Adaptive radar signal sorting and clustering optimization method based on improved density peak clustering

Abstract

The invention discloses a self-adaptive radar signal sorting and clustering optimization method based on improved density peak clustering. The method comprises the following steps: processing a radar pulse sequence to obtain a PDW sample, normalizing and constructing an Euclidean distance matrix, calculating potential energy of each pulse signal, and eliminating false alarm pulses; obtaining a new PDW sample and a Euclidean distance matrix; performing natural neighbor search, and determining K neighbor, inverse neighbor, natural neighbor and shared neighbor of each pulse signal; calculating a local density and a reachable distance, constructing a decision diagram, and adaptively determining an initial radar cluster center and number by using linear regression; constructing a distribution matrix by taking the center of the initial radar cluster as a starting point, and sequentially judging radar clusters to which core pulse signals, non-core pulse signals and residual pulse signals belong; and according to the nearest distance between the center of each radar cluster and other radar clusters, boundary points are distinguished by the optimal radiation factor and the cluster natural neighborhood set, and multi-layer judgment conditions are constructed, so that radar cluster merging is realized.

Description

Technical Field

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

[0002] Radar (Radio Detection and Ranging, Radar), which can be translated as "radio detection and ranging", is an important equipment for obtaining information, precise guidance, control and command by emitting and receiving electromagnetic waves. It is widely used in fighters, ships, aircraft carriers and other equipment. It is directly related to the information source and performance of the electronic reconnaissance system. Therefore, studying the modern "Clairvoyance" radar reconnaissance system to detect, sort and identify the radar radiation sources of non-cooperative parties and avoid interference and damage to one's own radar equipment is the basis for implementing electronic defense and electronic protection.

[0003] The basic components of radar reconnaissance system are as follows: Figure 1 As shown. The electronic reconnaissance system first processes the aliased signal, extracts parameter information, and obtains the pulse description word (PDW) information, including direction of arrival (DOA), carrier frequency (CF), pulse width (PulseWidth, PW), time of arrival (TOA) and pulse amplitude (Pulse Amplitude, PA). Then, the radar pulse description word is analyzed, and each radar signal is sorted out and identified from the interlaced pulse stream to obtain the model information of different radiation sources. Finally, the working mode, threat level and other information of each radar radiation source are analyzed based on 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 perform parameter analysis and extraction, and is an important technical basis for subsequent radar identification and positioning. Efficient and reliable sorting results are the primary prerequisite for the successful completion of the above tasks. Only after the signal of each radar is successfully sorted out from the highly overlapping pulse stream can the recognition algorithm be used to analyze the characteristic parameters and complete the identification work. The radar pulse sorting diagram is shown in the figure below. 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 them to predict unknown data. More and more scholars have begun to try to sort radar radiation source signals under the framework of ML. The specific framework is as follows: Figure 3 As shown in the figure, it mainly includes unsupervised clustering, neural network sorting, supervised classification model, deep learning and other methods. 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. The actual scene is mainly for real-time reconnaissance of non-cooperative targets, and the lack of prior knowledge leads to reduced algorithm performance. Summary of the invention

[0009] In order to overcome the limitations of radar signal sorting methods in the above-mentioned complex environment, solve the problems of pulse false alarm, pulse loss, low sorting accuracy, and serious increase in radar radiation sources in radar reconnaissance systems, and at the same time consider the actual application environment of the system, the present invention proposes an adaptive radar signal sorting and clustering optimization method based on improved density peak clustering.

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

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

[0012] Step 2) removing data corresponding to 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 natural 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, inverse 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 natural neighbor search, construct a decision graph, and use linear regression to adaptively determine the initial radar cluster center and number;

[0015] Step 5) Starting from the initial radar cluster center, a distribution matrix is ​​constructed to 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) Based on the shortest distance between the center of each radar cluster and other radar clusters, the boundary points are distinguished by the optimal radiation factor and the cluster natural neighborhood set, and multi-layer judgment conditions are constructed. If any two radar clusters meet the batch merging conditions, the corresponding radar clusters are merged;

[0017] Step 7) loops through step 6) until there are no clusters that meet the batch merging conditions.

