is the distance between the centroids. The smaller the DBI, the better the clustering effect.

[0173] Step 3.5 Calculate the silhouette index SI

[0174] This index is defined as:

[0175]

[0176] Among them, a(i) is the average Euclidean distance from sample i to the remaining samples in the same cluster; b(i) is the minimum average Euclidean distance between sample i and the samples in the remaining clusters. The higher the SI, the better the clustering scheme.

[0177] Step 4 To illustrate the effectiveness of the proposed method, several other improved particle swarm optimization methods are simulated for comparison, namely the PSO method, the DPSOK method, the MfPSO method, and the IPK-means method. The various clustering evaluation indexes involved in Step 3 are also calculated for these methods using the preprocessed data. In the experiment, the parameters involved include: the maximum number of iterations t max ; the population size P; the maximum particle velocity v max ; the inertia weight w; the acceleration coefficients c1 and c2; to ensure the effects of each method, according to the parameter descriptions and simulation experiments mentioned in the literature, the specific parameter settings for each method are shown in Table 1 below:

[0178] Table 2 Parameter settings

[0179]

[0180]

[0181] So far, from step 1 to step 4, the radar signal sorting method based on dynamic correction chaotic particle swarm optimization is completed.

[0182] Figure 3 This is a clustering result diagram obtained using the DMCPSO method, showing the impact of radar signal characteristics on sorting results under different overlaps. The points represent misclassified data.

[0183] To further demonstrate the superiority of the method, the iterative convergence time of different methods is analyzed, see Table 3, and the variation curve of fitness variance value with the number of iterations is plotted, see Figure 4 :

[0184] Table 3. Running time of the methods

[0185] PSO DPSOK MfPSO IPK-Means DMCPSO Running time / s 0.79 0.45 0.39 1.54 0.33

[0186] It can be seen from Table 3 that the DMCPSO method has the fastest convergence speed and the smallest stable variance value, which is significantly better than other methods, indicating that the group can always quickly find the optimal position during the iteration process and then converge to a satisfactory fitness value.

[0187] In order to further illustrate the effectiveness of the method, several clustering sorting indicators will be used to verify the method. The specific results are shown in Table 4:

[0188]

[0189] As shown in Table 4, although the K-means method is simple and converges quickly, its accuracy and matching degree are not as good as those of the PSO series methods, which shows that PSO can deal with complex radar data well. Compared with other latest improved PSO methods, the DMCPSO method has significant advantages in various indicators: the CQ value of the DMCPSO method reaches 94.99%, indicating that the clustering accuracy is the highest, the classified data is most inclined to the label data, and is almost not affected by the discrete data; the ARI value is the largest, indicating that the clustering result is more consistent with the actual situation, and the probability of correct decision is the highest; the NMI value is the largest, indicating that the uncertainty of the category information is lower, and the relationship between the classified data and the label data is closer; the CI drops to 0, indicating that there is a better match between the classified data and the label data, and the two have exactly the same structure; the SI is the largest, indicating that the cohesion and separation between the samples after clustering are both high; the DBI is the smallest, indicating that the intra-class distance is the smallest and the inter-class distance is the largest after clustering.

[0190] The above simulation results prove that, from all perspectives, under the radar simulation data with a high pulse overlap degree and a small number of partial pulses, the DMCPSO method achieves the best sorting effect.

[0191] Figure 2 FIG. 8 is a distribution diagram of the radar signal feature space constructed by the radar signal sorting method based on dynamic modified chaotic particle swarm optimization according to the present invention; the figure shows the feature distribution of radar pulse signals in a complex scenario from three dimensions of carrier frequency, arrival angle, and pulse width, and it can be seen that the signal features overlap significantly in space, and the traditional clustering method will not achieve good results.

[0192] Figure 3 FIG. 9 is a clustering result diagram of the radar signal sorting method based on dynamic modified chaotic particle swarm optimization according to the present invention; it can be seen from the figure that even for the 8-channel radar signal data with overlapping multi-parameter features in a complex background, the proposed method can still accurately cluster with excellent results.

[0193] Figure 4 FIG. 10 is a comparison diagram of the fitness variance convergence curves of the radar signal sorting method based on dynamic modified chaotic particle swarm optimization according to the present invention and other existing optimization clustering methods; it can be seen from the figure that as the number of iterations increases, the fitness variances of all methods decrease, and the change in the fitness value gradually decreases and tends to be stable. The methods search for the optimum by continuous convergence during the iteration process. However, the method proposed in this application has the fastest convergence speed and the smallest stable variance value, which is significantly better than other methods, indicating that the population can always quickly find the optimal position during the iteration process and then converge to a satisfactory fitness value.

[0194] The above are the preferred embodiments of the present invention, and the present invention should not be limited to the content disclosed in this embodiment and the drawings. Any equivalent or modified implementation completed without departing from the spirit disclosed by the present invention falls within the protection scope of the present invention.

