Adaptive Radar Signal Sorting and Cluster Optimization Method Based on Improved Density Peak Clustering

Abstract

The present invention discloses an adaptive radar signal sorting and cluster optimization method based on improved density peak clustering, including: processing the radar pulse sequence to obtain PDW samples, normalizing and constructing an Euclidean distance matrix, calculating the potential energy of each pulse signal, and eliminating false alarm pulses; obtaining new PDW samples and the Euclidean distance matrix; performing natural nearest neighbor search to determine the K-nearest neighbors, reverse nearest neighbors, natural nearest neighbors, and shared nearest neighbors of each pulse signal; calculating the local density and reachable distance, constructing a decision graph, and adaptively determining the initial radar cluster centers and the number thereof by using linear regression; starting from the initial radar cluster centers, constructing an assignment matrix, and sequentially determining the radar clusters to which the core pulse signals, non-core pulse signals, and remaining pulse signals belong; according to the nearest distances between the radar cluster centers and other radar clusters, distinguishing boundary points with the best radiation factor and the natural neighborhood set of the clusters and constructing multi-layer judgment conditions to realize radar cluster merging.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and particularly relates to an adaptive radar signal sorting and cluster optimization method based on improved density peak clustering. Background Art

[0002] Radar (Radio Detection and Ranging), which can be translated as "radio detection and ranging", that is, it detects target information in space by transmitting and receiving electromagnetic waves. It is an important equipment for obtaining information, precise guidance, control and command, and is widely used in equipment such as fighter jets, ships, aircraft carriers, etc. It is directly related to the information source and performance of the electronic reconnaissance system. Therefore, researching modern "clairvoyant" radar reconnaissance systems, realizing the detection, sorting, and identification of non-cooperative radar radiation sources, and avoiding interference and damage to one's own radar equipment are the basis for implementing electronic defense and electronic protection.

[0003] The basic composition of the radar reconnaissance system is as Figure 1 shown. The electronic reconnaissance system first processes the aliased signal, extracts parameter information, and obtains Pulse Description Word (PDW) information, including Direction of Arrival (DOA), Carrier Frequency (CF), PulseWidth (PW), Time of Arrival (TOA), and Pulse Amplitude (PA). Then, it analyzes the radar pulse description word, sorts out each radar signal from the interleaved pulse stream and conducts identification to obtain the model information of different radiation sources. Finally, it analyzes information such as the working mode and threat level of each radar radiation source according to the identification results. Therefore, radar signal sorting, as an important part of the reconnaissance system, is a necessary condition for the radar reconnaissance system to conduct parameter analysis and extraction, and is an important technical basis for subsequent radar identification and positioning. An efficient and reliable sorting result is the primary prerequisite for the successful completion of the above tasks. Only after successfully sorting out the signals of each radar from the highly overlapping pulse stream can the recognition algorithm be used to analyze the characteristic parameters and complete the recognition work. The schematic diagram of radar pulse sorting is as Figure 2 shown.

[0004] However, with the development of electronic technology, the widespread application of electromagnetic equipment such as new radars and technological innovation, the electromagnetic environment is becoming increasingly complex. On the one hand, the number of radiation sources has increased, the pulse flow density has increased, and the electromagnetic signals in space are of various types and densely distributed, resulting in frequent pulse false alarms and pulse losses, reduced signal parameter credibility, and reduced sorting accuracy, which poses a challenge to the existing radar radiation source sorting methods that rely on batch processing. On the other hand, radar signals are becoming increasingly complex and have a variety of modulation methods. A radar can switch between multiple modes in a short period of time, resulting in a serious "increase in batches" phenomenon, which poses a severe challenge to traditional radar reconnaissance systems that rely on a few stable characteristic parameters for sorting and identification. How to effectively solve the "increase in batches" problem has become a key issue that needs to be urgently solved in the field of radar reconnaissance technology.

[0005] The research on radar source signal sorting started in the 1970s, while the research by Chinese scholars started in the 1980s. The development of radar signal sorting mainly includes radar signal sorting based on inter-pulse modulation features, radar signal sorting based on intra-pulse modulation features, and radar signal sorting based on machine learning.

[0006] Sorting based on pulse-to-pulse modulation features mainly includes template matching method and pulse repetition interval (PRI) sorting method. The template matching method pre-establishes a database of the main characteristic parameters of the radar radiation source, and measures the PDW parameters of the received signal and compares them with the parameter information in the database, so as to sort pulses with the same or similar parameters. With the great enrichment of radar systems, this method has encountered a big bottleneck problem. The essence of sorting based on PRI is to use TOA information, analyze the TOA information of each pulse in the pulse stream, and try to dig out the PRI of each pulse sequence hidden under the TOA information. At present, with the continuous upgrading of radar signal modulation technology, the pulse density continues to increase. The method that relies solely on PRI sorting has been difficult to adapt to complex electromagnetic environments, and the processing performance has gradually declined.

[0007] The main research idea of sorting based on intra-pulse modulation features is to analyze the intercepted radar signals from the perspective of time-frequency domain or other transform domains, reduce the impact of noise on the features, and complete the sorting of overlapping pulse streams by mining intra-pulse modulation features with higher discrimination. At present, these methods have poor noise resistance on the one hand and cannot adapt to the complex electromagnetic environment with low signal-to-noise ratio. On the other hand, the methods are relatively scattered, with a wide variety but limited generalization, and often only have a certain degree of discrimination for certain specific modulation type signals, resulting in many features but few generalizable features.

[0008] Machine learning (ML) can obtain patterns from sample data and use these patterns to predict unknown data. More and more scholars have begun to attempt to implement the sorting of radar emitter signals within the framework of ML. The specific context and architecture are as Figure 3 shown, mainly including methods such as unsupervised clustering, neural network sorting, supervised classification models, and deep learning. However, except for unsupervised clustering, most supervised classification, neural network, and deep learning methods require certain prior knowledge and time for pre-training to achieve good results. In actual scenarios, the main focus is on the immediate reconnaissance of non-cooperative targets, lacking prior knowledge, which leads to a decrease in the performance of the algorithm. Summary of the Invention

[0009] To overcome the limitations of radar signal sorting methods in the above complex environment, solve the problems of pulse false alarms, pulse losses, low sorting accuracy, and serious increase in the number of radar emitters in the radar reconnaissance system, and considering the actual application environment of the system, the present invention proposes an adaptive radar signal sorting and cluster optimization method based on improved density peak clustering.