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

[0019] Preferably, the step 1) performs data normalization, constructs a Euclidean distance matrix, applies the data field to calculate the potential energy of each pulse signal, and eliminates false alarm pulses according to a potential energy normalization threshold; comprising:

[0020] The carrier frequency CF, pulse width PW and direction of arrival DOA of each pulse are normalized respectively to obtain the corresponding normalized value cf i ,pw i ,doa i , so as to obtain the normalized PDW sample pdw for each pulse i ={cf i ,pw i ,doa i}; where i represents the PDW sample number 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;

[0021] Calculate the Euclidean distance d(x) between each two pulse samples i ,x j ):

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

[0023] Among them, pdw j represents the normalized PDW sample of the jth pulse, and i≠j;

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

[0025] The radiation factor is determined by using the minimum value of the potential energy entropy of the data field. The potential energy value of each pulse signal is calculated based on the radiation factor. If the potential energy value corresponding to the pulse is lower than the set standardized threshold, it is identified as a false alarm and the corresponding pulse signal is eliminated.

[0026] Preferably, the step 2) comprises:

[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 PDW sample number after pulse normalization, i = 1, 2, ..., n', n' is the number of pulse samples after removing false alarm pulses, and the new Euclidean distance matrix D, in which the element d'(x i ,x j ) represents the value x after removing false alarm pulses i With x j The Euclidean distance.

[0028] Preferably, the step 3) comprises:

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

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

[0031] Step 3-3) If the natural neighbor sets of the current sample are not empty sets, go to step 3-4); otherwise, further determine whether the natural neighbors remain unchanged. If yes, go to step 3-4; if no, add 1 to K and go to step 3-2);

[0032] Step 3-4) Use the current K value as the natural neighborhood feature value.

[0033] Preferably, the K nearest neighbors are: pulse signal sample point x i The K points with the closest Euclidean distance to other sample points belonging to the radar pulse set X, the set size is K, and the other sample points are x i K nearest neighbors;

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

[0035] The natural neighbor is: i The K nearest neighbors of x j , x j The K nearest neighbors of x i , then x i With x j They are natural neighbors.

[0036] Preferably, the step 4) calculates the local density and the reachable distance according to the result of the natural nearest neighbor search and constructs a decision graph, including:

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

[0038]

[0039] In the formula, |SNN(x i ,x j )| is the pulse sample x i , x j Shared Neighborhood SNN(x i ,x j ) number; d'(x i ,x p ),d'(x j ,x p ) are x i , x j To the pulse sample x in the shared neighborhood of both p The shared neighbor SNN (x i ,x j ) is: Let KNN(x i ) is x i K nearest neighbor, KNN(x j ) is x j The K nearest neighbors of the sample point x i , x j The shared neighbors of are the intersection of the two;

[0040] 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

[0041]

[0042] Where L(i) is the pulse set X and the pulse sample x i The collection of K samples with the greatest similarity;

[0043] The reachable distance is obtained according to the following formula

[0044]

[0045] Where C(i) is the local density greater than x iThe pulse sample set; D is the Euclidean distance matrix; max(D) is the maximum distance in the Euclidean distance matrix;

[0046] Normalize the local density and reachable distance respectively to get the normalized local density And reachable distance

[0047] The product of local density and reachable distance is calculated and arranged in descending order. γ = δ' × ρ' is used as the ordinate and the order of γ values ​​of radar pulse samples in descending order is used as the abscissa to draw the cluster center candidate decision diagram, where γ represents the set of local density and reachable distance product of each sample; the reachable distance is divided by local density and arranged in descending order. clex = δ' / ρ' is used as the ordinate and the order of clex values ​​of radar pulse samples in descending order is used as the abscissa to draw the cluster center elimination decision diagram, where clex represents the set of local density and reachable distance divided by each sample.

[0048] Preferably, the step 4) uses linear regression to adaptively determine the initial radar cluster centers and numbers, including:

[0049] Apply second-order logistic regression to fit the data on the decision diagram, and use a fixed value given by the horizontal axis index value to find the average value estimation interval of the vertical axis γ, which is determined as the confidence interval; judge in descending order of γ values ​​until the γ value of a certain sample is less than the upper limit of the confidence interval, then the sample points before this are selected as candidate radar cluster centers;

[0050] Apply second-order logistic regression to fit the data on the decision diagram, and use a fixed value given by the horizontal axis index value to find the estimated interval of the specific value of clex and determine it as the prediction interval; judge in descending order of clex values ​​until the clex of a sample is less than twice the upper limit of the prediction interval, and the sample points before this are selected as boundary points;

[0051] The initial radar cluster centers are obtained by removing the boundary points from the candidate radar cluster centers, and the number is determined.

