SVD sea clutter suppression method based on improved k-means

Abstract

The SVD algorithm separates a clutter subspace, a target subspace and a noise subspace in radar echoes through singular value decomposition, and the purpose of clutter suppression is achieved. However, due to aliasing of the target and the sea clutter, the clutter suppression effect can be affected by clutter subspace division. In order to solve the problem that the clutter subspace is difficult to determine after the radar echo signal is subjected to SVD decomposition, the invention provides a method for adaptively selecting the clutter subspace by using an improved K-means clustering method. Aiming at the problems that K-means is sensitive to the initial centroid and different characteristic parameters are different in the aspects of statistical stability and anti-noise performance, the initial centroid is fixed, and the sample distance is calculated in a weighted mode. According to the method, after four characteristics of singular value distribution, echo component correlation, Doppler bandwidth and relative Doppler variable coefficient are used as K-means input, clutter subspaces are selected in a self-adaptive mode, and the purpose of clutter suppression is achieved by mapping signals into orthogonal spaces of the clutter subspaces.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing, specifically relating to an SVD sea clutter suppression method based on improved k-means. Technical Background

[0002] Sea clutter is a strong backscattered echo generated when electromagnetic waves emitted by a radar system interact with the rough, undulating ocean surface. Influenced by factors such as marine meteorology and geographical environment, the ocean surface structure is complex and variable, resulting in highly complex electromagnetic scattering mechanisms. Target echoes on the sea surface are easily interfered with by clutter signals, severely affecting target detection in sea clutter environments. The SVD decomposition method, belonging to the subspace suppression algorithm, is based on the difference in the aggregation characteristics of clutter and target components within a subspace, suppressing sea clutter by separating the clutter subspace. However, due to the complexity and variability of sea clutter, it is difficult to accurately delineate the clutter subspace of SVD decomposition, especially when clutter and targets overlap. The accuracy of clutter subspace decomposition directly affects clutter suppression and target detection. Simply selecting singular values ​​as the clutter subspace based on past experience or a fixed scenario is insufficient to effectively adapt to the complex and variable sea clutter environment. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies and propose an improved k-means-based method for suppressing sea clutter in SVD decomposition. This method addresses the need for accurate clutter subspace partitioning in SVD decomposition by using four features—singular value distribution, echo component correlation, Doppler bandwidth, and relative Doppler variation coefficient—as inputs to the improved k-means method. Singular values ​​are clustered, and the clutter subspace is adaptively selected. By mapping the signal to the orthogonal space of the clutter subspace, clutter suppression is achieved.

[0004] To achieve the above objectives, the present invention employs the following technical methods.

[0005] The SVD sea clutter suppression method based on improved k-means includes the following steps:

[0006] Step 1: After pulse compression of the radar echo signal, establish the radar echo fast and slow matrix Y. Then, perform SVD decomposition on the fast and slow matrix Y to obtain the left vector matrix U containing Doppler information, the right vector matrix V containing spatial information, and the singular value diagonal matrix S.

[0007] Step 2: Calculate the features of the four input K-means clusters using the SVD results obtained in Step 1. The four features are the singular value spectral distribution, echo component cross-correlation, Doppler bandwidth, and relative Doppler variation coefficient.

[0008] Step 3: Based on the four features corresponding to each singular value obtained in Step 2, the four statistical features are normalized by min-maximum and used as input for K-means singular value clustering. The singular values ​​representing the clutter subspace are determined by adaptive clustering of K-means sub-clusters. Finally, the echo signal is mapped to the orthogonal subspace of clutter to achieve the purpose of suppressing sea clutter.

[0009] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0010] K-means clustering was performed using the singular value distribution of radar echo components, echo component correlation, Doppler bandwidth, and relative Doppler variable coefficients to adaptively divide the clutter subspace. Attached Figure Description

[0011] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0012] Figure 1 This is a flowchart of the SVD sea clutter suppression method based on improved k-means.

[0013] Figure 2 This is a simulation of the original radar echo signal MTD plot on the Matlab platform.

[0014] Figure 3 This is a simulation on the Matlab platform of the MTD plot after traditional SVD processing, where only the first singular value is partitioned into a clutter subspace.