Claims

1. A radar signal sorting method based on dynamically corrected chaotic particle swarm, characterized in that: It includes the following steps: Step 1: Preprocess the radar pulse PDW stream data, construct a radar data set, and generate revised data to be sorted. Step 1 specifically includes the following sub-steps: Step 1.1: Construct a radar data set. Among them, the dimension of the constructed radar data set is D. The types of radar signals in the radar data set in Step 1.1 are M types. Step 1.2: Collect the data to be sorted from the radar data set constructed in Step 1.1, and record the total number of data to be sorted as S. Step 1.3: Revise the data to be sorted, that is, change the different pulse signal data in the data to be sorted into the same scale range to generate the revised data to be sorted. Among them, the maximum value of the data to be sorted is denoted as Mmax, and the minimum value of the data to be sorted is denoted as Mmin. Step 2: Sort the radar signals and generate the clustering centers of the sorted radar signals, that is, the sorted results, including the following sub-steps: Step 2.1: Initialize the parameters of the particle swarm optimization method. Among them, the parameters include the population size, the maximum number of iterations, the particle velocity, the maximum movement velocity of the particle, and the historical highest fitness function value of the particle. Among them, the population size is denoted as N, and the value range of N is from 10 to 20; the value range of the maximum number of iterations is from 50 to 200, denoted as Tmax; the particle velocity is an M×D×N-dimensional velocity matrix, and each element in this velocity matrix is a random number with a value in the range of 0 to 1, and the maximum value in this velocity matrix is between 0.5 and 1.0; the historical highest fitness function value of the particle is initialized to 0. Step 2.2: Initialize the M×D-dimensional particle positions using the Maxmin distance principle to obtain the initial clustering centers of the population. Step 2.3: Set the iteration loop variable t, and the initial loop variable is set to t = 1. Among them, the iteration loop variable t represents the t-th moment. Step 2.4: Calculate the clustering partition of the data set at the t-th moment and calculate the particle positions, specifically: divide all the samples in the data set according to the principle of the minimum Euclidean distance from the particle positions, and calculate the average value of the samples in each cluster as the new particle position according to the divided results. Step 2.5: Calculate the fitness function value of each particle. Step 2.6: For each particle, according to the fitness function value obtained at the t-th moment in Step 2.5, compare the size of this fitness function value and the fitness function value of its optimal position at the t - 1 moment it has experienced. If it is better, that is, the fitness function value is larger, then update the optimal position of the particle, and correct the particle position according to the centroid index to obtain the corrected particle position; if the fitness function value at the t-th moment is not greater than the fitness function value at the t - 1 moment, then do not update the optimal position of the particle, and continue to maintain the optimal position experienced at the previous moment, that is, the t - 1 moment. Among them, correcting the particle position according to the centroid index includes the following sub-steps: Step 2.6A: Calculate the total distance sum between all sample points, denoted as d. Step 2.6B Calculate the neighborhood radius of the sample, denoted as r, specifically: Divide the total distance d obtained in Step 2.6A by the a-th power of S and the a-th power of S - 1; where the value range of a is from 0 to 1; Step 2.6C Calculate the set of neighbors of the sample that are at a distance r from it, that is, obtain the centroid index of each in-class sample; Step 2.6D Compare the centroid index values of the in-class samples including the particle positions, and select the one with the largest centroid index as the corrected particle position; Step 2.6E Separate classes within each clustering cluster, specifically: If the distance between two samples is greater than a certain threshold, denoted as g, and their centroid indices are within the top h, then use these two as new clustering centroids, that is, new particle positions; where the value range of g is 2 to 4 times that of r, and the value range of h is 20% to 40%; Step 2.6F Merge all the clustering centers found in Step 2.6E, specifically: If the two closest clustering centers are merged, the new clustering center after merging is the mean of the two; Repeat Step 2.6F until M clustering centers are reached, which are the corrected particle positions; Step 2.7 Divide all the samples in the dataset according to the principle of the minimum Euclidean distance from the obtained corrected particle positions; Step 2.8 Execute Step 2.5 to recalculate the fitness function value of each corrected particle; Step 2.9 Calculate the global optimal value gbest of the particle swarm at the current time t, specifically: Select the global optimal particle with the largest fitness function value, and its corresponding position is the global optimal value gbest; Step 2.10 Use Tent chaos search to randomly perturb the particle positions, generate a chaos sequence, and generate new particles based on the generated chaos sequence, specifically including the following sub-steps: Step 2.10A Normalize the global optimal value gbest obtained in Step 2.9 from the optimization variable value range [Mmin, Mmax] to the chaos variable value range [0, 1]; Step 2.10B Perform J times of chaos perturbation on the global optimal value gbest to generate a chaos sequence, specifically: When the value of the chaos variable is less than y, the generated chaos sequence is twice the original chaos variable, and when the value of the chaos variable is greater than y, the generated chaos sequence is 2 minus twice the original chaos variable; Step 2.10C Generate new particles according to the generated chaos sequence, and the particle is equal to the global optimal value gbest plus k times the chaos variable, where the value range of k is 1% to 10%; Step 2.11 Calculate the fitness function value of the new particles generated according to the chaos sequence according to Step 2.5, and select the chaos sequence with the largest fitness function value to replace the particle individuals in the current particle swarm whose individual optimal values remain unchanged and are not the global optimal; Step 2.12 Update the acceleration coefficients c1 and c2 of the particle swarm, specifically: Calculate the ratio between the current iteration time t and the maximum iteration number Tmax, take the inverse exponent of this ratio and perform a two-fold operation to obtain the acceleration coefficient c1, and take the exponent operation of this ratio to obtain the acceleration coefficient c2; Step 2.13 Update the inertia weight w of the particle swarm, specifically: calculate the ratio of the fitness function value of the particle at the current time t to the global optimal fitness function value, and perform an inverse exponential operation on this ratio to obtain the inertia weight w; Step 2.14 Update the velocity and position of the particle swarm to generate a new particle population; the update method is specifically as follows: Step 2.14A Update the velocity of the particle swarm, specifically: add the inertia memory term, self-cognition term, and swarm cognition term of the particle; Among them, the inertia memory term is obtained by multiplying the inertia weight w by the velocity of the particle at time t - 1; the self-cognition term is a vector calculated from the particle position point at time t - 1 pointing to the particle's own best position point pbest, and is multiplied by the acceleration coefficient c1 and a random number within the range of 0 to 1; the swarm cognition term is a vector calculated from the particle position point at time t - 1 pointing to the best position point of the population, that is, the global optimal value gbest, and is multiplied by the acceleration coefficient c2 and a random number within the range of 0 to 1; Among them, if the updated velocity of the particle is greater than the maximum velocity of the particle obtained in Step 2.1, the updated velocity at the current time t is taken as the maximum velocity value; if the updated velocity of the particle is less than the negative value of the maximum velocity of the particle obtained in Step 2.1, the updated velocity at the current time t is taken as the negative value of the maximum velocity value; Step 2.14B Update the position of the particle swarm. The update method is specifically: add the position of the particle at time t - 1 to the velocity of the particle at the current time t to obtain the position of the particle at time t; judge whether the position of the particle at this time t is greater than the maximum value Mmax of the position. If so, take the maximum value Mmax as the position of the particle at time t; otherwise, if the position of the particle at time t is less than the minimum value Mmin of the position, take the minimum value Mmin as the position of the particle at time t; Step 2.15 Calculate the variance of the population fitness function value; Step 2.16 Judge whether the iteration termination condition is reached, specifically: compare whether the variance is less than a certain threshold v, or compare whether the time t is greater than the maximum number of iterations Tmax; If one or both of these two conditions are satisfied, take the position of the particle at time t as the clustering center for radar signal sorting; if neither of them is satisfied, update t: t = t + 1, and jump to Step 2.4; Step 3. Evaluate the clustering results obtained in Step 2 based on evaluation indicators; Among them, the evaluation indicators include clustering quality, adjusted Rand index, normalized mutual information, centroid index, Davies-Bouldin index, and silhouette index.

