A sea clutter suppression method

Abstract

The application discloses a sea clutter suppression method, step 1, after pulse compression of a target reflection echo signal sequence received by a radar, the echo signal is rearranged into a fast and slow time dimension echo matrix X c , one row represents one period; step 2, the target echo signal rearranged into the fast and slow time dimension echo matrix X c is removed from the correlation between the sea clutter by using a principal component analysis method without changing the feature dimension, and a decorrelated target echo signal X p is obtained; step 3, the decorrelated target echo signal X p is subjected to periodic singular value decomposition, the clutter is suppressed, and the target echo signal is reconstructed. The application does not depend on a sea clutter model, has good universality and effectiveness, and better solves the problem that a slow moving target with a spectrum coinciding with a target is difficult to distinguish by a traditional subspace type suppression algorithm, leading to a too high target false alarm rate.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of radar clutter processing, and relates to a sea clutter suppression method, in particular to a sea clutter suppression method adopting principal component analysis and periodic singular value decomposition (PCA-SVD). BACKGROUND

[0002] In the echo signal received by a radar receiver, not only target reflection echo but also a large amount of sea surface backscattering echo interference (i.e. sea clutter) is often submerged in the target echo signal, and when the sea wave length is approximately equal to the half wave length of the electromagnetic wave, resonance occurs, which increases the sea clutter energy and also produces Doppler frequency shift, seriously restricting the detectability of the sea surface slow small target.

[0003] At present, sea clutter suppression technologies based on different principles mainly include sea clutter suppression methods based on cyclic iteration cancellation, model prediction, fractal characteristics and subspace decomposition. The cyclic iteration cancellation refers to that the main component of the sea clutter is approximated as a sine signal, and then the time domain form of the radar echo and the estimated sine signal are subtracted one by one to realize the suppression of the sea clutter. This method cannot determine the specific number of cyclic cancellation iterations, and when the amplitudes of the target signal and the sea clutter are difficult to distinguish, the target signal is easily mistaken. The sea clutter model prediction refers to that a series of linear or nonlinear prediction methods are used to model the sea clutter, such as support vector machine (SVM) prediction. However, this method depends on the initialization of various training networks, and the structure parameters are mostly selected by humans, and do not have universal applicability. The sea clutter suppression method based on fractal characteristics is based on the different fractal dimensions of the sea clutter and the target echo. When an artificial target appears in the vicinity of the sea clutter, the Hurst index will change. However, this method is only suitable for low dimensions, and only relying on fractal theory cannot completely meet the needs of target detection. The subspace-based clutter suppression algorithm is based on the different clustering characteristics of the clutter in the subspace. When the target is in the Doppler frequency range of the sea clutter or the frequencies of the two are close, the target is mistaken. Therefore, for the sea surface slow small target, how to effectively suppress the clutter interference when the target and the sea clutter spectrum overlap is the research focus in the field of radar target detection. SUMMARY

[0004] In view of the above prior art, the technical problem to be solved by the present application is to provide a sea clutter suppression method adopting principal component analysis and periodic singular value decomposition (PCA-SVD) to effectively suppress the clutter interference when the target and the sea clutter spectrum overlap.

[0005] To solve the above technical problem, a sea clutter suppression method according to the present application comprises the following steps:

[0006] Step 1, after pulse compression of the target reflection echo signal sequence received by the radar, the echo signal is rearranged by period into a fast-slow time dimension echo matrix X c , and one row represents one period;

[0007] Step 2, the target echo signal rearranged by period into a fast-slow time dimension echo matrix X c is removed from the correlation between sea clutter by principal component analysis method without changing the feature dimension, and the decorrelated target echo signal X p is obtained.

[0008] Step 3, the decorrelated target echo signal X p is subjected to periodic singular value decomposition to suppress clutter and reconstruct the target echo signal.