[0010] In view of this, the present invention proposes an adaptive radar signal sorting and cluster optimization method based on improved density peak clustering, including:

[0011] Step 1) Process the radar pulse sequence in the specified area received by the receiving station during the observation period to obtain PDW samples, perform data normalization, construct an Euclidean distance matrix, calculate the potential energy of each pulse signal using the data field, and eliminate false alarm pulses according to the potential energy normalization threshold;

[0012] Step 2) Eliminate the data corresponding to the false alarm pulses from the PDW samples and their Euclidean distance matrix in Step 1) to obtain new PDW samples and their Euclidean distance matrix;

[0013] Step 3) Perform a natural nearest neighbor search based on the new Euclidean distance matrix to determine the value of K in the K nearest neighbors, and then determine the K nearest neighbors, reverse nearest neighbors, natural nearest neighbors, and shared nearest neighbors of each pulse signal;

[0014] Step 4) Calculate the local density and reachable distance based on the results of the natural nearest neighbor search, construct a decision graph, and adaptively determine the initial radar cluster centers and the number of clusters using linear regression;

[0015] Step 5) Starting from the initial radar cluster centers, construct an assignment matrix, and sequentially determine the radar clusters to which the core pulse signals, non-core pulse signals, and remaining pulse signals belong until all pulse signals are sorted;

[0016] Step 6) According to the minimum distances between the cluster centers of each radar and the nearest cluster of other radars, use the optimal radiation factor and the natural neighborhood set of the cluster to distinguish boundary points and construct multi-level judgment conditions. If any two radar clusters meet the batch combination conditions, combine the corresponding radar clusters;

[0017] Step 7) Loop Step 6) until there are no clusters that meet the batch combination conditions.

[0018] Preferably, the PDW data in Step 1) includes: direction of arrival DOA, carrier frequency CF, pulse width PW, time of arrival TOA, and pulse amplitude PA.

[0019] Preferably, in Step 1), data normalization is performed, an Euclidean distance matrix is constructed, the potential energy of each pulse signal is calculated using the data field, and false alarm pulses are eliminated according to the potential energy normalization threshold; it includes:

[0020] Normalize the carrier frequency CF, pulse width PW, and direction of arrival DOA of each pulse respectively to obtain the corresponding normalized values cf i , pw i , doa i , so as to obtain the PDW sample pdw of each pulse after normalization i = {cf i , pw i , doa i}; where i represents the serial number of the PDW sample of the pulse after normalization, i = 1, 2,..., n, and n is the number of PDW samples of the radar pulse signals detected by the receiving station;

[0021] Calculate the Euclidean distance d(x i , x j ):

[0022] d(x i , x j ) = ||pdw i - pdw j ||2

[0023] where pdw j represents the PDW sample of the jth pulse after normalization, and i ≠ j;

[0024] Construct an Euclidean distance matrix based on the Euclidean distances between all pulse samples;

[0025] Use the minimum value of the potential energy entropy of the data field to determine the radiation factor, calculate the potential energy value of each pulse signal based on this radiation factor, and if the potential energy value corresponding to the pulse is lower than the set normalization threshold, identify it as a false alarm and eliminate the corresponding pulse signal.

[0026] Preferably, Step 2) includes:

[0027] After removing the false alarm pulses, the normalized PDW sample is pdw'. i ={cf' i ,pw i ',doa i '}, i = 1, 2,..., n', where i represents the serial number of the PDW sample after pulse normalization, i = 1, 2,..., n', and n' is the number of pulse samples after removing the false alarm pulses. For the new Euclidean distance matrix D, the element d'(x i ,x j ) represents the Euclidean distance between x i and x j after removing the false alarm pulses.

[0028] Preferably, step 3) includes:

[0029] Step 3-1): Let K be a positive integer and 1 ≤ K ≤ n', and let K increase starting from 1;

[0030] Step 3-2): Traverse and search for the K-nearest neighbors and K-inverse nearest neighbors of each sample point;

[0031] Step 3-3): If the natural neighborhood sets of the current samples are all non-empty sets, go to step 3-4); otherwise, further determine whether the natural nearest neighbors remain unchanged. If the determination is yes, go to step 3-4); if the determination is no, increase K by 1 and go to step 3-2);

[0032] Step 3-4): Take the current K value as the natural neighborhood eigenvalue.

[0033] Preferably, the K-nearest neighbors are: the K points with the closest Euclidean distances to other sample points x i that belong to the same radar pulse set X as the pulse signal sample point x i . The set size is K, and the other sample points are the K-nearest neighbors of x

[0034] The K-inverse nearest neighbors are: if the K-nearest neighbors of other sample points x j in the radar pulse set X contain the sample point x i , then x j belongs to the K-inverse nearest neighbors of x i ;

[0035] The natural nearest neighbors are: when the K-nearest neighbors of x i contain x j , and the K-nearest neighbors of x j also contain x i , then x i and x j are called natural nearest neighbors of each other.

[0036] Preferably, step 4) calculates the local density and reachable distance based on the results of natural neighbor search and constructs a decision graph, including:

[0037] Calculate the similarity Sim(x i ,x j ) between samples according to the shared neighborhood value:

[0038]

[0039] In the formula, |SNN(x i ,x j )| is the number of the shared neighborhood SNN(x i ,x j ) of the impulse samples x i ,x j ; d'(x i ,x p ), d'(x j ,x p ) are the distances from x i ,x j to the impulse sample x p in their shared neighborhood respectively; the shared neighbor SNN(x i ,x j ) is: Let KNN(x i ) be the K nearest neighbors of x i , and KNN(x j ) be the K nearest neighbors of x j . Then the shared neighbor of the sample points x i ,x j is the intersection of the two;

[0040] Calculate the local density of each impulse signal according to the similarity Sim(x i ,x j ) and the number of natural neighbors |NaN(x i |

[0041]

[0042] In the formula, L(i) is the set of the K samples with the largest similarity to the impulse sample x i in the impulse set X;

[0043] Obtain the reachable distance according to the following formula

[0044]

[0045] In the formula, C(i) is the local density greater than x ia set of pulse samples; D is the Euclidean distance matrix; max(D) is the maximum distance in the Euclidean distance matrix;

[0046] Normalize the local density and reachability distance respectively to obtain the normalized local density and reachability distance

[0047] Calculate the product of the local density and the reachability distance and sort them in descending order. Take γ = δ'×ρ' as the ordinate and the descending order of the γ values of the radar pulse samples as the abscissa to draw the candidate decision diagram for the cluster center. Here, γ represents the collection of the products of the local density and the reachability distance of each sample; Divide the reachability distance by the local density and sort them in descending order. Take clex = δ' / ρ' as the ordinate and the descending order of the clex values of the radar pulse samples as the abscissa to draw the decision diagram for eliminating the cluster center. Here, clex represents the collection of the division of the local density by the reachability distance of each sample.

