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CN-121980294-A - SVD sea clutter suppression method based on improved k-means

CN121980294ACN 121980294 ACN121980294 ACN 121980294ACN-121980294-A

Abstract

The SVD algorithm separates clutter subspace, target subspace and noise subspace in radar echo through singular value decomposition, so as to achieve the purpose of clutter suppression. However, due to aliasing of the target and sea clutter, the clutter subspace partitioning affects the clutter suppression effect. Aiming at the problem that clutter subspaces are difficult to determine after radar echo signals are subjected to SVD decomposition, the adaptive selection of clutter subspaces by using a method for improving K-means clustering is provided. Aiming at the problems that K-means is sensitive to an initial centroid and different characteristic parameters have differences in the aspects of statistical stability and noise resistance, the method performs fixed initial centroid and weighted calculation on the sample distance. The method utilizes four characteristics of singular value distribution, echo component correlation, doppler bandwidth and relative Doppler change coefficient as the input of K-means to adaptively select a clutter subspace, and achieves the aim of clutter suppression by mapping signals into an orthogonal space of the clutter subspace.

Inventors

  • WANG FENG
  • FAN SHUQI
  • LIU HAIYUN

Assignees

  • 河海大学

Dates

Publication Date
20260505
Application Date
20260108

Claims (4)