[0052] Preferably, the step 5) of sorting and determining the core pulse signal comprises:

[0053] Initialize radar pulse to unassigned state;

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

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

[0056] Each iteration visits a sample x that has been allocated but not visited. p , if x p The K nearest neighbors x qThe following conditions must be met:

[0057]

[0058] In the formula, For x q The cluster type, if equal to -1, it means it is not assigned, if x q Unassigned and x p is a natural neighbor, and x q With x p If the number of shared neighbors exceeds K / 2, then x q Add to the tail of the queue of the collection to be visited, and at the same time q Assign to x p The cluster in which it is located; set x p After the state is visited, the queue is visited in sequence, and the above process is continued until the queue of the set to be visited is empty;

[0059] Distributing non-core pulse signals includes:

[0060] Construct an allocation matrix A, where the rows of the matrix represent the unassigned radar sample points and the columns of the matrix represent all the cluster class numbers;

[0061] Find the maximum value of the allocation 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 allocation matrix A is 0 or all samples have been assigned.

[0062] The remaining pulse signal allocation includes:

[0063] If there are still unassigned pulse sample points at this time, the unassigned samples are sorted in descending order according to local density, and the unassigned samples are assigned to the cluster of the nearest high-density neighbor according to this order. The process is repeated until all pulse signals are sorted.

[0064] Preferably, the step 6) comprises:

[0065] The radiation factor σ' after eliminating pulse false alarm is calculated based on the potential energy entropy;

[0066] The overall boundary points are distinguished based on the cutoff kernel distance;

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

[0068] When the closest distance is less than twice the optimal radiation factor or less than a standard threshold, two clusters are merged, and the standard threshold is 0.1;

[0069] Distinguish the boundary points of each cluster based on the cutoff kernel distance;

[0070] Eliminate boundary points and construct a natural neighborhood set between clusters;

[0071] The clusters are judged in pairs in turn. If the number of natural neighbor sets of two clusters is greater than 1, the two clusters are merged.

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

[0073] 1. An adaptive radar signal sorting and clustering optimization method based on improved density peak clustering of the present invention is unsupervised in the overall process compared to the existing sorting method, and does not require prior data and pre-training. Except for the pulse signal PDW data to be sorted, no other parameter input is required. The clustering parameters, cluster centers and numbers, K nearest neighbors, etc. in the method are all adaptively generated for dynamically changing PDW data, which can realize the autonomy of radar signal sorting and is more suitable for the real 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 neighborhood and shared neighborhood, so that it is suitable for scenarios with variable cluster shapes and uneven number of clusters. The invention optimizes and improves the allocation strategy and improves the accuracy of radar signal sorting.

[0075] 3. In view of the "increased batch" phenomenon in the existing sorting methods due to factors such as radar mode switching, the present invention constructs a progressive batching model to optimize the radar clustering judgment after preliminary sorting, effectively reducing the increased batch rate of radar signal sorting. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0078] Figure 3 This is a diagram of the radar signal sorting context architecture based on machine learning;

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

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

[0081] Figure 6 is the cluster center candidate decision graph;

[0082] Figure 7 It is the cluster center elimination decision diagram;

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

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

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

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

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

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

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

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

[0091] Fig.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, integrating natural neighbors and shared neighbors as judgment conditions, constructing an allocation matrix, and sorting and judging the radar clusters to which the core pulse signals, non-core pulse signals and remaining pulse signals belong in three steps until all pulse signals are sorted.

[0098] Step 6) Based on the shortest distance between the center of each radar cluster and other radar clusters, the boundary points are distinguished by the optimal radiation factor and the cluster natural neighborhood set and multi-layer judgment conditions are constructed. If any two radar clusters meet the batch merging conditions, the corresponding radar clusters are merged.

[0099] Step 7) loops through step 6) until there are no clusters that meet the batch merging conditions.

[0100] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0101] Example

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

[0103] 1. False alarm pulse elimination.

[0104] Assume that n pulse signals are (x1, x2, ..., x n ), X is the pulse signal set, the data field is used to calculate the potential value of each pulse signal, and compared with the standardized threshold to eliminate false alarm pulses. In order to calculate the potential value of the pulse signal, it is also necessary to normalize the existing pulse PDW data and construct the Euclidean distance matrix, as shown in formula (1), which is the dimension normalization formula.

[0105]

[0106] Where i = 1, 2, ..., n, where n is the number of PDW samples of the radar pulse signal detected by the receiving station; CF i ,PW i ,DOA i are the carrier frequency, pulse width and direction of arrival of the i-th PDW data before normalization; min(CF), min(PW), min(DOA) are the minimum values ​​of carrier frequency, pulse width and direction of arrival of all pulse signals; similarly, max(CF), max(PW), max(DOA) are the maximum values ​​of carrier frequency, pulse width and direction of arrival of 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 distance between all data objects. The matrix is ​​a symmetric matrix (data point x j To data point x i and data point x i To data point x j The Euclidean distance is equal).