[0009] Further, the echo signal rearranged by period into a fast-slow time dimension echo matrix form in step 1 is:

[0010]

[0011] Wherein, X c is an echo data matrix of N*L, N is the number of pulse accumulation, L is the number of distance units, j is the imaginary unit, w d is the Doppler frequency of the echo signal, T r is the pulse repetition period; x e (t) is the echo model of a single target in the nth period, which satisfies:

[0012]

[0013] Wherein, t is the time of the transmitted signal, n is the number of transmission periods, τ is the echo delay when t=0 and the target moves radially relative to the radar, τ=2(R0-vt n ) / c, wherein R0 is the distance of the target relative to the radar, v is the speed of uniform motion, t n =nT r , the frequency modulation is defined as μ=B / T p , T p is the pulse width of the radar, B is the frequency modulation bandwidth, f c is the carrier frequency, c(t) is the clutter, and n(t) is the Gaussian white noise generated by the receiver.

[0014] Further, the target echo signal rearranged by period into a fast-slow time dimension echo matrix X c in step 2 is removed from the correlation between sea clutter by principal component analysis method without changing the feature dimension, and the decorrelated target echo signal X p includes:

[0015] Step 2.1, centering all samples so that the fast and slow time dimension echo matrix X c The mean of each dimension of data is 0, and the centered matrix X c1 Satisfies:

[0016] Step 2.2, calculate the covariance matrix

[0017] Step 2.3, eigenvalue decomposition of the covariance matrix X, get the matrix composed of eigenvectors Φ and the diagonal matrix composed of eigenvalues Λ;

[0018] Step 2.4, convert the covariance matrix X into a diagonal matrix Λ to get the diagonalized covariance matrix Y:

[0019] Y = E(yy T )

[0020] = E(Φ T X c (Φ T X c ) T )

[0021] = Λ

[0022] Where, y = Φ T X c ;

[0023] Multiply Y and X c1 , get the dimension of N x L of the decorrelated target echo signal X p .

[0024] Further, step 3 described above for the decorrelated target echo signal X p Periodic singular value decomposition is performed to suppress clutter and reconstruct the target echo signal, including:

[0025] Step 3.1, the principal component analysis of the target echo signal is expressed as Each row of X p Hankel matrix is constructed in turn:

[0026]

[0027] Where, L = m + k - 1, m ≤ k, when L is even, m = L / 2, k = L / 2 + 1; When L is odd, m = (L + 1) / 2, k = (L + 1) / 2;

[0028] Step 3.2, singular value decomposition of X i

[0029] ​​

[0030] where C and D represent the singular value sets of the sea clutter subspace and the target subspace respectively, the superscript H represents the conjugate transpose of a matrix, u i and v i are the i-th left singular column vector and right singular column vector of the matrix X i respectively, and δ i is the i-th singular value arranged in descending order.

[0031] Step 3.3, after determining the singular value set D representing the target subspace, the target signal is recovered through matrix reconstruction:

[0032]

[0033] The present application has the following beneficial effects:

[0034] The present application is directed to the problem that the conventional subspace-based suppression algorithm is difficult to distinguish the slow target with the spectral overlap of the target and the sea clutter, and the target is often mis-eliminated. A sea clutter suppression method under PCA-SVD is provided. For the slow target with the spectral overlap of the target and the sea clutter, principal component analysis is performed according to the strong time correlation of the sea clutter in the echo, and decorrelation operation is performed without changing the feature dimension. On this basis, according to the characteristics of the sea clutter, periodic singular value decomposition is adopted to concentrate the sea clutter energy on a small number of singular values and concentrate the target signal energy on most singular values, so that the sea clutter can be suppressed while the target echo signal can be effectively protected. The present application does not depend on the sea clutter model, has good universality and effectiveness, and better solves the problem that the conventional subspace-based suppression algorithm is difficult to distinguish the slow target with the spectral overlap of the target and the sea clutter, resulting in the problem of too high target false alarm rate. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is the principle block diagram of the sea clutter suppression algorithm under PCA-SVD. DETAILED DESCRIPTION

[0036] The present application will be further described below in combination with the drawings and examples of the specification.