[0048] Preferably, step 4) adaptively determines the initial radar cluster center and the number by linear regression, including:

[0049] Apply second-order logistic regression to fit the data on the decision diagram. Using a fixed value given by the abscissa index value, find the average value estimation interval of the ordinate γ and determine it as the confidence interval; Judge in turn according to the decreasing order of the γ values until the γ value of a certain sample is less than the upper bound of the confidence interval. Then the sample points before this are selected as the candidate radar cluster centers;

[0050] Apply second-order logistic regression to fit the data on the decision diagram. Using a fixed value given by the abscissa index value, find the specific value estimation interval of clex and determine it as the prediction interval; Judge in turn according to the decreasing order of the clex values until the clex of a certain sample is less than twice the upper bound of the prediction interval. Then the sample points before this are selected as the boundary points;

[0051] Remove the boundary points from the candidate radar cluster centers to obtain the initial radar cluster centers and determine the number.

[0052] Preferably, step 5) sorting and judging the core pulse signals includes:

[0053] Initialize the radar pulse as unassigned;

[0054] Set the radar cluster center set as the initial queue of the set to be visited;

[0055] Assign an independent cluster number to each radar cluster center;

[0056] Each iteration visits a sample x that has been assigned but not visited p , if x p 's K nearest neighbor x qMeet the following conditions:

[0057]

[0058] Wherein, is x q the cluster class to which it belongs. If it is equal to -1, it means unassigned. If x q is unassigned and is a natural neighbor of x p and at the same time the number of shared neighbors between x q and x p exceeds K / 2, then add x q to the end of the queue of the set to be visited, and at the same time assign x q to the cluster where x p is located; after setting x p to the visited state, visit the queue in turn, and continue the above process until the queue of the set to be visited is empty;

[0059] Allocating non-core pulse signals includes:

[0060] Construct an allocation matrix A, where the rows of the matrix represent the unallocated radar sample points, and the number of columns of the matrix is the numbers of all cluster classes;

[0061] Find the maximum value of the allocation matrix A, assign the sample i corresponding to the row index of the maximum value to the cluster j represented by the column corresponding to the maximum value, and at the same time update the matrix A. Repeat this process until the maximum value of the allocation matrix A is 0 or all samples are allocated and then stop;

[0062] The allocation of the remaining pulse signals includes:

[0063] If there are still unallocated pulse sample points at this time, sort the unallocated samples in descending order of local density, and allocate the unallocated samples to the clusters of their nearest high-density neighbors according to this order. Repeat this process until all pulse signals are sorted.

[0064] Preferably, step 6) includes:

[0065] Calculate the radiation factor σ' after eliminating pulse false alarms according to potential entropy;

[0066] Distinguish the overall boundary points according to the truncated kernel distance;

[0067] Calculate the nearest distance from the center of each radar cluster to other radar clusters;

[0068] When the nearest distance is less than twice the optimal radiation factor or less than the standard threshold, merge the two clusters, and the standard threshold is 0.1;

[0069] Distinguish the boundary points of each cluster according to the truncated kernel distance;

[0070] Remove boundary points and construct the natural neighborhood set between clusters;

[0071] Judge the cluster classes pairwise in sequence. If the number of the natural neighborhood set of two clusters is greater than 1, then merge the two cluster classes.

[0072] Compared with the prior art, the advantages of the present invention are as follows:

[0073] 1. The adaptive radar signal sorting and cluster class optimization method based on improved density peak clustering of the present invention is unsupervised in the overall process compared with the existing sorting methods, without prior data and pre-training, and without other parameter inputs except the PDW data of the pulse signals to be sorted. The clustering parameters, cluster centers and numbers, K nearest neighbors, etc. in the method are all adaptively generated for the dynamically changing PDW data, which can realize the autonomy of radar signal sorting and is more suitable for the actual application scenarios of radar reconnaissance systems.

[0074] 2. The present invention introduces the concept of data field, can eliminate false alarm pulses according to the potential energy standard, introduces natural neighborhoods and shared neighborhoods, making it applicable to scenarios with variable cluster shapes and uneven numbers between clusters. The invention optimizes and improves the allocation strategy, improving the accuracy of radar signal sorting.

[0075] 3. Aiming at the "batch increase" phenomenon existing in the existing sorting methods due to factors such as radar mode switching, the present invention constructs a progressive batch combination model to judge and optimize the radar cluster classes after preliminary sorting, effectively reducing the batch increase rate of radar signal sorting. Description of the Drawings

[0076] Figure 1 is a schematic diagram of the basic composition of a radar reconnaissance system;

[0077] Figure 2 is a schematic diagram of radar pulse sorting;

[0078] Figure 3 is a framework diagram of radar signal sorting based on machine learning;

[0079] Figure 4 is the variation law of potential entropy and radiation factor;

[0080] Figure 5 is a flow chart of natural neighborhood eigenvalue search;

[0081] Figure 6 is a candidate decision diagram for cluster centers;

[0082] Figure 7 is a decision diagram for cluster center elimination;

[0083] Figure 8 is a schematic diagram of linear regression of the candidate decision diagram;

[0084] Figure 9 It is a schematic diagram of linear regression with elimination decision diagram;

[0085] Figure 10 It is the core pulse signal distribution flow chart;

[0086] Figure 11 It is a flow chart of non-core pulse signal allocation;

[0087] Figure 12 It is a flow chart of the distribution of residual pulse signals;

[0088] Figure 13 It is a cluster optimization batch flow chart;

[0089] Figure 14 It is a flow chart of radar signal sorting and cluster optimization algorithm based on improved density peak clustering;

[0090] Figure 15 It is a three-dimensional diagram of simulated received PDW data;

[0091] Figure 16 It is a three-dimensional graph of the data after removing false alarm pulses. DETAILED DESCRIPTION

[0092] Based on the radar radiation source receiving station, the radar radiation source pulse signal in the designated reconnaissance area is intercepted and detected, and the received pulse signal is processed to obtain PDW data; the method includes:

[0093] Step 1) The receiving station processes the PDW data of the pulse signal, applies the potential energy entropy minimum value of the data field to the potential energy optimal radiation factor, and calculates the potential energy value of each pulse signal based on the radiation factor. If the potential energy value is less than the standardized threshold, it means that the corresponding pulse is an outlier relative to other pulse signals, and the pulse is marked as a false alarm and removed, and does not participate in subsequent processing.