[0110] After completing the above operations, the data field potential energy calculation can be performed. The concept of "field" was originally used to describe the forces 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 believes 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 ranges of action between all data objects construct the data field. The field strength function value is large where the data objects are dense, and the field strength function value is small where the data objects are sparse. Generally, a Gaussian function is used to describe the forces of data objects. The field strength function describes the forces between data objects at points x and y as:

[0111]

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

[0113] The potential function is the scalar sum of the field strength functions that describe the data object. The sum of the field strength functions that the data object y is subjected to is expressed as:

[0114]

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

[0116] The value of the radiation factor σ is very critical to the potential energy value. In order to obtain the optimal radiation factor, the concept of entropy that describes the uncertainty of data distribution is used. Generally, the entropy that describes the uncertainty between data objects in the data field is expressed by potential entropy, which is used to optimize the selection of σ. Suppose the potential values ​​of n data objects are Ψ1, Ψ2, …, Ψ n , then the corresponding potential entropy calculation formula is:

[0117]

[0118] In the formula, is the normalization factor. The relationship between the potential entropy of the data object and the radiation factor is as follows: Figure 4 As 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 its own potential energy influence 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 gradually decreases until it reaches the lowest point. At this time, the distribution of data objects is basically arranged in order, and the uncertainty is minimized. When the value of σ increases again, the potential value of each point in the data field gradually approaches the same, and the potential 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 point, apply the optimal radiation factor to calculate the potential energy value of each radar pulse sample, consider the impact of the pulse signal on its own potential energy, and the potential value close to the standard value 1 is basically a false alarm pulse. The corresponding pulse signal is marked and removed. Suppose the number of pulse signals at this time is n', and the pulse set is X = {x1, x2, ..., x n'}. At the same time, the one-to-one correspondence between the current radar sequence and the original radar sequence is saved.

[0121] 2. Pulse data fractal normalization

[0122] After removing the false alarm pulses, it is still necessary to perform dimension normalization processing on the retained pulse signal PDW data. At this time, there is no need to recalculate the normalized value according to formula (1). It is only necessary to apply 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 now i = 1, 2, ..., n', where n' is the number of pulse samples after removing false alarm pulses.

[0123] 3. Constructing the Euclidean distance matrix

[0124] Similar to the data normalization method, the Euclidean distance matrix does not need to be calculated again according to formula (2). It only needs to retain the corresponding index of the current sequence in the original Euclidean distance matrix and remove the false alarm pulse index. The Euclidean distance matrix is ​​represented by D, d'(x i ,x j ) represents the value x after removing the false alarm pulses i With x jIt can be seen that false alarm pulse detection does not increase the complexity of the algorithm except for the calculation of potential energy value.

[0125] 4. K nearest neighbors determination

[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 based on experience. In practice, the value at the 1% to 2% position of the overall similarity of the data set is usually selected. On the one hand, this parameter setting method is more subjective and cannot achieve the optimal parameter setting for different data sets; on the other hand, even if the optimal setting is achieved, it tends to be more optimal for the overall distribution of pulse signals and cannot take into account the local characteristics of each pulse signal. It is inevitable that there will be problems such as missed batches, additional batches, and signal sorting errors. Therefore, the present invention introduces the concept of K nearest neighbors, calculates subsequent eigenvalues ​​based on its extended neighbors and number, and completes the sorting. The following defines K nearest neighbors, K inverse neighbors, natural neighbors, shared neighbors, and natural neighbor search methods:

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

[0128]

[0129] Definition 2: K inverse neighbors: If the other sample points x of the pulse set X j The K nearest neighbors include the sample point x i , then x j Belong to x i K inverse neighbors of x i The K inverse neighbors of the pulse set X include x i The collection size is uncertain and the expression is as follows:

[0130]

[0131] Definition 3: Natural neighbor: When x i The K nearest neighbors of x j , x j The K nearest neighbors of x i , then x i With x j They are natural neighbors, 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 Neighbors: Let KNN(x i ) is x i K nearest neighbor, KNN(x j ) is x j The K nearest neighbors of the sample point x i , x j The shared neighbors of are the intersection of the two, expressed as follows:

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

[0135] Definition 5: Natural neighbor search method: Let K be a positive integer, and 1≤K≤n', let K start increasing from 1, search the K nearest neighbors and K inverse neighbors of each pulse sample point until the intersection of the K nearest neighbors and K inverse neighbors of each pulse is not an empty set, that is, each pulse signal has a natural neighbor, increase the current K value by 1, and select this value as the natural neighborhood feature value, 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 respectively x under the current K value j , x i At the same time, if the natural neighborhood value of the pulse signal continues to remain unchanged as the K value increases, the K value is stopped from increasing, and the current value is used as the natural neighborhood feature value. The specific search process is as follows Figure 5 shown.