2. The method for sorting radar signals based on dynamically corrected chaotic particle swarm according to claim 1, wherein: The radar data set in Step 1.1 includes generating different types of radar signals to form the data to be sorted, and each type of radar signal is a set of PDW stream data.

3. A method for sorting radar signals based on dynamically corrected chaotic particle swarm according to claim 2, characterized in that: Step 2 is specifically: use the chaotic particle swarm optimization method based on dynamic correction to find the global optimal solution for the revised data to be sorted generated in Step 1.3, and this global optimal solution is the clustering center of the sorted data.

4. A method for sorting radar signals based on dynamically corrected chaotic particle swarm according to claim 3, characterized in that: Step 2.2 includes the following sub-steps: Step 2.2A Randomly select a sample from the constructed radar data set as the first clustering center; Step 2.2B Select the sample farthest from the first cluster center as the second cluster center; Step 2.2C Select the point with the largest maximum distance to the first and the second cluster centers as the center point of the third initial cluster, and so on, until M initial cluster center points are selected and used as the initial cluster centers of the population.

5. A method for sorting radar signals based on dynamically corrected chaotic particle swarm according to claim 4, characterized in that: Step 2.5, specifically: Step 2.5A Calculate the sum of the distances between all data samples and their cluster centroids in only one cluster, denoted as E1; Step 2.5B Calculate the sum of the within-cluster distances between the samples and their cluster centroids, denoted as E; Step 2.5C Calculate the maximum value of the distances between the samples, denoted as D; Step 2.5D Divide E1 by M, E, and D, and the fitness function value at time t is obtained.

6. A method for sorting radar signals based on dynamically corrected chaotic particle swarm according to claim 5, characterized in that: In Step 2.16, the value range of the threshold v is 0.2 to 0.8 times the fitness variance of the population at time t = 1.

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