Radar signal sorting method based on improved sparse subspace clustering, program, equipment and storage medium

Abstract

The invention belongs to the technical field of radar signal sorting, and particularly relates to a radar signal sorting method based on improved sparse subspace clustering, a program, equipment and a storage medium. According to the method, the radar pulse sequence is constructed into the complex network according to the self-representation attribute between the radar pulse data points in the same subspace, and the connection of pulses from different radars in the complex network is less by using the generalized orthogonal matching pursuit algorithm, so that the calculation complexity is reduced; by means of the thought of graph segmentation, the geometric incidence relation of the same radar pulse signal is excavated through Laplacian spectrum decomposition, so that efficient sorting of non-ideal radar signals in the complex electromagnetic environment is achieved. Meanwhile, the invention designs an algorithm based on an energy correction splitting threshold, so that the accurate solution of the number of clustering centers can be effectively realized. According to the method, the problem of wrong sorting caused by aliasing or missing of intercepted complex radar working state parameters can be effectively solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal sorting, and in particular relates to a radar signal sorting method, program, device and storage medium based on improved sparse subspace clustering. Background Art

[0002] The radar signal intercepted by the receiver can be regarded as a series of radar pulses characterized by multi-dimensional state parameters in an orderly manner. Only by screening out the pulse sequence belonging to the same radiation source from the intercepted random interlaced pulse stream can we "see clearly" the signals of various radiation sources in time, further complete the radiation source target identification and implement confrontation. This reconnaissance process of separating the pulse stream into pulse sequences of different transmitters based on the correlation of characteristic parameters of the signal from the same radiation source and the difference of characteristic parameters of different radiation source signals is called radar signal sorting.

[0003] According to the selection of intercepted radar signal parameters, the existing radar signal sorting methods can be mainly divided into two categories: sorting based on a single parameter and sorting based on multiple parameters. At the beginning of the research on radar signal sorting algorithms, since the pulse repetition interval (PRI) measurement was the most stable, scholars mainly used it as the key characteristic parameter for radar signal sorting. The published radar signal sorting methods based on single parameter PRI can be roughly divided into four categories: differential histogram algorithm, PRI transformation algorithm, sequence search algorithm, and period estimation algorithm. However, these methods are easily affected by PRI estimation errors, especially complex electromagnetic environments can easily cause PRI jitter and loss. Although the relevant PRI sorting algorithms in recent years have good adaptability to PRI jitter and loss, these algorithms cannot sort complex intentionally modulated pulse signals.

[0004] Due to the increasing number of radiation sources and the increasing diversity of systems, in order to improve the performance of radar signal sorting, researchers are no longer and cannot be limited to single-parameter sorting based on PRI, so radar working state parameters such as pulse descriptor word (PDW) are used as the basis for sorting. In addition to PRI, PDW also includes carrier frequency (Radio Frequency, RF), pulse width (Pulse Width, PW), pulse amplitude (Pulse Amplitude, PA) and direction of arrival (Direction of Arrival, DOA). In the field of multi-parameter sorting, scholars mainly focus on the application and improvement of machine learning methods. Commonly used multi-parameter radar signal sorting algorithms can be divided into three categories: prototype clustering, density clustering and deep learning clustering.

[0005] k-means is a typical algorithm in prototype clustering sorting. The basic idea is to calculate the distance relationship between multi-dimensional radar signals, determine the cluster center through iteration, and divide the nearest radar pulses. This algorithm can effectively sort mixed radar signals with high inter-class separation, but it is sensitive to the initial selection of cluster centers. In recent years, some improved algorithms of k-means have been proposed. These algorithms are less affected by the initial cluster center, but the amount of calculation is large and not suitable for application in practical environments. In addition, the prototype clustering sorting algorithm is very sensitive to radar signals with parameter aliasing, and the probability of sorting errors in the overlapping parts is high.

[0006] The density clustering algorithm determines the clustering structure based on the density of sample distribution, uses the number of points in a certain neighborhood as the connectivity standard, and continuously expands the clustering clusters based on the connectivity to obtain the final clustering result. Although the density clustering algorithm is insensitive to the initialization of the cluster center, an inappropriate threshold will lead to low robustness of the clustering algorithm. In recent years, with the rapid development of deep learning, radar signal sorting based on deep neural networks (DNNs) has become a research hotspot, such as relatively classic convolutional neural networks, autoencoders, and graph neural networks. This method is to achieve radar signal sorting in a data-driven manner, which usually requires a large number of labeled data samples to train the deep learning model to obtain good performance, which is severely limited in actual few-sample scenarios and requires a lot of computational costs.