[0094] Step 2) normalize the pulse signal PDW data after removing the false alarm pulses, and calculate the Euclidean distance matrix between the pulse signal PDWs.

[0095] Step 3) Perform a natural neighbor search on the data based on the Euclidean distance matrix to determine the value of K in the K nearest neighbors, and then determine the K nearest neighbors, inverse nearest neighbors, natural nearest neighbors and shared nearest neighbors of each pulse signal.

[0096] Step 4) Calculate the pulse local density and pulse reachable distance based on the shared neighbor similarity and the number of natural neighbors, construct a decision graph, and use linear regression to adaptively determine the appropriate initial cluster center and number.

[0097] Step 5) Pulse signal sorting: Starting from the initial cluster center, expanding with K-nearest neighbors, and using the fusion of natural neighbors and shared neighbors as the judgment condition, construct an allocation matrix, and use a three-step method to sequentially sort and judge the core pulse signals, non-core pulse signals, and the radar clusters to which the remaining pulse signals belong until all pulse signals are sorted.

[0098] Step 6) Based on the closest distance between the center of each radar cluster and other radar clusters, use the optimal radiation factor and the natural neighborhood set of the cluster to distinguish boundary points and construct multi-layer judgment conditions. If any two radar clusters meet the batch combination conditions, then combine the corresponding radar clusters.

[0099] Step 7) Loop Step 6 until there are no clusters that meet the batch combination conditions.

[0100] The technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings and embodiments.

[0101] Embodiment

[0102] The embodiment of the present invention provides an adaptive radar signal sorting and cluster optimization method based on improved density peak clustering, including the following steps:

[0103] 1. False alarm pulse rejection.

[0104] Suppose n pulse signals are respectively (x1, x2,..., x n ), X is the pulse signal set, apply the data field to calculate the potential value of each pulse signal, and compare it with the normalized threshold to reject false alarm pulses. To calculate the potential value of the pulse signal, first, it is also necessary to normalize the existing pulse PDW data and construct the Euclidean distance matrix. As shown in Equation (1), it is the formula for dimension-by-dimension normalization.

[0105]

[0106] In the formula, i = 1, 2,..., n, where n is the number of PDW samples of the radar pulse signals detected by the receiving station; CF i , PW i , DOA i are respectively the carrier frequency, pulse width, and direction of arrival before normalization of the i-th PDW data; min(CF), min(PW), min(DOA) are respectively the minimum values of the carrier frequency, pulse width, and direction of arrival among all pulse signals; similarly, max(CF), max(PW), max(DOA) are respectively the maximum values of the carrier frequency, pulse width, and direction of arrival among all pulse signals; pdw i ={cf i , pw i , doa i} is the normalized PDW sample.

[0107] Calculate the Euclidean distance between PDW data objects:

[0108] d(x i , x j ) = ||pdw i - pdw j ||2 (2)

[0109] The Euclidean distance matrix is constructed by calculating the distances between all data objects. This matrix is a symmetric matrix (the Euclidean distance from data point x j to data point x i and the Euclidean distance from data point x i to data point x j are equal).

[0110] After completing the above operations, the calculation of the potential energy of the data field can be carried out. The concept of "field" was initially used to describe the force between material objects. Inspired by the idea of field theory, Academician Li Deyi introduced physical forces into the field of data processing and creatively proposed the concept of data field. This theory holds that the state value of each data object is the accumulation of the forces of all other data objects in the field, and the forces and action ranges between all data objects construct the data field. The value of the field strength function is large where data objects are dense, and small where data objects are sparse. Generally, the Gaussian function is used to describe the force of data objects. The field strength function describing the force between data points x and y is:

[0111]

[0112] In the formula, ρ is the weight of the data point, and the parameter value is set to 1; d(x, y) is the Euclidean distance between data objects x and y; σ is the radiation factor variable that measures the action ability of data objects.

[0113] The potential function is the scalar sum of the field strength functions received by data objects. Then, the sum of the field strength functions received by data object y is expressed as:

[0114]

[0115] In the formula, Ψ y is the potential energy value of data object y.

[0116] The value of the radiation factor σ is crucial for the potential energy value. In order to obtain the optimal radiation factor, the concept of entropy, which describes the uncertainty of the distribution between data, is used. Generally, the entropy that expresses the uncertainty between data objects in the data field is expressed by potential entropy, and it is used to optimize and select σ. Let the potential values of n data objects be Ψ1, Ψ2,…, Ψ n ,, then the calculation formula for the corresponding potential entropy is:

[0117]

[0118] In the formula, is the normalization factor, and the relationship between the potential entropy of the data object and the radiation factor is as Figure 4 shown. When σ approaches zero, the potential energy of each point to other points approaches zero, and the potential energy of each point is approximately equal to the influence of its own potential energy on itself, that is, 1. At this time, the potential entropy approaches log(n). When σ continues to increase, the potential energy of each point to other points gradually increases, the potential entropy function gradually decreases, and the uncertainty also gradually decreases until it reaches the lowest point. At this time, the distribution of the data object is basically arranged in an orderly manner, and the uncertainty reaches the minimum. When the value of σ increases again, the potential values of each point in the data field gradually approach equality, and the potential energy entropy converges to log(n). Therefore, selecting the optimal radiation factor is to select the minimum value of the potential entropy, that is:

[0119]

[0120] Analyze the effective radiation range of the data field of the data pulse points, calculate the potential energy values of each radar pulse sample using the optimal radiation factor, and consider the influence of the pulse signal on its own potential energy. If the potential value is close to the standard value of 1, it is basically a false alarm pulse. Identify and remove the corresponding pulse signals. Let the number of pulse signals at this time be n', and the pulse set be X = {x1, x2, …, x n'}. At the same time, save the one-to-one correspondence between the current radar sequence and the original radar sequence.