[0037] The application is based on the time correlation characteristics of sea clutter and the different gathering characteristics of target signals and clutter signals in a subspace, and proposes a sea clutter suppression method under PCA-SVD. First, the radar receiver performs pulse compression on the received target reflection echo, rearranges the signal period into a fast-slow time dimension matrix, constructs a time correlation model of the target echo signal, and ensures that the principal component analysis (PCA) is performed without changing the feature dimension. On this basis, according to the characteristics of the clutter, periodic singular value decomposition (SVD) is used, and finally signal reconstruction is performed to realize adaptive suppression of sea clutter interference. For a slow-moving target with overlapping target and clutter spectra, the method can concentrate the dispersed sea clutter energy on a few singular values, reduce the overlap between the target signal and the sea clutter, effectively distinguish the target, and cause less damage to the target signal when eliminating the interference components. The application does not need to model the sea clutter, and through pulse compression, principal component analysis and periodic singular value decomposition, the sea clutter suppression problem is converted into the selection problem of the de-correlated singular values. The application can still accurately divide the signal and sea clutter when the target and sea clutter spectra overlap, and reduce the target false alarm probability.

[0038] To more clearly illustrate the method applied, the embodiments of the application perform flow process illustration and effect display through simulation experiments, but do not limit the scope of the embodiments of the application, and the specific parameter settings are shown in Table 1.

[0039] Table 1 Experimental parameter settings

[0040]

[0041] Figure 1 The figure is a principle block diagram of the method, and the method comprises:

[0042] Step 1: After pulse compression of the target reflection echo sequence received by the radar, the echo signal is rearranged into a fast-slow time matrix form according to the period, and one row represents one period. The specific steps are as follows:

[0043] ①The radar transmitter transmits a linear frequency modulation signal, t is the time of the transmitted signal, n is the number of transmission periods, the radar pulse width is T p , the pulse repetition period is T r , the frequency modulation bandwidth is B, the frequency modulation rate is defined as μ=B / T p , the carrier frequency is f c , j is the imaginary unit, and the transmitted signal S n (t) of the radar in the nth transmission period is

[0044]

[0045] ②Assume that the distance of the target relative to the radar is R0, the speed of uniform motion is v, and the target moves radially relative to the radar when t = 0, the echo delay of the target can be expressed as τ = 2(R0-vt n ) / c, t n =nT r , c is the speed of light, t is the time of receiving the signal, and the echo model x e (t) of a single target in the nth cycle can be obtained.

[0046]

[0047] In the formula, c(t) is clutter, and n(t) is Gaussian white noise generated by the receiver.

[0048] ③After pulse compression processing is performed on the obtained echo signal x e (t), the signal is rearranged into a fast-slow time dimension echo matrix according to the signal cycle.

[0049]

[0050] In the formula, X c is an N×L echo data matrix, N is the number of pulse accumulations, L is the number of distance units, j is an imaginary unit, and w d is the Doppler frequency of the echo signal.

[0051] Step 2: Construct a time correlation model for the target echo signal, and perform principal component analysis to ensure that the correlation between the sea clutter is removed without changing the feature dimension. The specific steps are as follows:

[0052] ①From the composite scattering theory, the time correlation of sea clutter is considered, and the sea clutter is divided into speckle components and texture components. The correlation time of the speckle component is millisecond level, and it obeys Rayleigh distribution within a short time resolution unit, and after frequency agility, the pulses can be considered as completely uncorrelated. The correlation time of the texture component is second level, and it is not affected by frequency agility, and its statistical characteristics represent the non-Gaussian nature of sea clutter. Therefore, the time correlation of sea clutter is a process of rapid decline first and then slow periodic decay. Generally speaking, the time of decorrelation of the texture component is much longer than the processing time of the sea clutter signal. Therefore, when the radar performs signal correlation processing, the time correlation of the texture component can be ignored, and the overall correlation of the target echo signal depends on the correlation of the speckle component. The time autocorrelation function R k of the target signal, i.e., the speckle component, is defined as:

[0053]

[0054] In the formula, R k represents the time correlation function with k sampling points, and X cis a complex echo data matrix of N x L, is the conjugate form of the matrix.

