Singular value decomposition-improved sea clutter suppression algorithm

Abstract

Provided in the present invention is a singular value decomposition-improved sea clutter suppression algorithm, comprising: first rearranging, according to periods, pulse-compressed target echo signals into a matrix having fast-time and slow-time dimensions, and carrying out periodic singular value decomposition; then constructing the relationship between a threshold of a singular value corresponding to the signals and an input signal to clutter plus noise ratio (SCNR), and using the threshold to judge a singular value index ratio, so as to realize self-adaptive differentiation between sea clutter and a target signal; and finally, performing double-delay line cancellation on the reconstructed target signal. The method of the present application can adapt to changes of the signal to clutter plus noise ratio of target echo sequences, ensuring minimization of loss of target signals while suppressing sea clutter.

Description

An improved singular value decomposition algorithm for sea clutter suppression Technical Field

[0001] The present invention belongs to the field of radar clutter processing and relates to a sea clutter suppression method based on improved singular value decomposition. Background Art

[0002] Sea clutter refers to the backscattered echoes from electromagnetic waves emitted by radar hitting the ocean surface. Influenced by the ocean's meteorological and geographical environments, the sea surface structure is complex and ever-changing, and the electromagnetic scattering mechanism is highly complex. At low angles of incidence and high resolution, sea clutter often exhibits "three non-" characteristics: non-uniformity, non-Gaussianity, and non-stationary statistical and physical properties. Furthermore, the echo signals of surface targets are subject to interference from sea clutter and other signals in both the time and frequency domains, severely limiting their detectability.

[0003] Currently, methods for suppressing sea clutter can be roughly divided into three categories: first, time-domain sea clutter cancellation, which includes model-based, cyclic, and predictive cancellation methods; second, wavelet transform-based methods; and third, subspace-based suppression algorithms. The first two methods face certain difficulties in practical engineering applications: time-domain sea clutter cancellation requires the establishment of a model that closely matches the performance of real sea clutter; otherwise, large errors will occur. However, existing sea clutter models are not universally applicable, resulting in limited sea clutter suppression effectiveness in practical applications; wavelet transform-based suppression methods can only achieve good results if appropriate basis functions are selected, and this method can destroy the phase information of the received signal. Subspace-based clutter suppression algorithms, however, have been widely used in radar target detection due to their strong ability to extract weak target features, simple algorithms, and ease of engineering implementation.

[0004] The essence of subspace-based suppression algorithms is to suppress sea clutter by separating clutter subspaces based on the differences in the aggregation characteristics of clutter and target signals within a subspace. Depending on the clutter subspace estimation method, they can be further categorized into eigenvalue decomposition and singular value decomposition. Eigenvalue decomposition primarily improves spectral resolution by increasing the coherent integration time of radar echoes. This not only increases the dimensionality of the radar echo covariance matrix, making it difficult to determine the thresholds for singular values ​​corresponding to sea clutter, but also incurs a significant computational overhead during eigenvalue decomposition. Traditional SVD suppression methods set the first few large singular values ​​to zero. However, under varying sea conditions, the target signal energy is not always less than the sea clutter signal energy. Setting only large singular values ​​to zero significantly increases the probability of target mis-cancellation.

[0005] Therefore, how to effectively suppress sea clutter is a research focus in the field of radar target detection.

[0006] Summary of the Invention

[0007] The present invention addresses the problem that traditional subspace-based suppression algorithms have large computational complexity and difficulty in determining the number of singular values ​​corresponding to sea clutter, resulting in unsatisfactory suppression effects. The present invention proposes a sea clutter suppression method based on improved singular value decomposition.

[0008] The present invention performs pulse compression on data received by a radar receiver, rearranges the echo signal into a fast and slow time dimension matrix according to a period, and performs a singular value decomposition algorithm; then uses the singular value index ratio to determine the target signal and sea clutter; and finally performs pulse cancellation on the reconstructed target signal.

[0009] The purpose of the present invention is achieved in this way: the specific steps are as follows:

[0010] Step 1: After pulse compression of the echo sequence received by the radar, the echo signal is rearranged into a fast and slow time dimension matrix according to the period, with one row representing one period.

[0011] The radar signal after pulse compression can be expressed as

[0012] Where, is the radar signal echo vector under the i-th observation.

[0013] Rearrange the fast and slow time dimension echo matrices according to the period, and compress the fast time dimension pulse of the matrix to obtain

[0014] Where, X c is an N×L echo data matrix, where N is the number of pulse accumulations, L is the number of distance units, j is the imaginary unit, and w d is the Doppler frequency of the echo signal.

[0015] Step 2: Construct a Hankel matrix for the signal in step 1 according to the fast time dimension and perform singular value decomposition. Calculate the singular value energy index ratio. Adaptively select singular values ​​based on the ratio to separate the target and clutter. Then, perform reconstruction on the selected singular values ​​to recover the signal. The specific steps are:

[0016] To X c Each row of x i Construct the Hankel matrix one by one:

[0017] Here, L = m + k - 1, m ≤ k, and the closer m and k are, the better the signal processing effect. Therefore, when L is an even number, m = L / 2, k = L / 2 + 1; when L is an odd number, m = (L + 1) / 2, k = (L + 1) / 2.

[0018] X i Perform singular value decomposition

[0019] 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 the matrix. i and v i The matrix X i The i-th left singular value column vector and right singular value column vector of , δ i is the i-th singular value in descending order.