[0015] Figure 4 The MTD plot is simulated on the Matlab platform after processing by the improved k-means SVD algorithm. Detailed Implementation

[0016] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0017] like Figure 1 The flowchart shown below illustrates the SVD sea clutter suppression method based on improved k-means, which includes the following steps:

[0018] After pulse compression of the radar echo signal, a radar echo fast and slow matrix Y is established. Then, the fast and slow matrix Y is decomposed by SVD to obtain a left vector matrix U containing Doppler information, a right vector matrix V containing spatial information, and a singular value diagonal matrix S.

[0019] Specifically, step 1 includes the following sub-steps:

[0020] Sub-step 1.1: The radar transmits a linear frequency modulated signal S.chrip (t), the radar transmits N pulses, and each pulse has M sampling points. The expression for the nth echo signal received by the radar is:

[0021]

[0022] Where s n (t) represents the signal component in the echo, c n (t) represents the clutter component, and n(t) represents the noise component. A represents the amplitude of the received signal, and T r T represents the repetition period of the radar pulse. p Let f0 represent the radar pulse width, f0 be the carrier frequency, τ be the signal echo delay, and μ be the tuning frequency. Their expressions are as follows:

[0023]

[0024]

[0025] Where R0 represents the distance between the target and the radar, v0 represents the target's speed, and B represents the frequency modulation bandwidth.

[0026] Sub-step 1.2: Arrange the N radar echo pulses into a one-dimensional array according to the echo order to obtain the total radar echo signal E(t). Then, combine E(t) and S... chrip (t) After discretization, pulse compression is performed. The expression for pulse compression is:

[0027]

[0028] Where FFT[·] represents the Fourier transform, IFFT[·] represents the inverse Fourier transform, and [·]... * Indicates conjugate.

[0029] The radar echo time matrix Y, rearranged according to the transmitted pulse order, is expressed as:

[0030]

[0031] Sub-step 1.3: Based on the radar echo fast / slow matrix Y obtained in sub-step 1.2, perform SVD decomposition, the expression of which is:

[0032]

[0033] Where U is the left vector matrix, D is the diagonal matrix composed of singular values, and V is the right vector matrix. S, C, and N represent the sets of singular values ​​represented by the target, clutter, and noise subspaces. The superscript H denotes the conjugate transpose. λ i Let u represent the i-th singular value, and let u be the singular value arranged in descending order. iLet v represent the column vector corresponding to the i-th singular value of U. i This represents the right column vector corresponding to the i-th singular value.

[0034] Step 2: Calculate the features of the four input K-means clusters using the SVD results obtained in Step 1. The four features are the singular value spectral distribution, echo component cross-correlation, Doppler bandwidth, and relative Doppler variation coefficient.

[0035] Sub-step 2.1 calculates the eigenvalue spectrum distribution of the radar echo data. In a strong sea clutter environment, the signal-to-clutter ratio (SCR) of slow-moving, small target echoes will be lower, and the energy of the clutter component will be much greater than that of the target component. Therefore, the energy proportions of clutter, signal, and noise in the echo signal can be used as an important feature for distinguishing singular values. Each singular value D = {d1, d2, ..., d...} is obtained by performing SVD decomposition on the radar echo time matrix Y. N This can characterize the energy distribution of different echo components.

[0036] Since the largest singular value is usually significantly larger than other singular values, directly using the original singular values ​​as features for cluster analysis can easily lead to the clustering process being dominated by large singular values, thereby reducing the ability to distinguish weak targets or detailed features. Therefore, it is necessary to perform logarithmic compression on the singular values ​​to reduce the amplitude differences between singular values, reduce the dominance of large singular values ​​in the feature space, and distribute the singular value features within a certain order of magnitude, thereby improving the stability and effectiveness of clustering based on singular value features. The expression for the logarithmically compressed i-th singular value is as follows:

[0037] d′ i =log 10 (1+d i (7)