[0007] The above methods cannot be used to sort radar signals with serious aliasing of radar state parameters in the PDW domain under non-ideal conditions. Therefore, the problem of low inter-class separation and intra-class aggregation of pulse sequences caused by aliasing and partial information loss of intercepted radar pulse signals in complex electromagnetic environments is the focus of research in the field of radar signal sorting. Summary of the invention

[0008] The purpose of the present invention is to provide a radar signal sorting method, program, device and storage medium based on improved sparse subspace clustering to solve the problem of low inter-class separation and intra-class aggregation of pulse sequences caused by aliasing and partial information loss of intercepted radar pulse signals in complex electromagnetic environments.

[0009] A radar signal sorting method based on improved sparse subspace clustering comprises the following steps:

[0010] Step 1: Obtain the time series X of multiple pulses of radar signals, use the self-representation property between multi-state parameter pulse signals in the same subspace to represent the intimacy relationship, that is, the spatial correlation relationship of pulses, and solve the self-representation relationship matrix C through the generalized orthogonal matching pursuit algorithm;

[0011] Step 2: Construct the intimacy matrix A based on the self-representation relationship matrix C, which is the adjacency matrix representing the topological relationship;

[0012] Step 3: Construct the standard form of the Laplacian matrix corresponding to the adjacency matrix A According to the graph characteristics of the Laplacian matrix, the number of cluster centers k, that is, the number of radars, is solved by using the "mutation" of the eigenvalue spectrum and the proportion of the minimum eigenvalue energy;

[0013] Step 4: Take the eigenvectors corresponding to the smallest k eigenvalues ​​in the matrix L to form the feature matrix F; select the first k row vectors of the feature matrix F as the initial clustering centers, use the clustering algorithm to cluster the radar signal pulses in X, output the predicted labels of each radar signal pulse, and realize radar signal sorting.

[0014] Furthermore, the time series X of multiple pulses of the radar signal obtained in step 1 is specifically:

[0015] X={x1,x2,...,x i ,...,x N}

[0016] Among them, x i represents the pulse description word vector of the i-th pulse of the radar signal; N represents the number of radar signal pulses;

[0017] The self-representation property of pulse data distributed in the same subspace is that the data points in the subspace can be represented by linear combinations of other data points in the same space, specifically:

[0018] X=XC,diag(C)=0

[0019] Among them, 0 is the zero vector, is a sparse coefficient matrix, also known as a self-representation relationship matrix. Because the data points originally belonging to the subspace are linearly represented by other data points in the subspace, the self-representation relationship matrix satisfies the subspace preservation property. To solve the self-representation relationship matrix, rewrite the above formula as follows:

[0020]

[0021] Among them, S is the sparsity, that is, c i The upper limit of the number of non-zero values ​​in ; ||·||2 is the l2 norm, ||·||0 is the l0 norm, which represents the number of non-zero elements in the vector;

[0022] The generalized orthogonal matching pursuit algorithm is used to perform a fixed number N using the similarity between the perception matrix X and the residual r. i Atom recognition, expansion of the support set Λ, and then the sparse signal is completed using the column vector in the perception matrix corresponding to the support set Reconstruct and update the residual signal until the specified number of cycles is completed or the residual is less than or equal to the iteration termination threshold ε; the residual of the first iteration defaults to the observation vector x i ; is the i-th column of the self-representation relation matrix C.

[0023] Furthermore, in step 2, the intimacy matrix A is constructed according to the self-representation relationship matrix C, specifically:

[0024] A=|C|+|C T |

[0025] Among them, C T is the transpose of the self-representation relation matrix C;

[0026] In graph theory, the intimacy matrix A is the adjacency matrix representing the topological relationship, expressed as:

[0027]

[0028] Among them, a ij Represents the connection weight between the i-th radar signal pulse node and the j-th radar signal pulse node. The larger the weight, the higher the intimacy between the two nodes, and the more likely they are from the same radar. When the weight is 0, it means there is no edge connection between the nodes.