  1. 1. An SVD sea clutter suppression method based on improved K-means is characterized by comprising the following steps: Step 1, a radar echo signal is subjected to pulse compression, a radar echo speed matrix Y is established, and then SVD decomposition is carried out on the speed matrix Y to obtain a left vector matrix U containing Doppler information, a right vector matrix V containing space information and a singular value diagonal matrix S; And 2, calculating characteristics of four input K-means clusters by using the SVD result obtained in the step 1. The four characteristics are singular value spectrum distribution, echo component cross correlation, doppler bandwidth and relative Doppler variation coefficient respectively; And 3, according to the four features corresponding to each singular value obtained in the step 2, carrying out minimum-maximum normalization on the four statistic features, then carrying out singular value clustering as the input of K-means, adaptively dividing the singular value of the clutter subspace through the K-means clustering, and finally mapping echo signals to the clutter orthogonal subspace to achieve the aim of suppressing sea clutter.
  2. 2. The improved K-means based SVD sea clutter suppression method of claim 1, wherein step 1 comprises the sub-steps of: In the substep 1.1, the radar transmitting signal is a linear frequency modulation signal, the number of transmitting pulses of the radar is N, the number of sampling points of each pulse is M, and the expression of an nth echo signal x n (t) received by the radar is: Where S n (t) represents a signal component in the echo, c n (t) represents a clutter component, and n (t) represents a noise component. A represents the amplitude of the received signal, T r represents the repetition period of the radar pulse, T p represents the radar pulse width, and f 0 is the carrier frequency. τ is the echo delay of the signal, μ is the tuning frequency and its expressions are: where R 0 represents the distance of the target from the radar, v 0 represents the speed of motion of the target, and B represents the frequency modulation bandwidth. Step 1.2, arranging N radar echo pulses into a one-dimensional array according to an echo sequence to obtain a total radar echo signal E (t), and rearranging the radar echo signals into a radar echo speed time matrix Y according to a transmitting pulse sequence after pulse compression, wherein the expression is as follows: And (3) performing SVD decomposition according to the radar echo speed matrix Y obtained in the substep 1.2, wherein the expression is as follows: Wherein U is a left vector matrix, D is a diagonal matrix formed by singular values, and V is a right vector matrix. S, C and N represent singular values represented by the target, clutter and noise subspaces. The superscript H represents the conjugate transpose. Lambda i represents the ith singular value, the singular values being arranged from large to small. U i denotes a column vector corresponding to the ith singular value of U, and v i denotes a right column vector corresponding to the ith singular value.
  3. 3. The improved K-means based SVD sea clutter suppression method of claim 2, wherein step 2 comprises the sub-steps of: In the substep 2.1, the singular value spectrum distribution of the radar echo data is calculated, the signal-to-clutter ratio of the slow target echo is lower under the environment background of strong sea clutter, and the energy of the clutter component is far greater than that of the target component. Thus, the energy duty cycle of clutter, signal and noise in echo signals can be used as an important feature of singular value discrimination. The energy distribution of different echo components can be represented by each singular value obtained by SVD (singular value decomposition) of the radar echo fast and slow time matrix Y. Because the maximum singular value is usually significantly larger than the rest singular values, if the original singular value is directly used as a feature for clustering analysis, the clustering process is easily subjected to the dominant of the large singular value, so that the distinguishing capability of weak targets or detail features is reduced. Therefore, the singular values are required to be subjected to logarithmic compression processing so as to reduce the amplitude difference between the singular values, reduce the dominant effect of the large singular values on the feature space, and enable the singular value features to be distributed in the same magnitude, thereby improving the clustering stability and effectiveness based on the singular value features. And 2.2, calculating Doppler bandwidth of the radar echo data. In Jiang Hai clutter environments, the sea surface is affected by weather environments such as wind, waves and the like, and the Doppler bandwidth of the sea clutter can be widened. The moving speed of the target in the range gate is basically kept unchanged, and the Doppler bandwidth is narrower compared with the clutter, so that the Doppler bandwidth of each component can be calculated as the characteristic for distinguishing the clutter from the target. The Doppler bandwidth represents the physical meaning of the second-order center distance of the Doppler spectrum, the Doppler bandwidth w k of the k singular value corresponding component can be obtained through the left characteristic matrix U= [ U 1 ,u 2 ,…,u N ] T ] after SVD decomposition by Y, and the calculation formula is as follows: w k ＝E{[u k -E(u k )] 2 } and 2.3, calculating the relative Doppler change coefficient of the radar echo data. The Doppler peak of the target under the range gate is clearer and sharper than the clutter, and the Doppler peak of the sea clutter is more dispersed. Clutter and target can therefore be distinguished by calculating the concentration of doppler peaks for each singular value corresponding component. The Doppler coefficient CV k expression for the kth singular value corresponding component is: The relative Doppler coefficient RCV k expression for the kth singular value corresponding component is: In sub-step 2.4, the cross correlation of the echo components of the radar echo data is calculated, and the target component only exists in a certain or a plurality of range gates due to the fact that the spatial cross correlation between the clutter scattering points under different range gates is high and the randomness of the noise component is high. The spatial correlation between the clutter component and the target and noise components in the echo signal is low. The fourth set of features can be obtained by calculating the cross-correlations in the subspaces represented by the individual singular values. And because the energy distribution of the sea clutter is far greater than that of the target component and the noise component, the clutter component is characterized by the first singular value of the singular value sequence sequenced from large to small. The cross-correlation of the different components and clutter components can thus be obtained by calculating the cross-correlation of the remaining singular value vector with the first singular value vector. The cross-correlation expression between the kth component and the clutter component after SVD decomposition is: Wherein u k represents the eigenvector of the left vector matrix corresponding to the kth singular value, k is 1≤N, σ 1 and σ k are standard deviations of u 1 and u k , respectively, and E represents the expected value.
  4. 4. The improved K-means based SVD sea clutter suppression method of claim 3, wherein step 3 comprises the sub-steps of: And 3.1, performing normalization operation on the data according to the four features calculated in the step 2. The core idea of K-means is to calculate the similarity between the data point and the cluster center based on Euclidean distance, and adjust the position of the center point through repeated iterative optimization until the algorithm converges or the maximum iterative times are met. In order to avoid that the clustering result is biased to the high-scale feature and the rest features are weakened due to the fact that the numerical value difference of the feature data is too large, the effectiveness and the correctness of clustering are affected. The four feature data obtained in the step 2 are required to be subjected to minimum-maximum normalization processing, so that the data values are all between [0,1 ]. The min-max normalized calculation formula is: Where x i represents the ith value in a certain set of feature data, and x max and x min represent the minimum and maximum values in a certain set of feature data. Normalizing the four characteristic data in the step 2 to obtain a data set I to be subjected to K-means clustering And 3.2, carrying out K-means clustering on the data set I. Since the echo contains three components of clutter, signal and noise, the clustering result is divided into 3 types. And the method is used for overcoming the defect that K-means is very sensitive to the initial centroid, and replacing the original randomly selected centroid by a mode of designating the initial centroid when initializing the centroid. The k-means clustering steps are as follows: (1) Initializing, wherein 3 data sets are fixedly selected from a given data set to serve as initial centroids respectively. (2) The weighted euclidean distance of each sample from 3 centroids is calculated and assigned to a cluster where the closest centroid is located. (3) And (3) calculating the average value of the samples in each divided cluster, and updating the mass center in each cluster. (4) And judging whether the iteration times are reached or whether the distance between the newly selected centroid result and the last centroid is smaller than a threshold value. Outputting the data contained in the final 3 clusters and the data thereof if the stop condition is reached, and repeating (2) and (3) if the stop condition is not reached. After K-means clustering, N singular values are divided into three clusters, and as the largest singular value is necessarily representative of clutter subspace, the class of the largest singular value is the singular value set C c of clutter. And 3.3, constructing a clutter subspace matrix P c by using the clutter singular value set C c according to the clustering result obtained in the step 3.2, wherein the calculation formula is as follows: Constructing a subspace matrix P1/c expression orthogonal to the clutter subspace based on a least square method: Where I is the identity matrix. Finally, mapping the radar fast and slow time echo signal matrix Y into the P1/c subspace to finish clutter suppression. And (5) carrying out MTI and MTD on the processed echo signals to observe clutter suppression results.