[0038] Sub-step 2.2: Calculate the Doppler bandwidth of the radar echo data. In a strong sea clutter environment, the sea surface is affected by weather conditions such as wind and waves, causing the Doppler bandwidth of sea clutter to broaden. However, the target's velocity within the range gate remains relatively constant, resulting in a narrower Doppler bandwidth compared to clutter. Therefore, calculating the Doppler bandwidth of each component can be used as a feature to distinguish clutter from the target. The Doppler bandwidth represents the physical meaning of the second-order center distance of the Doppler spectrum, which can be obtained by performing SVD decomposition on Y, resulting in the left characteristic matrix U = [u1, u2, ..., u...]. N ] T The Doppler bandwidth w corresponding to the kth singular value component is obtained. k The calculation formula is as follows:

[0039] w k =E{[u k -E(u k )]2} (8)

[0040] Sub-step 2.3: Calculate the relative Doppler variation coefficient of the radar echo data. Compared to clutter, the Doppler peaks of targets at range gates are clearer and sharper, while the Doppler peaks of sea clutter are more dispersed. Therefore, clutter and targets can be distinguished by calculating the concentration of the Doppler peaks of the components corresponding to each singular value. The Doppler variation coefficient CV of the component corresponding to the k-th singular value. k The expression is:

[0041]

[0042] The relative Doppler coefficient (RCV) of the component corresponding to the k-th singular value. k The expression is:

[0043]

[0044] Sub-step 2.4 calculates the cross-correlation of the radar echo components. Since the spatial cross-correlation between clutter scattering points at different range gates is high, while the noise component exhibits high randomness, and the target component exists only in one or a few range gates, the spatial correlation between the clutter component, target component, and noise component in the echo signal is low. Therefore, the fourth set of features can be obtained by calculating the cross-correlation within the subspace represented by each singular value.

[0045] Since the energy distribution of sea clutter is much larger than that of the target component and the noise component, the first singular value in the singular value sequence after sorting from largest to smallest represents the clutter component. Therefore, the cross-correlation between different components and the clutter component can be obtained by calculating the cross-correlation between the remaining singular value vectors and the first singular value vector. The expression for the cross-correlation between the k-th component and the clutter component after SVD decomposition is:

[0046]

[0047] Among them, u k Let σ1 and σN be the eigenvectors of the left vector matrix corresponding to the k-th singular value, 1≤k≤N. k They are u1 and u k The standard deviation is E[*], which represents the expected value.

[0048] Step 3: Based on the four features corresponding to each singular value obtained in Step 2, the four statistical features are normalized by min-maximum and used as input for K-means singular value clustering. The singular values ​​representing the clutter subspace are determined by adaptive clustering of K-means sub-clusters. Finally, the echo signal is mapped to the orthogonal subspace of clutter to achieve the purpose of suppressing sea clutter.

[0049] Sub-step 3.1 involves normalizing the data for the four features calculated in step 2. Since the core idea of ​​K-means is to calculate the similarity between data points and cluster centers based on Euclidean distance, and to iteratively optimize and adjust the position of the center points until the algorithm converges or meets the maximum number of iterations, to avoid significant differences in the units and scales of different feature data, which could cause features with larger numerical ranges to dominate the distance calculation between samples and mask the role of other discriminative features, thus causing the clustering results to deviate from the true data structure, it is necessary to perform min-max normalization on the four feature data obtained in step 2. This maps each feature to a uniform numerical scale, eliminating the influence of unit and scale differences on the distance calculation, thereby improving the stability and rationality of the clustering results. The min-max normalization formula is:

[0050]

[0051] Where x i Let x represent the i-th value in a set of feature data. max and x min These represent the minimum and maximum values ​​in a set of feature data. After normalizing the four feature data from step 2, we obtain the dataset I = {x1, x2, ..., x...} for K-means clustering. N}

[0052] Sub-step 3.2 involves performing K-means clustering on dataset I. Since the echo contains clutter, signal, and noise components, the clustering results can be divided into three classes. The K-means clustering steps are as follows:

[0053] (1) Initialization: Select the first group, the last group and the middle group from the given dataset as the initial cluster centers as the initial centroid set O = (o1, o2, o3).

[0054] (2) Calculate x for each sample i With each centroid o i The weighted Euclidean distance d(x) i o j The i-th sample is assigned to the cluster containing the nearest centroid. The weighted Euclidean distance between the i-th sample and the j-th centroid is defined as the weighted sum of squares of the differences in each feature dimension, and its calculation formula is:

[0055]

[0056] Where x i，l o represents the value of the i-th sample in the l-th feature dimension. i，l λ represents the value of the j-th centroid on the l-th feature dimension. lThis represents the weighting coefficient for the l-th feature.