[0029] Furthermore, the standard form of the Laplacian matrix corresponding to the adjacency matrix A constructed in step 3 is Specifically:

[0030] L=DA

[0031]

[0032] Among them, the Laplacian matrix is ​​a matrix that represents a weighted undirected graph, D is the degree matrix of the weighted undirected graph, and the element D in the matrix D is pq Calculated from the degree of each vertex:

[0033]

[0034] Among them, p and q are both pulse vertices, deg(v p ) is the sum of the weights of all adjacent edges of the pulse vertex p.

[0035] Furthermore, the number k of cluster centers in step 3 is calculated as follows:

[0036]

[0037] Among them, σ1,...,σ Nis the eigenvalue spectrum of the matrix L arranged in increasing order, that is, σ1≤σ2≤…≤σ N ; a is an arbitrary constant and a>1;

[0038] After the number of cluster centers is initially obtained, the energy proportion of the corresponding number of "extremely small" eigenvalues ​​is calculated

[0039]

[0040] If Ep>τ, then intercept the first N k = k eigenvalues ​​are reinserted into the formula The calculation is performed until Ep≤τ, where τ is a preset energy percentage threshold.

[0041] Furthermore, in step 4, the smallest k eigenvalues ​​σ1,...,σ k The corresponding eigenvectors f1,...,f k The feature matrix F is composed of i ,…,f k ) and use the k-means algorithm to cluster the radar signal pulses in F.

[0042] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the radar signal deinterleaving method based on complex network and Laplacian graph clustering.

[0043] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the radar signal deinterleaving method based on complex network and Laplacian graph clustering.

[0044] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the radar signal deinterleaving method based on complex network and Laplacian graph clustering.

[0045] The beneficial effects of the present invention are:

[0046] The present invention constructs the radar pulse sequence into a complex network based on the self-representation property between radar pulse data points in the same subspace, and uses the generalized orthogonal matching pursuit algorithm to make the pulses from different radars have fewer connections in the complex network, thereby reducing the computational complexity; borrowing the idea of ​​graph segmentation, the Laplace spectral decomposition is used to mine the geometric correlation relationship of the same radar pulse signal to obtain efficient sorting of non-ideal radar signals in complex electromagnetic environments. At the same time, the present invention designs an algorithm based on energy-corrected splitting thresholds that can effectively realize the accurate solution of the number of cluster centers. The present invention can effectively solve the problem of wrong batch sorting caused by the aliasing or missing of intercepted complex radar working state parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a sample diagram of the radar working status described in the pulse description word format.

[0048] Figure 2 It is a schematic diagram of the sliding modulation of the state parameters.

[0049] Figure 3 This is a schematic diagram of the splitting threshold solution algorithm based on energy correction.

[0050] Figure 4 It is a principle flow chart of the present invention.

[0051] Figure 5 It is a radar working status simulation experiment data table.

[0052] Figure 6 It is a graph of radar signal sorting accuracy under different jitter ranges when the loss probability is 50%.

[0053] Figure 7 It is a radar signal sorting result diagram under the low-dimensional interception parameter scenario. Among them, (a), (c), (e), and (g) are the sorting results of SSC-gOMP, RSS-ComNet, SDADPC, and k-means algorithms when PA is fixed; (b), (d), (f), and (h) are the sorting results of SSC-gOMP, RSS-ComNet, SDADPC, and k-means algorithms when DOA is fixed.

[0054] Figure 8 It is the original two-dimensional distribution diagram of the intercepted radar pulse signal.

[0055] Fig. 9 It is the radar signal sorting accuracy and ARI data table in the low-dimensional interception parameter scenario. DETAILED DESCRIPTION

[0056] The present invention is further described below in conjunction with the accompanying drawings.

[0057] The pulse sequence corresponding to the radar working state is a series of radar pulses arranged in an orderly manner. In this paper, this series of radar pulses is characterized by multi-dimensional pulse state parameters PDWs, in which the modulation methods of the five state parameters are different. The multi-layer characterization definition of the working state of a single radar is given below.