[0055] After the target signal time correlation formula is constructed according to the sea clutter characteristics, the radar received data is subjected to principal component analysis operation. The main principle of the PCA algorithm is to map the n-dimensional characteristics of high-dimensional data to k-dimensional, and reduce the dimension k of the low-dimensional space. The new matrix X obtained after the sea radar receiver performs pulse compression on the target scattering echo signal is known from step 1. c One row represents one target signal period. When the PCA operation is performed on the matrix to remove the correlation between the sea clutter, it is necessary to ensure that the dimensions have distinguishability without changing the feature dimension. The specific steps are as follows:

[0056] 1. Center all samples to make the fast and slow time echo matrix X c The mean value of each dimension of data is 0, and the centered matrix is X c1

[0057] 2. Calculate the covariance matrix of the data

[0058] 3. Perform eigenvalue decomposition on the covariance matrix X to obtain the matrix Φ composed of eigenvalue vectors and the diagonal matrix Λ composed of eigenvalues.

[0059] 4. De-correlation: convert the covariance matrix X into a diagonal matrix Λ, and Y is the diagonalized covariance matrix. It can be known from the covariance matrix formula that

[0060] X = E(X c X c T )

[0061] It can be known from the matrix theory knowledge that

[0062] Φ T = Φ -1

[0063] XΦ = ΦΛ

[0064]

[0065] Let y = Φ T X c , and

[0066] Y = E(yy T )

[0067] = E(Φ T X c (Φ T X​c ) T )

[0068] =Λ

[0069] After diagonalization, the covariance matrix Y is obtained, all elements on the main diagonal are not the same, and it is multiplied by X c1 , to obtain the decorrelated target echo signal X p with a dimension of N×L.

[0070] Step 3: Perform periodic singular value decomposition on the target reflection echo signal, concentrate the decorrelated sea clutter energy on a few singular values, and concentrate the target signal energy on most singular values, suppress the clutter and reconstruct the target echo signal.

[0071] ①The echo signal after principal component analysis can also be expressed as Each row of X p Hankel matrix is constructed in turn:

[0072]

[0073] Where, L=m+k-1, m≤k, and the closer m and k are, the better the processing effect on the signal. Therefore, when L is even, take m=L / 2, k=L / 2+1; when L is odd, then m=(L+1) / 2, k=(L+1) / 2.

[0074] ②Perform singular value decomposition on X i

[0075]

[0076] In the formula, C and D represent the singular value set of the sea clutter subspace and the target subspace respectively, the superscript H represents the conjugate transpose of the matrix, u i and v i are the i-th left singular column vector and right singular column vector of matrix X i , respectively, and δ i is the i-th singular value arranged in descending order.

[0077] ③After determining the singular value set D representing the target subspace, the target signal is recovered by matrix reconstruction, that is,

[0078]

[0079] ​​To verify the performance of the PCA-SVD algorithm under different input signal-to-clutter ratios, we will test the suppression effect of the OP algorithm, the OP-SVD algorithm, the SVD-FRFT algorithm and the PCA-SVD algorithm according to different input signal-to-clutter ratios before detection, and the results are shown in Table 2. It can be found that the PCA-SVD algorithm is still effective when the input signal-to-clutter ratio is-20 dB, while the other three algorithms are not as wide-ranging as the SVD-MTI algorithm, and the output signal-to-clutter ratio is lower than that of the SVD-MTI. The OP algorithm only achieves one clutter suppression in the orthogonal subspace, so the suppression effect is not as significant as the method in this paper; although the SVD-FRFT algorithm achieves signal energy aggregation under the optimal order, it still cannot detect the target signal when the radar echo signal-to-clutter ratio is low; and the OP-SVD algorithm relies on the correlation between the unit to be tested and the adjacent unit, and the suppression effect is not obvious.

[0080] As can be seen from Table 2, as the input signal-to-clutter ratio increases, the output signal-to-clutter ratio gain after PCA-SVD processing shows a gradually decreasing trend. This is because when the input target signal power is too large, the target signal will gradually disperse into multiple signal components, and only part of the signal components are retained during signal purification, causing a small amount of target signal power leakage.

[0081] Table 2 Suppression of four algorithms under different input signal-to-clutter ratios

[0082]

[0083] In summary, in this embodiment, the target echo signal after pulse compression is rearranged according to the period to form a fast-slow time dimension matrix; then a time correlation model of the target echo signal is constructed and principal component analysis is performed without changing the feature dimension; on this basis, periodic singular value decomposition is used according to the characteristics of the clutter, and finally signal reconstruction is performed to achieve adaptive suppression of sea clutter interference. The method can still suppress most of the clutter and accurately detect the target signal when the target and sea clutter spectrum overlap, and while suppressing the clutter, it also ensures that the loss of the target signal is minimized.