[0121] 2. Pulse data fractal dimension normalization

[0122] After removing the false alarm pulses, it is still necessary to perform fractal dimension normalization processing on the retained pulse signal PDW data. At this time, there is no need to recalculate the normalization value according to formula (1). Just use the one-to-one correspondence between the current sequence and the original sequence to obtain pdw' i = {cf' i , pw i ', doa i '}, the difference is that at this time i = 1, 2,..., n', where n' is the number of pulse samples after removing the false alarm pulses.

[0123] 3. Construct the Euclidean distance matrix

[0124] Similar to the data normalization method, there is no need to recalculate the Euclidean distance matrix according to formula (2) again. Just retain the corresponding indexes of the current sequence in the original Euclidean distance matrix and remove the false alarm pulse indexes at the same time. This Euclidean distance matrix is represented by D, and d'(x i , x j ) represents the Euclidean distance between x i and x j after removing the false alarm pulses.The Euclidean distance. It can be seen that false alarm pulse detection does not increase the algorithm complexity except for potential value calculation.

[0125] 4. Determination of K nearest neighbors

[0126] The original input parameter of density peak clustering is the distance cutoff factor d c (Cutoff-distance). For different data sets, different sizes need to be set according to experience. In practice, the value at the 1% to 2% position of the overall similarity of the data set is usually selected. This parameter setting method is subjective to a large extent and cannot achieve the optimal parameter setting for different data sets. On the other hand, even if the optimal setting is achieved, it is more inclined to the optimality of the overall distribution of pulse signals and cannot take into account the local characteristics of each pulse signal, inevitably resulting in problems such as missed batches, additional batches, and signal sorting errors. Therefore, the present invention introduces the concept of K nearest neighbors, and calculates subsequent eigenvalue and completes sorting based on its extended neighbors and numbers. The following gives the definitions of K nearest neighbors, K inverse nearest neighbors, natural neighbors, shared neighbors, and natural neighbor search methods:

[0127] Definition 1: K nearest neighbors: The K points with the closest Euclidean distance to the pulse signal sample point x i among other sample points belonging to the radar pulse set X, the set size is K, and the expression of the K nearest neighbors of x i is as follows:

[0128]

[0129] Definition 2: K inverse nearest neighbors: If the K nearest neighbors of other sample points x j in the pulse set X contain the sample point x i , then x j belongs to the K inverse nearest neighbors of x i , and the K inverse nearest neighbors of x i are the set of K nearest neighbors in the pulse set X that contain x i , the set size is uncertain, and the expression is as follows:

[0130]

[0131] Definition 3: Natural neighbors: When the K nearest neighbors of x i contain x j , and the K nearest neighbors of x j also contain x i , then it is said that x i and x j are natural neighbors to each other, and the expression is as follows:

[0132] NaN(x i ) = {x j ∈X / {x i}|x i∈KNN(x j ),x i ∈RKNN(x j )} (9)

[0133] Definition 4: Shared Nearest Neighbor: Let KNN(x i ) be the K nearest neighbors of x i , and KNN(x j ) be the K nearest neighbors of x j . Then the shared nearest neighbor of the sample points x i , x j is the intersection of the two, and the expression is as follows:

[0134] SNN(x i ,x j ) = KNN(x i ) ∩ KNN(x j ) (10)

[0135] Definition 5: Natural Nearest Neighbor Search Method: Let K be a positive integer, and 1 ≤ K ≤ n'. Let K increase starting from 1, and search for the K nearest neighbors and K reverse nearest neighbors of each pulse sample point until the intersection of the K nearest neighbors and K reverse nearest neighbors of each pulse is not an empty set, that is, each pulse signal has a natural nearest neighbor. On the basis of the current K value, increase it by 1, and select this value as the natural neighborhood eigenvalue, that is, the value of K. The expression is as follows:

[0136]

[0137] In the formula, KNN K (x j ), KNN K (x i ) are the K nearest neighbors of x j , x i respectively under the current K value. At the same time, if the natural neighborhood value of the pulse signal remains unchanged as the K value increases, stop increasing the K value and use the current value as the natural neighborhood eigenvalue. The specific search process is as Figure 5 shown.

[0138] 5. Calculate the local density and reachable distance. Calculate the similarity between samples with the help of the shared neighborhood value:

[0139]

[0140] In the formula, |SNN(x i ,x j )| is the number of shared neighborhoods of the pulse signals x i , x j ; d'(x i ,x p ), d'(x j ,xp ) are the sample x i , x j to the distance of the sample x p in the shared neighborhood of the two. It should be noted that the similarity needs to be calculated only when the shared neighbors between two pulses are not an empty set, otherwise the similarity is 0.

[0141] Next, according to the similarity and the number of natural neighborhoods, the local density of each pulse signal can be calculated, and the calculation method is as follows:

[0142]

[0143] In the formula, L(i) is the set of the K samples with the largest similarity to the pulse sample x i in the pulse set X; |NaN(x i )| is the number of the natural neighborhood of x i . At the same time, the reachable distance represents the Euclidean distance between the pulse sample point x i and its nearest point where the local density is greater than this pulse sample point x i . If there is no sample point with a local density greater than the pulse sample point x i , then the maximum distance in the Euclidean distance matrix is taken as the reachable distance of x

[0144]

[0145] In the formula, C(i) is the set of pulse samples with a local density greater than x i ; D is the Euclidean distance matrix; max(D) is the maximum distance in the Euclidean distance matrix.

[0146] Normalize the local density and the Euclidean distance respectively, as shown in the following formula:

[0147]

[0148] In the formula, min(δ) and max(δ) are the minimum and maximum values of the reachable distances of all pulse sample points respectively; min(ρ) and max(ρ) are the minimum and maximum values of the local densities of all pulse sample points respectively.

[0149] As Figure 6 shown, calculate the product of the local density and the reachable distance and sort them in descending order. Take γ = δ'×ρ' as the ordinate and the descending order of the γ values of the radar pulse samples as the abscissa to draw the cluster center candidate decision diagram, where γ represents the set of the products of the local density and the reachable distance of each sample. Similarly, as Figure 7As shown, the reachable distance is divided by the local density and arranged in descending order. Taking clex = δ' / ρ' as the ordinate and the descending order of the clex values of the radar pulse samples as the abscissa, a decision diagram for eliminating cluster centers is plotted, where clex represents the collection of the division of the local density of each sample by the reachable distance.

[0150] 6. Determination of the initial radar cluster center.