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

[0139]

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

[0141] Next, the local density of each pulse signal can be calculated based on the similarity and the number of natural neighbors. The calculation method is as follows:

[0142]

[0143] Where L(i) is the pulse set X and the pulse sample x i The K sample collections with the greatest similarity; |NaN(x i )| is x i The number of natural neighbors. At the same time, the reachable distance Indicates that the local density is greater than the pulse sample point x i And the Euclidean distance to the nearest point, if there is no sample point with a local density greater than the pulse sample point x i , then take the maximum distance in the Euclidean distance matrix as x i The reachable distance is defined as follows:

[0144]

[0145] Where C(i) is the local density greater than x i The pulse sample set; D is the Euclidean distance matrix; max(D) is the maximum distance in the Euclidean distance matrix.

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

[0147]

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

[0149] like Figure 6 As shown in the figure, the product of local density and reachable distance is calculated and arranged in descending order. The cluster center candidate decision diagram is drawn with γ = δ'×ρ' as the ordinate and the descending order of the radar pulse sample γ value as the abscissa, where γ represents the set of the product of local density and reachable distance of each sample. Similarly, Figure 7As shown in the figure, the reachable distance is divided by the local density and arranged in descending order. The cluster center elimination decision diagram is drawn with clex = δ' / ρ' as the ordinate and the descending order of the clex values ​​of the radar pulse samples as the abscissa, where clex represents the set of the local density of each sample divided by the reachable distance.

[0150] 6. Determine the initial radar cluster center.

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

[0152] Logistic regression is a generalized linear model that uses second-order logistic regression to fit the data on the decision diagram. Figure 8 As shown in the figure, the red dotted line represents the confidence interval, which quantifies the uncertainty of estimating the overall parameters of the γ sample set, that is, using a fixed value given by the horizontal axis index value to find the estimated interval of the average value of the vertical axis γ; and the blue dotted line represents the prediction interval, which quantifies the uncertainty of the prediction of a single observation value, that is, using a fixed value given by the horizontal axis index value to find the estimated interval of the individual specific value of the vertical axis γ. In order to avoid the occurrence of missed batches, the confidence interval that is closer to the original data is selected as the judgment condition, and the judgment is made in descending order according to the γ value until the γ value of a certain sample is less than the upper limit of the confidence interval. The sample points before this are selected as candidate radar cluster centers.

[0153] At this point, the candidate radar cluster centers include the maximum density peak point, the local center, and the boundary point. The boundary points need to be eliminated based on the cluster center elimination decision diagram. Since the boundary points have a large reachable distance and a small local density, the value clex divided by the two will be very large, and the distribution of the remaining points can be regarded as a linear relationship. The second-order logistic regression is also used to fit the data on the decision diagram, such as Fig. 9 As shown in the figure. Since the difference in clex values ​​of different types of points can be large, it is more appropriate to select a larger prediction interval as the judgment condition. The judgment is made in descending order of clex values ​​until the clex of a sample is less than twice the upper limit 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, and the expression is as follows:

[0155] Icl=Cand-(Cand∩Holo) (16)

[0156] Where Cand is the candidate radar cluster center set, and Holo is the boundary point set.

[0157] 7. Pulse signal sorting strategy.

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

[0159] Allocation strategy 1: core pulse signal allocation

[0160] Initialize all radar pulse signals to an unassigned state, set the initial queue to be accessed to the selected radar cluster center set, and assign an independent cluster number to each cluster center. Each iteration accesses a sample x that has been assigned but not accessed. p , if x p The K nearest neighbors x q The following conditions must be met:

[0161]

[0162] In the formula, For x q The cluster type it belongs to, if it is equal to -1, it means it is not assigned. That is, the above condition is x q Unassigned and x p is a natural neighbor, and x q With x p If the number of shared neighbors exceeds K / 2, then x q Add to the tail of the queue of the collection to be visited, and at the same time q Assign to x p The cluster in which it belongs. Set x p After the accessed state, the queue is accessed in sequence, and the above process is continued until the queue of the collection to be accessed is empty. The specific process is as follows Fig.10 shown.