[0058] Definition 1: The radar working state is described by a series of radar pulses with different state parameters arranged in an orderly manner. From the perspective of signal processing of the reconnaissance receiver, the number of pulses received by a single radar is N. l As the number of state parameters D is finite, the pulse train of a single radar can be expressed as Each pulse can be characterized by the state parameter

[0059] Definition 2: Modulation type refers to the generation of different radar operating states by controlling state parameters. Common modulation types include fixed, agile, and staggered. To generate different radar operating states, the same state parameter can load different modulation types, such as the PRI state parameter can be fixed PRI, Gaussian jitter PRI, staggered PRI, etc.

[0060] Definition 3: The modulation parameters are the control parameters of different modulation types of state parameters. For example, the modulation parameters of the sliding modulation type include the sliding initial value, cycle and step size.

[0061] Figure 1 A sample example of radar operating status described by pulse description word format is given. Each status parameter can be modulated by different modulation types. is the modulation type set corresponding to the dth working state parameter, M d is the number of corresponding modulation types, The first state parameter representing the working state sample of the radar is denoted as pdw, and the corresponding modulation type is sliding. M1=5 means that there are 5 modulation types of the state parameter pdw. In this article, the modulation types of the state parameters include sliding, fixed, staggered, agile, and jitter.

[0062] To further describe the concept of modulation parameters, Figure 2 The influence of different modulation parameters on the pdw distribution when the modulation mode is sliding is demonstrated. represents the set of modulation parameters corresponding to the cth modulation type of the dth state parameter, N c Represents the number of modulation parameters. Different modulation types correspond to different modulation parameters. d=1 means that the state parameter in the figure is pdw, c=1 means that the first modulation type of pdw is slip, N1=3 means that the number of slip modulation parameters is 3, including slip initial value, slip cycle, and slip step size.

[0063] In the actual complex electromagnetic environment, the reconnaissance system will simultaneously receive radar interleaved pulse trains composed of all radars with unknown state parameters in the space, that is, the integration of multiple radar working state models. The radar working state interleaving model can be expressed as:

[0064]

[0065] Among them, L is the number of radars in the space where the reconnaissance system is located, X l is the first radar signal.

[0066] According to PRI, the pulse arrival time is set, and the state parameters such as PW, RF, DOA, etc. are used as the characteristic parameters of the sorted pulses. The working state interleaving model of L radars contains a total of N pulses, which can be rewritten as where x i is a multi-dimensional state parameter vector. Multi-parameter radar signal sorting is to separate L radar pulses from the working state interleaving model of L radars and cluster the pulses belonging to the same radar.

[0067] x i = {PW i ,RF i ,DOA i , ...}

[0068] x i The pulse description word vector representing the i-th pulse of the radar signal. The elements in the vector include but are not limited to, PW i Indicates pulse width, RF i Indicates carrier frequency, DOA i represents the arrival time; N is the total number of pulses;

[0069] The present invention is inspired by image classification in the field of computer vision, that is, data of the same category can be well approximated as being distributed in the same low-dimensional subspace. We introduce this idea into the field of radar signal sorting and use the self-representation properties between multi-state parameter pulse signals in the same subspace to represent the intimacy relationship.

[0070] The self-representation property of pulse data distributed in the same subspace is that the data points in the subspace can be represented by linear combinations of other data points in the same space, specifically:

[0071] X=XC,diag(C)=0

[0072] Among them, 0 is the zero vector, It is a sparse coefficient matrix, also known as a self-representation relationship matrix, which satisfies the subspace preservation property because the data points originally belonging to the subspace are linearly represented by other data points in the subspace.

[0073] Obviously, the above formula is a special form of the compressed sensing model. To further see the similarities between the two, the compressed sensing model is expressed as follows:

[0074] X=ΦC

[0075] The matrix C is sparse, and the purpose of compressed sensing is to restore the sparse representation C of the signal through the observed X and the perception matrix Φ. Therefore, the above formula can be split into:

[0076] min||x i || l ,subject to x i =Xc i

[0077] where ||·|| l is the l-norm, and in general problems it takes the value of 1 or 2.