Description

SVD sea clutter suppression method based on improved k-means Technical Field The invention belongs to the field of radar signal processing, and particularly relates to an SVD sea clutter suppression method based on improved k-means. Technical Field Sea clutter is a strong back-scattered echo generated by the interaction of electromagnetic waves emitted by radar systems and impinging on rough ocean surfaces. The structure of the ocean surface is complex and changeable under the influence of factors such as ocean weather, geographical environment and the like, and the electromagnetic scattering mechanism is very complex. Target echoes on the sea surface are extremely easy to be interfered by clutter signals, and target detection in a sea clutter environment is seriously affected. SVD decomposition belongs to subspace suppression algorithms, and is based on the difference of aggregation characteristics of clutter components and target components in subspaces, sea clutter is suppressed by separating clutter subspaces. However, due to the complex and changeable conditions of the sea clutter, it is difficult to accurately divide the clutter subspace of the SVD decomposition, and especially when the clutter and the target are aliased, the accuracy of the clutter subspace division can directly affect clutter suppression and target detection. If the singular value is selected as the clutter subspace only according to the past experience or the fixed specific scene, the complex and changeable sea clutter environment cannot be effectively adapted. Disclosure of Invention The invention aims to overcome the defects of the prior art, and provides an SVD sea clutter suppression method based on improved K-means, which aims at the difference of the requirements of accurately dividing the clutter subspace in the SVD decomposition method, the four characteristics of singular value distribution, echo component correlation, doppler bandwidth and relative Doppler change coefficient are calculated to be used as the input of the improved K-means. Clustering singular values, adaptively selecting a clutter subspace, and mapping signals into an orthogonal space of the clutter subspace to achieve the purpose of clutter suppression In order to achieve the above object, the present invention is realized by the following technical means. SVD sea clutter suppression method based on improved k-means comprises the following steps: Step 1, a radar echo signal is subjected to pulse compression, a radar echo speed matrix Y is established, and then SVD decomposition is carried out on the speed matrix Y to obtain a left vector matrix U containing Doppler information, a right vector matrix V containing space information and a singular value diagonal matrix S; And 2, calculating characteristics of four input K-means clusters by using the SVD result obtained in the step 1. The four characteristics are singular value spectrum distribution, echo component cross correlation, doppler bandwidth and relative Doppler variation coefficient respectively; and 3, according to the four features corresponding to each singular value obtained in the step 2, carrying out minimum-maximum normalization on the four statistic features, then carrying out singular value clustering as the input of K-means, determining the singular value representing the clutter subspace through the self-adaptive clustering of the K-means sub-use clustering, and finally mapping the echo signal to the clutter orthogonal subspace to achieve the aim of suppressing the sea clutter. Compared with the prior art, the invention has the beneficial effects that: k-means clustering is carried out by utilizing singular value distribution of radar echo components, echo component correlation, doppler bandwidth and relative Doppler variation coefficient, and a clutter subspace is adaptively partitioned. Drawings The invention will now be described in further detail with reference to the drawings and to specific examples. FIG. 1 is a flow chart of an SVD sea clutter suppression method based on improved k-means. Fig. 2 is a diagram of the simulation of the original radar return signal MTD on a Matlab platform. FIG. 3 is a graph of MTD after only the first singular value is divided into clutter subspaces in a simulation of a conventional SVD process on a Matlab platform FIG. 4 is a graph of MTD after processing by simulation of the modified k-means based SVD algorithm on a Matlab platform. Detailed Description The invention is further described below with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention. As shown in FIG. 1, the SVD sea clutter suppression method flow chart based on the improved k-means comprises the following steps: and (3) after pulse compression of radar echo signals, a radar echo speed matrix Y is established, and then SVD