[0163] Allocation Strategy 2: Non-core Pulse Signal Allocation

[0164] Construct the allocation matrix A, where the rows of the matrix represent the unassigned radar sample points, and the number of matrix columns represents all the current cluster class numbers. A(i,j) represents the number of neighbors with cluster label j among the neighbors of the i-th unassigned radar sample point. Each iteration finds the maximum value in the allocation matrix, assigns the row index sample i corresponding to the maximum value to the cluster j represented by the column corresponding to the maximum value, and updates the matrix A at the same time. At this time, only the corresponding sample value of the inverse neighbor of radar sample i needs to be updated. Repeat the above process until the maximum value of the allocation matrix A is 0 or all samples are assigned. The specific process is as follows: Fig.11 shown.

[0165] Allocation strategy 3: residual pulse signal allocation

[0166] If there are still unassigned pulse sample points at this time, according to the nearest neighbor principle, the unassigned samples are sorted in descending order according to local density, and the unassigned samples are assigned 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 follows: Fig.12 shown.

[0167] 8. Radar clusters are batched together.

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

[0169] The first step is more about the overall cluster merging, and the radiation factor σ' after eliminating the pulse false alarm is calculated based on the potential energy entropy. Analyze the potential energy formula (4), combine the density peak clustering original density truncated kernel calculation method, take σ' as the truncation radius, and calculate the truncated kernel density of the sample, as shown in the following formula:

[0170]

[0171] Wherein, parameter σ' is the cutoff radius; in the pulse set X, the sample x i The number of samples within the cutoff radius is the sample x i Truncated kernel density.

[0172] The boundary points are distinguished according to the cut-off kernel density. If the cut-off kernel density satisfies the following formula:

[0173]

[0174] Then mark it as a boundary point, let N0(X) be the set of boundary points, C1 i For the i-th radar cluster set after removing the boundary points, the closest distance from the center of each cluster to other clusters except the boundary points is calculated, as shown in the following formula:

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

[0176] Where Dist_min(m,h) represents the shortest distance from the center of the mth cluster to the hth radar cluster; icl(m) is the center of the mth cluster; C1 h is the h-th radar cluster collection 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 the normalized distance), it is determined that the two clusters can be merged. In one embodiment, the standard threshold is 0.1. The first step of batch merging is more focused on the overall distribution of pulses. If no clusters are merged in this step, the second step of merging is skipped directly.

[0179] The second step is more about merging the radar cluster itself with other clusters, without considering the overall cluster distribution. The radiation factor is used to determine the boundary points again. The difference is that the boundary point threshold of each cluster is different, as shown in the following formula:

[0180]

[0181] In the formula, j represents the jth cluster, C j represents the j-th cluster radar sample collection, Num j Then represents the number of radar samples contained in the jth cluster. Let C2 i This is the i-th radar cluster collection with the boundary points removed. After removing the boundary points, the NaN collections between clusters are constructed in sequence, that is, C2 i The natural neighbors of all pulses in the union are NaN_C2 i , C2 j The natural neighbors of all pulses in the union are NaN_C2 j , NaN_C2 i with NaN_C2 j Find the intersection, which is the NaN union of cluster i and cluster j.

[0182] The clusters are judged in pairs. If the number of NaN sets of two clusters is greater than 1, it is determined that the two clusters need to be merged.

[0183] Simulation example:

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

[0185] 15 radar radiation sources are set, and their radiation source parameters are shown in Table 1. In order to simulate the real situation, each cluster of radars is similar in some dimensions and the number of pulses is uneven. The present invention takes into account the PDW parameter estimation error and noise, and takes the parameters of each cluster of radars as the benchmark. The PW parameter is added with a Gaussian noise with a mean of the PW parameter value and a standard deviation of 5μs; the DOA parameter is added with a Gaussian noise with a mean of the DOA parameter value and a standard deviation of 3°; CF has a variety of modulation modes such as pulse group agility and inter-pulse agility, and at the same time adds a Gaussian noise with a mean of the CF parameter value and a standard deviation of 20MHz; PRI has modulation modes such as staggered, sinusoidal, and jitter. The radar pulse description word PDW data received by the receiving station is generated according to the parameter information provided in Table 1. Here, a 200ms pulse sequence is taken as an example, and 5% of the pulses in the sequence are randomly lost, and 0% to 30% of the pulse false alarms are set.