[0078] However, the distribution of pulse state parameters is unknown and contains a lot of noise when radar signals are sorted in a complex electromagnetic environment. In addition, the excessive number of electromagnetic radiation sources in a battlefield environment leads to a large amount of signal data intercepted by the reconnaissance receiver, making the above-mentioned minimization solution complicated and inefficient. Most importantly, in a complex electromagnetic space, it is impossible to determine whether the subspaces are independent or non-intersecting. Therefore, we can further rewrite the above formula as:

[0079]

[0080] Where S is the sparsity, i.e. c i The upper limit of the number of non-zero values ​​in , in this paper, is between 1% and 2% of the total number of received radar pulses. ||·||2 is the l2 norm, which is ||0 is the l0 norm, which represents the number of non-zero elements in the vector. For the above problem, the present invention adopts the generalized orthogonal matching pursuit algorithm (gOMP) to solve it. The idea of ​​gOMP is to use the perception matrix X and the residual r (the residual of the first iteration defaults to the observation vector x i ) are similar to each other with a fixed number N i Atom recognition, expansion of the support set Λ, and then the sparse signal is completed using the column vector in the perception matrix corresponding to the support set Reconstruct and update the residual signal until the specified number of cycles is completed or the residual is less than or equal to the iteration termination threshold ε, where is the i-th column of the self-representation relation matrix C.

[0081] The present invention can construct an intimacy matrix A=|C|+|C T |, where C Tis the transpose of matrix C. In graph theory, the intimacy matrix A is the adjacency matrix representing the topological relationship, which can be specifically expressed as:

[0082]

[0083] Among them, a ij Represents the connection weight between the i-th and j-th radar pulses. The larger the weight, the higher the intimacy between the two nodes, and the more likely they are from the same radar. When the weight is 0, it means there is no edge connection between the nodes.

[0084] After obtaining the adjacency matrix, if it is directly used as the input of spectral clustering, the eigenvector will have a large amount of redundant information. Generally, after obtaining the adjacency matrix A, it is necessary to simplify it, that is, remove the edges with too small weights, lightweight the complex network while ensuring the integrity of the information, and reduce the computational complexity. Different from the construction of complex networks based on global distances, the self-representation solution of the present invention adopts the gOMP algorithm, and the sparsity S needs to be set for initialization, so that the complex network in this article has the characteristics of being lightweight. In this article, the sparsity S is the number of neighbor connections of the node, which is generally between 1% and 2% of the total number of received pulses, which can ensure that pulses with high global intimacy are closely connected.

[0085] Furthermore, in order to determine the number of radiation sources in radar signal sorting, that is, the number of classification clusters in the clustering problem, the present invention uses the spectral characteristics of the Laplacian matrix to solve the number of cluster centers, and proposes a method for solving the number of cluster centers based on the energy correction splitting threshold.

[0086] The Laplacian matrix, also known as the Kirchhoff matrix, is a matrix that represents a weighted undirected graph. The Laplacian matrix corresponding to the complex network in the present invention and its standard form are:

[0087] L=DA

[0088]

[0089] Where D is the degree matrix of the graph, which is calculated from the degree of each vertex and can be expressed as follows:

[0090]

[0091] Among them, deg(v p ) is the sum of the weights of all adjacent edges of vertex p.

[0092] In order to improve the performance of the clustering algorithm, the number of initial cluster centers in this paper can be solved based on the spectral characteristics of the Laplacian matrix. The solution of the number of cluster centers in the improved sparse subspace clustering algorithm is equivalent to the estimation of the number of subspaces. Inspired by the estimation of the number of subspaces, the number of subspaces is equal to the standard form of the Laplacian matrix constructed by the intimacy matrix A. The number of "minimum" eigenvalues. Ideally, after the eigenvalues ​​are sorted from small to large, a "mutation" will occur between two eigenvalues, and at this time the splitting threshold is relatively easy to determine. However, in a complex electromagnetic environment, radar signals containing noise and interference will weaken or transfer the "mutation", and at this time the splitting threshold is prone to error in solution. In response to the above problems, the present invention proposes a splitting threshold solution algorithm based on energy correction.

[0093] First, the eigenvalues ​​of the normalized Laplacian matrix are Arrange them in order from small to large, that is, σ1≤σ2≤…≤σ N The number of cluster centers can be estimated as follows:

[0094]

[0095] First iteration N k =N, where:

[0096]

[0097] After the number of cluster centers is initially obtained, the energy proportion of the corresponding number of "extremely small" eigenvalues ​​is calculated:

[0098]

[0099] If Ep>τ, then intercept the front The eigenvalues ​​are then brought back into the formula The calculation is performed until Ep≤τ, where τ is the energy proportion threshold, which is close to 0 in an ideal situation and is set to 0.2 in the complex electromagnetic case in this paper. The specific algorithm for solving the number of cluster centers based on energy correction is shown in Figure 3 .