[0084] Those skilled in the art can understand that in the above method of the specific embodiments of the present application, the sequence number of each step does not mean the order of execution, and the execution order of each step should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the specific embodiments of the present application.

[0085] Finally, it should be noted that the above embodiments are only used to describe the technical solutions of the present application and not to limit the technical method, and the present application can be extended to other modifications, changes, applications and embodiments, and therefore all such modifications, changes, applications, embodiments are considered to be within the spirit and teachings of the present application.

Claims

1. A sea clutter suppression method, characterized by, The method comprises the following steps: Step 1, after pulse compression of the target reflection echo signal sequence received by the radar, the echo signal is rearranged into a fast-slow time dimension echo matrix X according to the period c , and one row represents one period; The echo signal is rearranged into a fast-slow time dimension echo matrix form in a cycle: where X c is an N x L echo data matrix, N is the number of pulse accumulations, L is the number of range bins, j is the imaginary unit, w d is the Doppler frequency of the echo signal, T r is the pulse repetition period; x e (t) is the echo model of a single target in the n-th cycle, which satisfies: where t is the time of the transmitted signal, n is the number of transmitted periods, τ is the echo delay when t = 0 and the target moves radially relative to the radar, τ = 2(R0-vt) / c, where R0 is the distance of the target relative to the radar, v is the speed of uniform motion, t = nT, the frequency modulation is defined as μ = B / T, T is the radar pulse width, B is the frequency modulation bandwidth, f is the carrier frequency, c(t) is clutter, and n(t) is the Gaussian white noise generated by the receiver. n n r p p c where t is the time of the transmitted signal, n is the number of transmitted periods, τ is the echo delay when t = 0 and the target moves radially relative to the radar, τ = 2(R0-vt) / c, where R0 is the distance of the target relative to the radar, v is the speed of uniform motion, t = nT, the frequency modulation is defined as μ = B / T, T is the radar pulse width, B is the frequency modulation bandwidth, f is the carrier frequency, c(t) is clutter, and n(t) is the Gaussian white noise generated by the receiver.​​​​​ Step 2, rearranging the echo matrix X into fast and slow time dimensions by period c The principal component analysis method is used to remove the correlation between sea clutter and target echo signals without changing the feature dimension, and the decorrelated target echo signal X p is obtained. Step 2.

1. Center all samples so that the fast and slow time dimension echo matrix X c The mean of each dimension of data is 0, the centered matrix X c1 Satisfies: Step 2.2, computing the covariance matrix Step 2.3, eigenvalue decomposition is performed on the covariance matrix X to obtain a matrix Φ composed of eigenvalue vectors and a diagonal matrix Λ composed of eigenvalues; Step 2.4, the covariance matrix X is converted into the diagonal matrix Λ to obtain a diagonalized covariance matrix Y: Y = E(yy T ) = E(Φ T X c (Φ T X c ) T ) Wherein, L = m + k - 1, m <= k, when L is even, m = L / 2, k = L / 2 + 1; when L is odd, m = (L + 1) / 2, k = (L + 1) / 2; where y = Φ T X c ; Y is multiplied by X to obtain a decorrelated target echo signal X of dimension N x L c1 p ;​ Step 3, decorrelating the target echo signal X p performing periodic singular value decomposition, suppressing clutter and reconstructing the target echo signal Step 3.1, Represent the target echo signal after principal component analysis as For X p each row Hankel matrix is constructed sequentially: Step 3.3, after the singular value set D representing the target subspace is determined, the target signal is recovered through matrix reconstruction: Step 3.2, X i Perform singular value decomposition: where C, D represent the singular value sets of the sea clutter subspace and the target subspace respectively, the superscript H represents the conjugate transpose of a matrix, u i and v i are the i-th left singular column vector and right singular column vector of the matrix X i respectively, and δ i is the i-th singular value arranged in descending order; ​

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