[0186] Table 1 Radar radiation source position and parameters

[0187]

[0188] On the one hand, the sorting performance of the present invention is judged by comparing the difference between the sorting result and the true value with the help of the clustering external evaluation indicators Adjusted Mutual Information (AMI), Adjusted Rand Index (ARI), and FMI (Fowlkes-Mallows Index). The results of the effectiveness evaluation of the above indicators are all in [0,1]. The larger the value, the higher the sorting performance; on the other hand, the radar signal pulse sorting accuracy PA, batch increase rate PF, and missed batch rate PM are used to further verify the actual sorting effect of the present invention. The calculation method is as follows:

[0189]

[0190] Generate 3D distribution of PDW data as Fig.15 As shown in the figure, after the false alarm pulse elimination method is used, the PDW three-dimensional distribution is obtained as follows Fig.16 As shown in Table 2, it can be seen that isolated false alarm pulses are basically eliminated, which is beneficial to subsequent processing.

[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 are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art 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 should be included in the scope of the claims of the present invention.

Claims

1. An adaptive radar signal sorting and clustering optimization method based on improved density peak clustering, comprising: Step 1) Process the radar pulse sequence of the designated area received by the receiving station during the observation period to obtain PDW samples, perform data normalization, and construct a Euclidean distance matrix, apply the data field to calculate the potential energy of each pulse signal, and eliminate false alarm pulses based on the potential energy normalization threshold; Step 2) removing data corresponding to 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 natural 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, inverse 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 natural neighbor search, construct a decision graph, and use linear regression to adaptively determine the initial radar cluster center and number; Step 5) Starting from the initial radar cluster center, a distribution matrix is ​​constructed to 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 shortest distance between the center of each radar cluster and other radar clusters, the boundary points are distinguished by the optimal radiation factor and the cluster natural neighborhood set, and multi-layer judgment conditions are constructed. If any two radar clusters meet the batch merging conditions, the corresponding radar clusters are merged; Step 7) loops through step 6) until there are no clusters that meet the batch merging conditions.

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

3. The adaptive radar signal sorting and clustering optimization method based on improved density peak clustering according to claim 1 is characterized in that: The step 1) performs data normalization, constructs a Euclidean distance matrix, applies the data field to calculate the potential energy of each pulse signal, and eliminates false alarm pulses according to a potential energy normalization threshold; including: The carrier frequency CF, pulse width PW and direction of arrival DOA of each pulse are normalized respectively to obtain the corresponding normalized value cf i ,pw i ,doa i , so as to obtain the normalized PDW sample pdw for each pulse i ={cf i ,pw i ,doa i }; where i represents the PDW sample number 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 every two pulse samples x i ,x j The Euclidean distance d(x i ,x j ): d(x i ,x j )=||pdw i -pdw j ||2 Among them, pdw j represents the normalized PDW sample of the jth pulse, and i≠j; Construct a Euclidean distance matrix based on the Euclidean distances between all pulse samples; The radiation factor is determined by using the minimum value of the potential energy entropy of the data field. The potential energy value of each pulse signal is calculated based on the radiation factor. If the potential energy value corresponding to the pulse is lower than the set standardized threshold, it is identified as a false alarm and the corresponding pulse signal is eliminated.

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

5. The adaptive radar signal sorting and clustering optimization method based on improved density peak clustering according to claim 4 is characterized in that: The step 3) comprises: Step 3-1) Let K be a positive integer, and 1≤K≤n', let K start from 1 and increase; Step 3-2) Traverse and search the K nearest neighbors and K inverse nearest neighbors of each sample point; Step 3-3) If the natural neighbor sets of the current sample are not empty sets, go to step 3-4); otherwise, further determine whether the natural neighbors remain unchanged. If yes, go to step 3-4; if no, add 1 to K and go to step 3-2); Step 3-4) Use the current K value as the natural neighborhood feature value.

6. The adaptive radar signal sorting and clustering optimization method based on improved density peak clustering according to claim 1 is characterized in that: The K nearest neighbors are: pulse signal sample point x i The K points with the closest Euclidean distance to other sample points belonging to the radar pulse set X, the set size is K, and the other sample points are x i K nearest neighbors; The K inverse neighbors are: if the other sample points x of the radar pulse set X j The K nearest neighbors include the sample point x i , then x j Belong to x i K inverse neighbors of ; The natural neighbor is: i The K nearest neighbors of x j , x j The K nearest neighbors of x i , then x i With x j They are natural neighbors.