[0100] Finally, after obtaining the number of cluster centers k, the feature matrix F can be composed of the eigenvectors corresponding to the smallest k eigenvalues ​​of the Laplace matrix. i The corresponding eigenvector is f i When , the feature matrix F can be expressed as:

[0101] F=(f1,f2,…,f i ,…,f k )

[0102] Each row in F can be regarded as a sample in the k-dimensional feature space, and radar signal sorting can be completed by performing k-means clustering on the samples in F. The specific operation of the k-means algorithm is: select the first k row vectors of F as the initial cluster center; calculate the distance from the remaining sample points to the cluster center and assign them to the nearest class; if the class to which the sample belongs changes, update the cluster center point of the class; finally return k classes, that is, the predicted label of each pulse, where the convergence test of the algorithm uses the square sum criterion function.

[0103] In order to solve the problem of low sorting accuracy caused by severe radar signal aliasing or information loss in complex electromagnetic environments, the present invention proposes a radar signal sorting method SSC-gOMP based on improved sparse subspace clustering. Different from traditional distance-based clustering algorithms, the method of the present invention uses the self-representation properties between radar pulse data points to construct a complex network, explores the geometric relationship between radar pulses from the same part from the topological structure between data points, and uses the idea of ​​graph segmentation to perform Laplace spectral clustering on the topological structure. The threshold is analyzed to complete the solution of the number of clusters, thereby realizing radar signal sorting in complex electromagnetic environments. The method mainly consists of three parts, namely the construction of a complex network, the solution of the number of cluster centers and spectral clustering. The principle flow chart of the present invention is shown below. Figure 4 shown.

[0104] Embodiment 1:

[0105] Three multi-function radars are selected to simulate intercepted radar signals in a complex electromagnetic environment. Radar 2 has two working modes, and radar 1 and radar 3 have three working modes. Different radars or different working modes of the same radar will have overlapping parameters, which is closer to the actual receiver receiving signals. The working state parameters of each radar include PW, RF, PRI, DOA, and PA. Each state parameter can adopt a variety of modulation modes, including fixed, staggered, agile, sliding, and jitter. The radar working state simulation experimental data in this embodiment is shown in Figure 2. Figure 5 In addition, referring to the general definition of the overlap ratio of a large number of clusters in the field of clustering, that is, an overlap ratio of more than 30% to 50% can usually be considered as a situation of a large number of clusters overlapping, so this paper defines that the overlap ratio of the parameter feature distribution space exceeding 30% is severe aliasing.

[0106] In order to verify the effectiveness and stability of the method proposed in this patent, this paper uses the pulse-level sorting accuracy as the sorting performance evaluation index, which is:

[0107]

[0108] Among them, B i and are the true label and cluster label corresponding to the i-th pulse, N is the total number of radar pulse observation pulses, and δ represents the indicator function as follows:

[0109]

[0110] Since the correspondence between the sorting results and the true labels is uncertain, the mapping function map() is needed to find the best match between the clustering result labels and the true labels. The best match in this paper is implemented by the Hungarian algorithm, which can effectively align the clustering result labels with the true labels, thereby calculating the sorting accuracy.

[0111] In addition, in order to make up for the limitation of sorting accuracy in evaluating clustering results under random clustering or cluster size imbalance, we further add the adjusted Rand index (ARI) as the second evaluation indicator of this paper. The specific indicators are:

[0112]

[0113] Where RI is the Rand coefficient, E[RI] is the expected value of RI, and max(RI) is the maximum value of RI. The RI calculation formula is as follows:

[0114]

[0115] Among them, the relationship between the clustering result label and the true label can be divided into the following four types:

[0116] a) The true label is e, the clustering result category label is e, and the corresponding number of pulses is denoted as TP e .

[0117] b) The true label is not e, the clustering result category label is not e, and the corresponding number of pulses is expressed as TN e .

[0118] c) The true label is e, the clustering result category label is not e, and the corresponding number of pulses is expressed as FN e .