[0057] The mean of the samples within each cluster after partitioning (2) is used to update the new centroid of each cluster. The formula for calculating the new centroid is as follows:

[0058]

[0059] Determine whether the number of iterations has been reached or whether the distance between the newly selected centroid and the previous centroid is less than a threshold. If the stopping condition is met, output the data contained in the final three clusters and their data; if the stopping condition is not met, repeat (2) and (3).

[0060] After K-means clustering, the N singular values ​​will be divided into three clusters. Since the largest singular value must represent the clutter subspace, the cluster containing the largest singular value is the set of singular values ​​C of the clutter. c .

[0061] Sub-step 3.3: Based on the clustering results obtained in step 3.2, utilize the clutter singular value set C c Constructing the clutter subspace matrix P c The calculation formula is as follows:

[0062]

[0063] A subspace matrix P orthogonal to the clutter subspace is constructed based on the least squares method. 1 / c expression:

[0064]

[0065] Where I is the identity matrix.

[0066] Finally, the radar fast and slow time echo signal matrix Y is mapped to P. 1 / c Clutter suppression is performed in the subspace, and the processed echo signal is then subjected to MTI and MTD before target detection.

[0067] Step 4: Assuming the radar transmit waveform is a linear frequency modulated signal, the target and clutter are superimposed in both the time and frequency domains, and the clutter broadens in the Doppler domain with varying scattering velocities at each clutter point, a simulation experiment is conducted on a computer. K-means adaptive partitioning of the clutter subspace is used to achieve both sea clutter suppression and target detection.

[0068] Specifically, step 4 includes the following:

[0069] The simulation parameter settings are shown in Table 1:

[0070] Table 1 Simulation parameter settings

[0071] Parameter name Parameter size <![CDATA[Initial carrier frequency f0]]> 3GHz Number of transmitted pulses N 16 <![CDATA[Pulse repetition period T r > 1200us <![CDATA[Time width T p > 100us Bandwidth B 1MHz <![CDATA[Sampling frequency f s > 2MHz

[0072] Target 1 is positioned 63.6 km from the radar with a radial velocity of 9 m / s. Target 2 is positioned 55 km from the radar with a radial velocity of 1 m / s. The clutter range is 50 km–70 km, with an average radial velocity of 5 m / s at the clutter scattering point and a velocity variance of 0.2 m / s.

[0073] The MTD result of radar echo signals without any processing is as follows: Figure 2 As shown in the figure, the targets overlap with clutter in both the time and frequency domains. The calculated signal-to-clutter ratio (SCR) for target 1 is -6.6 dB, and for target 2 it is -6.9 dB. The targets are completely submerged by strong sea clutter and cannot be effectively detected.

[0074] Based on experience, the MTD result of the SVD algorithm, which only partitions the largest singular value into a clutter subspace, is as follows: Figure 3 As shown. By Figure 3 It is evident that using only the largest singular value to construct the clutter subspace has limited suppression effect. After discarding the largest component within the clutter, the clutter power decreases somewhat; the calculated signal-to-clutter ratio (SCR) for target 1 is 24.46 dB, and for target 2 it is 24.1 dB. However, due to the insufficient precision in the clutter subspace division, there is a significant residual clutter power, which is detrimental to target detection.

[0075] The MTD result of the SVD algorithm for subspace partitioning of sea clutter using K-means clustering results is as follows: Figure 4 As shown. By Figure 4 It can be seen that by using clustering results to divide the clutter subspace, four features can be adaptively used to select singular values ​​within the singular values ​​after SVD decomposition. This allows for accurate and effective construction of the clutter subspace, mapping the target signal into the orthogonal space of the constructed clutter subspace, effectively suppressing sea clutter. The calculated signal-to-clutter ratio (SCR) for target 1 is 37.5, and for target 2 it is 36.9 dB. Based on... Figure 4 The results show that the SVD sea clutter suppression method based on improved k-means can effectively suppress sea clutter and is helpful for target detection.