7. The adaptive radar signal sorting and clustering optimization method based on improved density peak clustering according to claim 1 is characterized in that: The step 4) calculates the local density and the reachable distance according to the result of the natural neighbor search and constructs a decision graph, including: Calculate the similarity Sim(x) between samples based on the shared neighborhood value i ,x j ): In the formula, |SNN(x i ,x j )| is the pulse sample x i , x j Shared Neighborhood SNN(x i ,x j ) number; d'(x i ,x p ),d'(x j ,x p ) are x i , x j To the pulse sample x in the shared neighborhood of both p The shared neighbor SNN (x i ,x j ) is: Let KNN(x i ) is x i K nearest neighbor, KNN(x j ) is x j The K nearest neighbors of the sample point x i , x j The shared neighbors of are 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 pulse set X and the pulse sample x i The collection of K samples with the greatest similarity; The reachable distance is obtained according to the following formula Where C(i) is the local density greater than x i The pulse sample set; D is the Euclidean distance matrix; max(D) is the maximum distance in the Euclidean distance matrix; Normalize the local density and reachable distance respectively to get the normalized local density And reachable distance The product of local density and reachable distance is calculated and arranged in descending order. γ = δ' × ρ' is used as the ordinate and the order of γ values ​​of radar pulse samples in descending order is used as the abscissa to draw the cluster center candidate decision diagram, where γ represents the set of the product of local density and reachable distance of each sample; the reachable distance is divided by local density and arranged in descending order. clex = δ' / ρ' is used as the ordinate and the order of clex values ​​of radar pulse samples in descending order is used as the abscissa to draw the cluster center elimination decision diagram, where clex represents the set of local density and reachable distance of each sample divided.

8. The adaptive radar signal sorting and clustering optimization method based on improved density peak clustering according to claim 7 is characterized in that: The step 4) uses linear regression to adaptively determine the initial radar cluster centers and numbers, including: Apply second-order logistic regression to fit the data on the decision diagram, and use a fixed value given by the horizontal axis index value to find the average value estimation interval of the vertical axis γ, which is determined as the confidence interval; judge in descending order of γ values ​​until the γ value of a certain sample is less than the upper limit of the confidence interval, then the sample points before this are selected as candidate radar cluster centers; Apply second-order logistic regression to fit the data on the decision diagram, and use a fixed value given by the horizontal axis index value to find the estimated interval of the specific value of clex and determine it as the prediction interval; judge in descending order of clex values ​​until the clex of a sample is less than twice the upper limit of the prediction interval, and the sample points before this are selected as boundary points; The initial radar cluster centers are obtained by removing the boundary points from the candidate radar cluster centers, and the number is determined.

9. The adaptive radar signal sorting and clustering optimization method based on improved density peak clustering according to claim 8, characterized in that: The step 5) of sorting and determining the core pulse signal comprises: Initialize radar pulse to unassigned state; Set the radar cluster center set as the initial set queue to be visited; Assign an independent cluster number to each radar cluster center; Each iteration visits a sample x that has been allocated but not visited. p , if x p The K nearest neighbors x q The following conditions must be met: In the formula, For x q The cluster type, if equal to -1, it means it is not assigned, if x q Unassigned and x p is a natural neighbor, and x q With x p If the number of shared neighbors exceeds K / 2, then x q Add to the tail of the queue of the collection to be visited, and at the same time q Assign to x p The cluster in which it is located; set x p After the state is visited, the queue is visited in sequence, and the above process is continued until the queue of the set to be visited is empty; Distributing non-core pulse signals includes: Construct an allocation matrix A, where the rows of the matrix represent the unassigned radar sample points and the columns of the matrix represent all the cluster class numbers; Find the maximum value of the allocation 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 allocation matrix A is 0 or all samples have been assigned. The remaining pulse signal allocation includes: If there are still unassigned pulse sample points at this time, the unassigned samples are sorted in descending order according to local density, and the unassigned samples are assigned to the cluster of the nearest high-density neighbor according to this order. The process is repeated until all pulse signals are sorted.

10. The adaptive radar signal sorting and clustering optimization method based on improved density peak clustering according to claim 9, characterized in that: The step 6) comprises: The radiation factor σ' after eliminating pulse false alarm is calculated based on the potential energy entropy; The overall boundary points are distinguished based on the cutoff kernel distance; Calculate the shortest distance from the center of each radar cluster to other radar clusters; When the closest distance is less than twice the optimal radiation factor or less than a standard threshold, two clusters are merged, and the standard threshold is 0.1; Distinguish the boundary points of each cluster based on the cutoff kernel distance; Eliminate boundary points and construct a natural neighborhood set between clusters; The clusters are judged in pairs in turn. If the number of natural neighbor sets of two clusters is greater than 1, the two clusters are merged.

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