[0119] d) The true label is not e, the clustering result category label is e, and the corresponding number of pulses is expressed as FP e .

[0120] In order to verify the sensitivity of the proposed method to pulse jitter, the latest methods ComNet, SDADPC and traditional algorithm k-means are compared in recent years. When the loss probability is 50%, the jitter range is set to [3%, 30%] and the interval is 3%. The experimental results are as follows: Figure 6As shown. As can be seen from the figure, the sorting accuracy of the four algorithms shows a downward trend with the increase of the jitter degree, and under different jitter degrees, the sorting accuracy of the method proposed in the patent is the highest. The relationship between data points is established by using self-representation attributes, and the intrinsic association of the same radar signal is mined by constructing a complex network. The complex topological structure is segmented by spectral clustering to complete clustering. Compared with the traditional method of directly inputting the received signal into the k-means algorithm for clustering, the method proposed in this patent is more conducive to extracting the intrinsic characteristics of radar pulse signals and can better complete the radar signal sorting in a complex electromagnetic environment. Although the RSS-ComNet algorithm also mines the correlation relationship of signals by building a complex network, the algorithm uses the finite traversal visible graph algorithm to construct a complex network. When the radar signal parameters are jittered, it may make it impossible to establish a connection between the pulse signals of the same radar, or establish an incorrect connection, which has a great impact on the accuracy of radar signal sorting. The SDADPC algorithm will lose parameter information in the process of dimensionality reduction, and the accuracy of solving the number of cluster centers is not high when the radar signal parameters are severely aliased in a complex electromagnetic environment, resulting in a decrease in sorting accuracy. In summary, the method proposed in the patent can perform better in the problem of radar signal sorting in complex electromagnetic environments.

[0121] Embodiment 2:

[0122] Not all parameters in the radar operating state parameters actually intercepted can be used as inputs for sorting. In the increasingly complex and dense modern electromagnetic environment, receiver gain control, radiation source antenna scanning, and receiver antenna pointing will have a great impact on PA measurement. Therefore, the smoothness of pulse amplitude has always been the worst of the PDW parameters and is sometimes not used as a parameter for signal sorting. In addition, if the radar radiation source intercepted by the reconnaissance receiver may come from the same direction due to the long distance, that is, the DOA parameters of multiple radars will overlap seriously, the DOA parameters at this time will not be used as signal sorting parameters. Based on this, Figure 5 The radar working state parameters PA and DOA are set as constants respectively to verify the sorting performance of the SSC-gOMP method proposed in this patent under the low-dimensional interception parameter scenario.

[0123] The radar sorting experimental results of the proposed algorithm under fixed PA and DOA state parameters are shown as follows: Figure 7 As shown in (a) and (b), the experimental results of the comparison algorithm are as follows: Figure 7 The distribution of pulse data points in two-dimensional space is shown in (c)-(h). Figure 8As shown in the figure, by comparison, it is found that the proposed method in this project has better sorting performance than the current advanced clustering algorithm when the radar signal dimension is low, proving that the complex network constructed by the SSC-gOMP algorithm using self-representation attributes can deeply explore the intrinsic correlation between the same radar data points. However, the traditional sorting algorithm based on distance relationship is prone to incorrect selection of cluster centers, resulting in large-scale clustering errors of radar data points, such as Figure 7 In (g) and (h), a large number of data points of radar 1 and radar 3 are misclassified as radar 2. The RSS-ComNet algorithm establishes the connection between each parameter between pulses and constructs a complex network by summing them up. Therefore, after reducing the parameter dimension, the sorting accuracy of the algorithm is greatly affected. The specific numerical experimental results are shown in Fig. 9 As shown, the sorting accuracy and ARI of the method proposed in this patent are both optimal, which further proves the superiority of the method proposed in this patent.