Claims

1. A method for suppressing SVD sea clutter based on improved K-means, characterized in that, Includes the following steps: Step 1: After pulse compression of the radar echo signal, establish the radar echo fast and slow matrix Y. Then, perform SVD decomposition on the fast and slow matrix Y to obtain the left vector matrix U containing Doppler information, the right vector matrix V containing spatial information, and the singular value diagonal matrix S. Step 2: Calculate the features of the four input K-means clusters using the SVD results obtained in Step 1. The four features are the singular value spectral distribution, echo component cross-correlation, Doppler bandwidth, and relative Doppler variation coefficient. Step 3: Based on the four features corresponding to each singular value obtained in Step 2, the four statistical features are normalized by min-maximum and used as input for K-means singular value clustering. The singular values ​​of the clutter subspace are adaptively divided by K-means clustering. Finally, the echo signal is mapped to the orthogonal subspace of the clutter to achieve the purpose of suppressing sea clutter.

2. The SVD sea clutter suppression method based on improved K-means as described in claim 1, characterized in that, Step 1 includes the following sub-steps: Sub-step 1.1: The radar transmits a linear frequency modulated signal, with N transmitted pulses and M sampling points per pulse. The radar receives the nth echo signal x. n The expression for (t) is: Where S n (t) represents the signal component in the echo, c n (t) represents the clutter component, and n(t) represents the noise component. A represents the amplitude of the received signal, and T r T represents the repetition period of the radar pulse. p Let f0 represent the radar pulse width, f0 be the carrier frequency, τ be the signal echo delay, and μ be the tuning frequency. Their expressions are as follows: Where R0 represents the distance between the target and the radar, v0 represents the target's speed, and B represents the frequency modulation bandwidth. Sub-step 1.2: Arrange the N radar echo pulses into a one-dimensional array according to the echo order to obtain the total radar echo signal E(t). After pulse compression, rearrange the radar echo signal according to the transmitted pulse order to form the radar echo time matrix Y, expressed as: Sub-step 1.3: Based on the radar echo fast / slow matrix Y obtained in sub-step 1.2, perform SVD decomposition, the expression of which is: Where U is the left vector matrix, D is the diagonal matrix composed of singular values, and V is the right vector matrix. S, C, and N represent the singular values ​​represented by the target, clutter, and noise subspaces. The superscript H represents the conjugate transpose. λ i Let u represent the i-th singular value, and let u be the singular value arranged in descending order. i Let v represent the column vector corresponding to the i-th singular value of U. i This represents the right column vector corresponding to the i-th singular value.