[0151] According to the definitions of the local density and reachable distance of the radar signal, the maximum density peak of the radar sample set has the maximum reachable distance at the same time, so it is the highest point of the decision diagram; the boundary points have a small local density but a large reachable distance; the local center points have a large local density and a large reachable distance. The reachable distances of the remaining non-center points are very low, and the local density distribution is relatively uniform. Therefore, in the candidate decision diagram for clusters, most of the pulse signal distributions show a linear relationship, and the discrete points that do not satisfy linear regression can be regarded as candidate radar cluster centers.

[0152] Logistic regression is a generalized linear model, and second-order logistic regression is applied to fit the data on the decision diagram. As Figure 8 shown, the red dotted line represents the confidence interval, which quantifies the uncertainty when estimating the population parameters of the γ sample set, that is, using a fixed value given by the abscissa index value to find the average value estimation interval of the ordinate γ; while the blue dotted line represents the prediction interval, which quantifies the uncertainty of predicting a single observed value, that is, using a fixed value given by the abscissa index value to find the estimation interval of an individual specific value of the ordinate γ. To avoid the occurrence of missed batches, the confidence interval closer to the original data is selected as the judgment condition, and the judgment is made in turn according to the decreasing order of the γ values until the γ value of a certain sample is less than the upper bound of the confidence interval. The sample points before this are selected as candidate radar cluster centers.

[0153] At this time, the candidate radar cluster centers include the maximum density peak point, the local center, and the boundary points. It is necessary to eliminate the boundary points according to the decision diagram for eliminating cluster centers. Since the boundary points have a large reachable distance and a small local density, the value clex obtained by dividing the two will be very large. The distributions of the remaining points can be regarded as showing a linear relationship. Second-order logistic regression is also applied to fit the data on the decision diagram, as Figure 9 shown. Since the clex differences of different types of points will be very large, it is more appropriate to select a prediction interval with a larger range as the judgment condition. The judgment is made in turn according to the decreasing order of the clex values until the clex of a certain sample is less than twice the upper bound of the prediction interval. The sample points before this are selected as boundary points.

[0154] The radar cluster center is the intersection of the candidate radar cluster center set and the boundary points removed, and the expression is as follows:

[0155] Icl = Cand - (Cand ∩ Holo) (16)

[0156] Wherein, Cand is the set of candidate radar cluster class centers, and Holo is the set of boundary points.

[0157] 7. Pulse signal sorting strategy.

[0158] The three-step allocation strategy of the present invention allocates core pulse signals in the first step, non-core pulse signals in the second step, and remaining pulse signals in the third step. The main allocation strategies are as follows:

[0159] Allocation strategy 1: Allocation of core pulse signals

[0160] Initialize all radar pulse signals to the unallocated state, set the initial set of samples to be visited as the selected set of radar cluster class centers, and at the same time assign an independent cluster class number to each cluster class center. Each iteration visits a sample x that has been allocated but not visited p , if x p 's K nearest neighbors x q meet the following conditions:

[0161]

[0162] Wherein, is the cluster class to which x q belongs, and being equal to -1 indicates unallocated. That is, the above condition is that x q is unallocated and is a natural neighbor of x p , and at the same time the number of shared neighbors between x q and x p exceeds K / 2, then add x q to the tail of the queue of the set of samples to be visited, and at the same time allocate x q to the cluster where x p is located. Set x p to the visited state and then visit the queue in sequence, and continue the above process until the queue of the set of samples to be visited is empty. The specific process is as Figure 10 shown.

[0163] Allocation strategy 2: Allocation of non-core pulse signals

[0164] Construct an allocation matrix A. The rows of the matrix represent the unallocated radar sample points, and the number of columns of the matrix is the current set of all cluster class numbers. A(i,j) represents the number of neighbors with cluster class label j among the neighbors of the i-th unallocated radar sample point. Each iteration finds the maximum value in the allocation matrix, and allocates the sample i corresponding to the row index of the maximum value to the cluster j represented by the column corresponding to the maximum value. At the same time, update the matrix A. At this time, only need to update the corresponding sample values of the reverse neighbors of the radar sample i. Repeat the above process until the maximum value of the allocation matrix A is 0 or all samples are allocated, then stop. The specific process is as Figure 11 shown.

[0165] Allocation Strategy 3: Allocation of Remaining Pulse Signals

[0166] If there are still unallocated pulse sample points at this time, according to the nearest neighbor principle, the unallocated samples are sorted in descending order of local density, and the unallocated samples are allocated to the cluster of the nearest high-density neighbor according to this order. Repeat this step until all pulse signals are sorted. The specific process is as Figure 12 shown.

[0167] 8. Radar Cluster Batching

[0168] The batching strategy is mainly divided into two steps. The batching process is as Figure 13 shown, and the batching strategy is as follows:

[0169] The first step is more targeted at the overall cluster merging. Calculate the radiation factor σ' after removing pulse false alarms based on potential entropy. Analyze the potential energy formula (4), and combine the density peak clustering original density truncation kernel calculation method. Taking σ' as the truncation radius, calculate the truncation kernel density of the samples as shown in the following formula:

[0170]

[0171] In the formula, the parameter σ' is the truncation radius; in the pulse set X, the number of samples within the truncation radius of the sample x i is the truncation kernel density of the sample x i .

[0172] Distinguish boundary points according to the truncation kernel density. If the truncation kernel density satisfies the following formula:

[0173]

[0174] then mark it as a boundary point. Let N0(X) be the set of boundary points, and C1 i be the i-th radar cluster set after removing boundary points. Calculate the nearest distance from the center of each cluster except boundary points to other clusters as shown in the following formula:

[0175] Dist_min(m,h) = min{d'(icl(m)),x j )|x j ∈C1 h} (20)

[0176] In the formula, Dist_min(m,h) represents the nearest distance from the center of the m-th cluster to the h-th radar cluster; icl(m) is the center of the m-th cluster; C1 h is the h-th radar cluster set after removing boundary points.

[0177] Dist_min(m,h) < min{2σ', 0.1} (21)

[0178] When the distance between the two is less than twice the optimal radiation factor or less than the standard threshold (since the data has been normalized, the distance is also a normalized distance), it is determined that the two cluster classes can be merged. In one embodiment, the standard threshold is 0.1. The first step of batch merging focuses more on the overall distribution of pulses. If no cluster classes are merged in this step, the second step of merging is directly skipped.