[0124] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A radar signal sorting method based on improved sparse subspace clustering, characterized in that: The following steps are involved: Step 1: Obtain the time series X of multiple pulses of radar signals, use the self-representation property between multi-state parameter pulse signals in the same subspace to represent the intimacy relationship, that is, the spatial correlation relationship of pulses, and solve the self-representation relationship matrix C through the generalized orthogonal matching pursuit algorithm; Step 2: Construct the intimacy matrix A based on the self-representation relationship matrix C, which is the adjacency matrix representing the topological relationship; Step 3: Construct the standard form of the Laplacian matrix corresponding to the adjacency matrix A According to the spectral characteristics of the Laplacian matrix, the number of cluster centers k, that is, the number of radars, is solved by using the "mutation" of the eigenvalue spectrum and the proportion of the minimum eigenvalue energy; Step 4: Take the eigenvectors corresponding to the smallest k eigenvalues ​​in the matrix L to form the characteristic matrix F; The first k row vectors of the feature matrix F are selected as the initial clustering centers, and the radar signal pulses in X are clustered using the clustering algorithm. The predicted labels of each radar signal pulse are output to realize radar signal sorting.

2. The radar signal sorting method based on improved sparse subspace clustering according to claim 1, characterized in that: The time series X of multiple pulses of the radar signal obtained in step 1 is specifically: X={x1,x2,…,x i ,…,x N } Among them, x i represents the pulse description word vector of the i-th pulse of the radar signal; N represents the number of radar signal pulses; The self-representation property of pulse data distributed in the same subspace is that the data points in the subspace can be represented by linear combinations of other data points in the same space, specifically: X=XC,diag(C)=0 Among them, 0 is the zero vector, is a sparse coefficient matrix, also known as a self-representation relationship matrix. Because the data points originally belonging to the subspace are linearly represented by other data points in the subspace, the self-representation relationship matrix satisfies the subspace preservation property. To solve the self-representation relationship matrix, rewrite the above formula as follows: Among them, S is the sparsity, that is, c i The upper limit of the number of non-zero values ​​in ; 2 is the l2 norm, 0 is the l0 norm, which represents the number of non-zero elements in the vector; The generalized orthogonal matching pursuit algorithm is used to perform a fixed number N using the similarity between the perception matrix X and the residual r. i Atom recognition, expansion of the support set Λ, and then the sparse signal is completed using the column vector in the perception matrix corresponding to the support set Reconstruct and update the residual signal until the specified number of cycles is completed or the residual is less than or equal to the iteration termination threshold ε; the residual of the first iteration defaults to the observation vector x i ; is the i-th column of the self-representation relation matrix C.

3. The radar signal sorting method based on improved sparse subspace clustering according to claim 1, characterized in that: In step 2, the intimacy matrix A is constructed according to the self-representation relationship matrix C, specifically: A=C+C T Among them, C T is the transpose of the self-representation relation matrix C; In graph theory, the intimacy matrix A is the adjacency matrix representing the topological relationship, expressed as: Among them, a ij Represents the connection weight between the i-th radar signal pulse node and the j-th radar signal pulse node. The larger the weight, the higher the intimacy between the two nodes, and the more likely they are from the same radar. When the weight is 0, it means there is no edge connection between the nodes.

4. The radar signal sorting method based on improved sparse subspace clustering according to claim 1, characterized in that: The standard form of the Laplacian matrix corresponding to the adjacency matrix A constructed in step 3 Specifically: L=DA Among them, the Laplacian matrix is ​​a matrix that represents a weighted undirected graph, D is the degree matrix of the weighted undirected graph, and the element D in the matrix D pq Calculated from the degree of each vertex: Among them, p and q are both pulse vertices, deg(v p ) is the sum of the weights of all adjacent edges of the pulse vertex p.

5. The radar signal sorting method based on improved sparse subspace clustering according to claim 4 is characterized in that: The calculation method of the number k of cluster centers in step 3 is: Among them, σ1,...,σ N is the eigenvalue spectrum of the matrix L arranged in increasing order, that is, σ1≤σ2≤…≤σ N ; a is an arbitrary constant and a>1; After the number of cluster centers is initially obtained, the energy proportion of the corresponding number of "extremely small" eigenvalues ​​is calculated. If Ep>τ, then intercept the first N k = k eigenvalues ​​are reinserted into the formula The calculation is performed until Ep≤τ, where τ is a preset energy percentage threshold.

6. The radar signal sorting method based on improved sparse subspace clustering according to claim 1, characterized in that: In step 4, the smallest k eigenvalues ​​σ1,...,σ of the matrix L are taken. k The corresponding eigenvectors f1,...,f k The feature matrix F is composed of i ,…,f k ) and use the k-means algorithm to cluster the radar signal pulses in F.

7. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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