3. The SVD sea clutter suppression method based on improved K-means according to claim 2, characterized in that, Step 2 includes the following sub-steps: Sub-step 2.1 calculates the singular value spectrum distribution of the radar echo data. In a strong sea clutter environment, the signal-to-clutter ratio (SCR) of small, slow-moving target echoes will be lower, and the energy of the clutter component will be much greater than that of the target component. Therefore, the energy proportions of clutter, signal, and noise in the echo signal can be used as an important feature for distinguishing singular values. Each singular value obtained by performing SVD decomposition on the radar echo time matrix Y can characterize the energy distribution of different echo components. Since the largest singular value is usually significantly larger than the others, directly using the original singular values ​​as features for cluster analysis can easily lead to the clustering process being dominated by the large singular value, thereby reducing the ability to distinguish weak targets or detailed features. Therefore, it is necessary to perform logarithmic compression on the singular values ​​to reduce the amplitude differences between them, decrease the dominance of the large singular value in the feature space, and ensure that the singular value features are distributed within the same order of magnitude, thereby improving the stability and effectiveness of clustering based on singular value features. Sub-step 2.2: Calculate the Doppler bandwidth of the radar echo data. In a strong sea clutter environment, the sea surface is affected by weather conditions such as wind and waves, causing the Doppler bandwidth of sea clutter to broaden. However, the target's velocity within the range gate remains relatively constant, resulting in a narrower Doppler bandwidth compared to clutter. Therefore, calculating the Doppler bandwidth of each component can be used as a feature to distinguish clutter from the target. The Doppler bandwidth represents the physical meaning of the second-order center distance of the Doppler spectrum, which can be obtained by performing SVD decomposition on Y, resulting in the left characteristic matrix U = [u1, u2, ..., u...]. N ] T The Doppler bandwidth w corresponding to the kth singular value component is obtained. k The calculation formula is as follows: w k =E{[u k -E(u k )] 2 } Sub-step 2.3: Calculate the relative Doppler variation coefficient of the radar echo data. Compared to clutter, the Doppler peaks of targets at range gates are clearer and sharper, while the Doppler peaks of sea clutter are more dispersed. Therefore, clutter and targets can be distinguished by calculating the concentration of the Doppler peaks of the components corresponding to each singular value. The Doppler variation coefficient CV of the component corresponding to the k-th singular value. k The expression is: The relative Doppler coefficient (RCV) of the component corresponding to the k-th singular value. k The expression is: Sub-step 2.4 calculates the cross-correlation of the radar echo components. Since the spatial cross-correlation between clutter scattering points at different range gates is high, while the noise component exhibits high randomness, and the target component exists only in one or a few range gates, the spatial correlation between the clutter component, target component, and noise component in the echo signal is low. Therefore, the fourth set of features can be obtained by calculating the cross-correlation within the subspace represented by each singular value. Furthermore, since the energy distribution of sea clutter is much larger than that of the target component and the noise component, the first singular value in the singular value sequence after sorting from largest to smallest represents the clutter component. Therefore, the cross-correlation between different components and the clutter component can be obtained by calculating the cross-correlation between the remaining singular value vectors and the first singular value vector. The expression for the cross-correlation between the k-th component and the clutter component after SVD decomposition is: Among them, u k Let σ1 and σN be the eigenvectors of the left vector matrix corresponding to the k-th singular value, 1≤k≤N. k They are u1 and u k The standard deviation is E[*], which represents the expected value.

4. The SVD sea clutter suppression method based on improved K-means according to claim 3, characterized in that, Step 3 includes the following sub-steps: Sub-step 3.1 involves normalizing the data for the four features calculated in step 2. Since the core idea of ​​K-means is to calculate the similarity between data points and cluster centers based on Euclidean distance, and to iteratively optimize and adjust the position of the center points until the algorithm converges or meets the maximum number of iterations, to avoid excessively large differences in feature data values ​​leading to a bias towards high-scale features and weakening other features, thus affecting the effectiveness and correctness of clustering, it is necessary to perform min-max normalization on the four feature data obtained in step 2, ensuring that all data values ​​are between [0, 1]. The min-max normalization formula is: Where x i Let x represent the i-th value in a set of feature data. max and x min These represent the minimum and maximum values ​​in a set of feature data. After normalizing the four feature data from step 2, we obtain the dataset I to be used for K-means clustering. Sub-step 3.2 involves performing K-means clustering on dataset I. Since the echo contains clutter, signal, and noise components, the clustering results are divided into three classes. Furthermore, to address the sensitivity of K-means to initial centroids, a specified initial centroid is used instead of the original random selection. The k-means clustering steps are as follows: (1) Initialization: Select three centroids from the given dataset as initial centroids. (2) Calculate the weighted Euclidean distance between each sample and the three centroids, and assign it to the cluster containing the nearest centroid. (3) Calculate the mean of the samples in each cluster after (2) partitioning, and update the centroid of each cluster. (4) Determine if the iteration count has been reached or if the distance between the newly selected centroid and the previous centroid is less than a threshold. If the stopping condition is met, output the data contained in the final three clusters and their data. If the stopping condition is not met, repeat (2) and (3). After K-means clustering, the N singular values ​​will be divided into three clusters. Since the largest singular value must represent the clutter subspace, the cluster containing the largest singular value is the set of singular values ​​C of the clutter. c . Sub-step 3.3: Based on the clustering results obtained in step 3.2, utilize the clutter singular value set C c Constructing the clutter subspace matrix P c The calculation formula is as follows: The expression for the subspace matrix P1 / c, which is orthogonal to the clutter subspace, is constructed based on the least squares method: Where I is the identity matrix. Finally, the radar fast and slow time echo signal matrix Y is mapped onto the P1 / c subspace to complete clutter suppression. The processed echo signal is then subjected to MTI and MTD tests to observe the clutter suppression results.

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