[0179] The second step focuses more on the process of merging the radar cluster itself with other clusters and does not consider the overall cluster distribution. The radiation factor is applied to re-determine the boundary points. The difference is that the boundary point threshold for each cluster class is different, as shown in the following formula:

[0180]

[0181] In the formula, j represents the j-th cluster class, C j represents the set of radar samples of the j-th cluster class, and Num j represents the number of radar samples contained in the j-th cluster class. Let C2 i be the set of the i-th radar cluster class after removing the boundary points at this time. After removing the boundary points, the NaN sets between clusters are constructed in sequence, that is, the union of the natural neighborhoods of all pulses in C2 i is obtained as NaN_C2 i ; the union of the natural neighborhoods of all pulses in C2 j is obtained as NaN_C2 j ; the intersection of NaN_C2 i and NaN_C2 j is the NaN set of cluster i and cluster j.

[0182] The cluster classes are judged pairwise in sequence. If the number of the NaN set of the two clusters is greater than 1, it is determined that the two need to be merged.

[0183] Simulation example:

[0184] The results of the present invention can be verified by the following simulation data:

[0185] Fifteen radar radiation sources are set, and their radiation source parameters are shown in Table 1. To simulate a real scenario, the radars in each cluster are similar in some dimensions and the number of pulses is uneven. The present invention takes into account the PDW parameter estimation error and noise. Based on the parameters of each cluster of radars, Gaussian noise with a mean equal to the value of the PW parameter and a standard deviation of 5 μs is added to the PW parameter; Gaussian noise with a mean equal to the value of the DOA parameter and a standard deviation of 3° is added to the DOA parameter; the CF has various modulation methods such as pulse group agility and pulse-to-pulse agility, and at the same time Gaussian noise with a mean equal to the value of the CF parameter and a standard deviation of 20 MHz is added; the PRI has modulation methods such as staggering, sine, and jitter. According to the parameter information provided in Table 1, radar pulse description word PDW data received by the receiving station is generated. Here, taking a 200-ms pulse sequence as an example, 5% of the pulses in the sequence are randomly lost, and 0% - 30% of the pulses are false alarms.

[0186] Table 1 Radar Radiation Source Positions and Parameters

[0187]

[0188] On the one hand, by means of the adjusted mutual information (AMI), adjusted Rand index (ARI), and FMI (Fowlkes-Mallows Index) adjusted by the external evaluation index of clustering, the sorting performance of the present invention is judged by comparing the gap between the sorting result and the true value. The results of the effectiveness evaluation of the above indexes are all in [0, 1], and the larger the value, the higher the sorting performance; on the other hand, the radar signal pulse sorting correct rate PA, batch increase rate PF, and batch leakage rate PM are used to further verify the actual sorting effect of the method of the present invention. The calculation methods are as follows:

[0189]

[0190] The three-dimensional distribution of the generated PDW data is as Figure 15 shown. After being processed by the false alarm pulse elimination method, the three-dimensional distribution of the obtained PDW is as Figure 16 shown. It can be seen that the isolated false alarm pulses are basically eliminated, which is beneficial to subsequent processing. The specific sorting results of the example are shown in Table 2.

[0191] Table 2 Sorting Results of Simulation Examples

[0192]

[0193] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

Claims

1. An adaptive radar signal sorting and cluster optimization method based on improved density peak clustering, comprising: Step 1) Process the radar pulse sequence in the specified area received by the receiving station during the observation period to obtain PDW samples, perform data normalization, construct an Euclidean distance matrix, calculate the potential energy of each pulse signal using the data field, and eliminate false alarm pulses according to the potential energy normalization threshold; Step 2) Eliminate the data corresponding to the false alarm pulses from the PDW samples and their Euclidean distance matrix in Step 1) to obtain a new PDW and its Euclidean distance matrix; Step 3) Perform a natural nearest neighbor search based on the new Euclidean distance matrix to determine the value of K in the K nearest neighbors, and then determine the K nearest neighbors, reverse nearest neighbors, natural nearest neighbors, and shared nearest neighbors of each pulse signal; Step 4) Calculate the local density and reachable distance based on the results of the natural nearest neighbor search, construct a decision graph, and adaptively determine the initial radar cluster centers and the number using linear regression; Step 5) Starting from the initial radar cluster centers, construct an assignment matrix, and sequentially determine the radar clusters to which the core pulse signals, non-core pulse signals, and remaining pulse signals belong until all pulse signals are sorted; Step 6) Based on the nearest distances between the centers of each radar cluster and other radar clusters, distinguish boundary points with the best radiation factor and the natural neighborhood set of the cluster and construct multi-layer judgment conditions. If any two radar clusters meet the batch combination conditions, combine the corresponding radar clusters; Step 7) Loop Step 6) until there are no clusters that meet the batch combination conditions.

2. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 1, characterized in that The PDW data in Step 1) includes: direction of arrival DOA, carrier frequency CF, pulse width PW, time of arrival TOA, and pulse amplitude PA.

3. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 1, characterized in that In Step 1), data normalization is performed, an Euclidean distance matrix is constructed, the potential energy of each pulse signal is calculated using the data field, and false alarm pulses are eliminated according to the potential energy normalization threshold, including: Normalize the carrier frequency CF, pulse width PW, and direction of arrival DOA for each pulse respectively to obtain the corresponding normalized values cf i , pw i , doa i , thereby obtaining the PDW sample pdw after normalization for each pulse i = {cf i , pw i , doa i}; where i represents the serial number of the PDW sample after pulse normalization, i = 1, 2,..., n, and n is the number of PDW samples of the radar pulse signal detected by the receiving station; Calculate the Euclidean distance d(x i , x j ) between every two pulse samples x i , x j ): d(x i ,x j )=||pdw i -pdw j ||2 where pdw j represents the normalized PDW sample of the j-th pulse, and i ≠ j; Construct an Euclidean distance matrix based on the Euclidean distances between all pulse samples; Determine the radiation factor using the minimum value of the potential energy entropy of the data field, calculate the potential energy value of each pulse signal based on this radiation factor, and if the potential energy value corresponding to the pulse is lower than the set normalization threshold, identify it as a false alarm and eliminate the corresponding pulse signal.

4. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 1, wherein Step 2) includes: After eliminating false alarm pulses, the normalized PDW sample is pdw'. i ={cf' i ,pw i ',doa i '}, where i represents the serial number of the PDW sample after pulse normalization, i = 1, 2,..., n', n' is the number of pulse samples after eliminating false alarm pulses, and the new Euclidean distance matrix D, where the element d'(x i ,x j ) represents the Euclidean distance between x i and x j after eliminating false alarm pulses.

5. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 4, characterized in that Step 3) includes: Step 3-1) Let K be a positive integer, and 1 ≤ K ≤ n', and let K start increasing from 1; Step 3-2) Traverse and search for the K nearest neighbors and K reverse nearest neighbors of each sample point; Step 3-3) If the natural neighborhood sets of the current samples are all non-empty sets, go to Step 3-4); otherwise, further determine whether the natural nearest neighbors remain unchanged. If the determination is yes, go to Step 3-4); if the determination is no, add 1 to K and go to Step 3-2); Step 3-4) Take the current K value as the natural neighborhood eigenvalue.

6. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 5, characterized in that The K nearest neighbors are: the pulse signal sample point x i and the K points with the closest Euclidean distance to other sample points that also belong to the radar pulse set X. The size of the set is K, and the other sample points are x i which are the K nearest neighbors; The K reverse nearest neighbor is defined as follows: if the K nearest neighbors of other sample points x in the radar pulse set X j include the sample point x i , then x j belongs to the K reverse nearest neighbor of x i ; The natural neighbor is defined as follows: when x i is included in the K-nearest neighbors of x j , and the K-nearest neighbors of x j simultaneously include x i , then x i and x j are called natural neighbors of each other.

7. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 1, characterized in that In Step 4), the local density and reachable distance are calculated based on the results of the natural nearest neighbor search, and a decision graph is constructed, including: Calculate the similarity Sim(x i , x j ) between samples based on the shared neighborhood values: wherein, |SNN(x i ,x j )| is the number of the shared neighborhood SNN(x i ,x j ) of the pulse samples x i ,x j ; d'(x i ,x p ), d'(x j ,x p ) are respectively the distances from x i , x j to the pulse sample x p in their shared neighborhood; the shared nearest neighbor SNN(x i ,x j ) is as follows: Let KNN(x i ) be the K nearest neighbors of x i , and KNN(x j ) be the K nearest neighbors of x j , then the shared nearest neighbor of the sample points x i , x j is the intersection of the two; According to the similarity Sim(x i , x j ) and the number of natural neighbors |NaN(x i )|, calculate the local density of each pulse signal where L(i) is the set of K samples in the pulse set X that have the greatest similarity to the pulse sample x i with the greatest similarity The reachable distance is obtained according to the following formula where C(i) is the set of pulse samples with local density greater than x i ; D is the Euclidean distance matrix; max(D) is the maximum distance in the Euclidean distance matrix; Normalize the local density and the reachability distance respectively to obtain the normalized local density and the reachability distance Calculate the product of the local density and the reachability distance and sort them in descending order. Using γ = δ'×ρ' as the ordinate and the descending order of the γ values of the radar pulse samples as the abscissa, plot the candidate decision diagram for the cluster center, where γ represents the collection of the products of the local density and the reachability distance of each sample; divide the reachability distance by the local density and sort them in descending order. Using clex = δ' / ρ' as the ordinate and the descending order of the clex values of the radar pulse samples as the abscissa, plot the decision diagram for eliminating the cluster center, where clex represents the collection of the division of the local density by the reachability distance of each sample.

8. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 7, characterized in that The step 4) adaptively determines the initial radar cluster center and the number by using linear regression, including: Apply second-order logistic regression to fit the data on the decision diagram. Using a fixed value given by the abscissa index value, find the average value estimation interval of the ordinate γ and determine it as the confidence interval; sequentially judge according to the decreasing order of the γ values until the γ value of a certain sample is less than the upper bound of the confidence interval, then the sample points before this are selected as the candidate radar cluster centers; Apply second-order logistic regression to fit the data on the decision diagram. Using a fixed value given by the abscissa index value, find the estimation interval of the specific clex value and determine it as the prediction interval; sequentially judge according to the decreasing order of the clex values until the clex of a certain sample is less than twice the upper bound of the prediction interval, then the sample points before this are selected as the boundary points; Obtain the initial radar cluster center by removing the boundary points from the candidate radar cluster centers and determine the number.

9. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 8, wherein The step 5) for sorting and judging the core pulse signals includes: Initialize the radar pulses as unassigned; Set the radar cluster center set as the initial queue of the set to be visited; Assign an independent cluster number to each radar cluster center; Access a sample x that has been assigned but not visited in each iteration p , if x p 's K nearest neighbors x q meet the following conditions: Wherein, is x q the cluster it belongs to. If it equals -1, it means it is unassigned. If x q is unassigned and is a natural neighbor of x p , and at the same time the number of shared neighbors between x q and x p exceeds K / 2, then add x q to the end of the queue of the set to be visited, and at the same time assign x q to the cluster where x p is located; after setting x p to the visited state, visit the queue in sequence, and continue the above process until the queue of the set to be visited is empty; The assignment of non-core pulse signals includes: Construct the assignment matrix A, where the rows of the matrix represent the unassigned radar sample points and the number of columns of the matrix is all the cluster numbers; Find the maximum value of the assignment matrix A, assign the row index sample i corresponding to the maximum value to the cluster j represented by the column corresponding to the maximum value, and update the matrix A at the same time. Repeat this process until the maximum value of the assignment matrix A is 0 or all samples are assigned and then stop; The assignment of the remaining pulse signals includes: If there are still unassigned pulse sample points at this time, sort the unassigned samples in descending order according to the local density, and assign the unassigned samples to the cluster of their nearest high-density neighbors according to this descending order. Repeat this process until all pulse signals are sorted.

10. The adaptive radar signal sorting and cluster optimization method based on improved density peak clustering according to claim 9, characterized in that, The step 6) includes: Calculate the radiation factor σ' after eliminating the pulse false alarms according to the potential entropy; Distinguish the overall boundary points according to the truncated core distance; Calculate the nearest distance from each radar cluster center to other radar clusters; When the nearest distance is less than twice the optimal radiation factor or less than the standard threshold, merge the two clusters, and the standard threshold is 0.1; Distinguish the boundary points of each cluster according to the truncated core distance; Eliminate the boundary points and construct the collection of the natural neighborhoods between clusters; Judge the clusters pairwise in turn. If the number of the collection of the natural neighborhoods of the two clusters is greater than 1, merge the two clusters.

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