[0020] The present invention proposes the definition of singular value index ratio from the perspective of considering the overall distribution of singular values

[0021] Among them, in order to more accurately distinguish the target echo and clutter, b m The ratio of is more obvious, k is a positive integer, and its value depends on the multiple ratio of the clutter energy to the target signal energy. ε is a positive number, and its value changes with the input signal-to-noise ratio. i ∈D, q is the number of sets in D, and m is the value obtained when the loop first satisfies the above formula. At this time, we believe that the set The signal recovered by the singular values ​​in is the target signal.

[0022] After multiple experimental analyses, the input signal-to-noise ratio SCNR_IN is used as the independent variable. is a function of the dependent variable and obeys the Gaussian distribution, that is:

[0023] a, b, and c are constants. Through a large number of experimental analyses, the values ​​of a, b, and c are in the range of 0.5-1, 5-10, and 6-10. In the present invention, the best effect is achieved when a, b, and c are 0.8012, 9.29, and 9.378, respectively.

[0024] After determining the singular value set D1 that represents the target subspace, the target signal is restored by matrix reconstruction, that is,

[0025] Step 3: Perform double delay line cancellation on the signal in step 2 to further suppress the noise. The impulse response of the MTI double delay line cancellation algorithm is: h(t) = δ(t) - 2δ(tT) + δ(t-2T)

[0026] Where δ(t) represents the impulse response and T is the period of the target signal.

[0027] The core technology of the present invention lies in the following: first, the echo signal after pulse compression is rearranged into a matrix of fast and slow time dimensions according to the period, and it is derived that the signal energy is equal to the sum of the squares of the singular values ​​corresponding to the periodic matrix; then, based on this, the definition of the singular value exponent ratio is further proposed. Based on this, the echo signal is adaptively decomposed according to the period, and the relationship between the threshold of the singular value corresponding to the signal and the input signal-to-noise ratio is proposed. By determining the size of the singular value exponent ratio and the threshold, the echo signal is decomposed into the sea clutter part and the signal part, thereby removing the clutter and recovering the signal; finally, the MTI dual delay line cancellation algorithm is used to suppress the clutter, ensuring that the loss of the target signal is minimized while suppressing the clutter.

[0028] Compared with existing technologies, the present invention offers the following advantages: an improved singular value decomposition sea clutter suppression algorithm adaptively determines the number of singular values ​​corresponding to sea clutter based on the input signal-to-noise ratio (SNR), effectively protecting target echo signals while suppressing sea clutter. This algorithm is independent of the sea clutter model, exhibits high versatility and effectiveness, and effectively addresses the problem of conventional subspace-based suppression algorithms, which suffer from high computational complexity and difficulty determining the number of singular values ​​corresponding to sea clutter, resulting in suboptimal suppression results. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] FIG1 is a block diagram of the principle of the sea clutter suppression algorithm based on the improved singular value decomposition;

[0030] Figure 2 is a table of experimental parameter settings;

[0031] Figure 3 is a table showing the suppression of four algorithms under different input signal-to-noise ratios. DETAILED DESCRIPTION

[0032] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0033] The method of the present invention is further described in detail below with reference to FIG1 and examples. The following examples are used to illustrate the present application but are not intended to limit the scope of the present application.

[0034] Based on the different aggregation characteristics of sea clutter and target echo signals within subspace, the present invention proposes a sea clutter suppression algorithm using an improved singular value decomposition (SVD-MTI algorithm). This method eliminates the need for sea clutter modeling. By using pulse compression, periodic singular value decomposition, and a dual-delay line cancellation algorithm, the sea clutter suppression problem is transformed into a trade-off problem involving corresponding singular values. This method precisely separates the target echo signal into a sea clutter component and a signal component, minimizing damage to the target signal when eliminating clutter components.

[0035] In order to more clearly illustrate the method applied for, the embodiment of the present application uses simulation experiments to illustrate the process and demonstrate the effects, but does not limit the scope of the embodiment of the present application. The specific parameter settings are shown in Table 1.

[0036] FIG1 is a block diagram of the principle of the method of the present invention, which includes:

[0037] Step 1:

[0038] ①The radar transmitter transmits a linear frequency modulation signal, t is the time of transmitting the signal, n is the number of transmitting cycles, and the radar pulse width is T p , the pulse repetition period is T r , the frequency modulation bandwidth is B, and the frequency modulation rate is defined as μ=B / T p , the carrier frequency is f c , j is an imaginary unit, then the radar's transmission signal S in the nth transmission cycle is n (t) is

[0039] ② Assume that at t = 0, the distance of the target relative to the radar is R0, and the speed of uniform motion is v. At this time, 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 of a single target in the nth cycle can be obtained e (t) is

[0040] Where c(t) is the clutter and n(t) is the Gaussian white noise generated by the receiver.

[0041] ③The obtained echo signal x e (t) is rearranged into a fast and slow time dimension echo matrix according to the period, and the matrix fast time dimension pulse compression is obtained

[0042] Where, X c is an N×L echo data matrix, where N is the number of pulse accumulations, L is the number of distance units, j is the imaginary unit, and w d is the Doppler frequency of the echo signal.

[0043] Step 2:

[0044] ①The radar signal after pulse compression can also be expressed as

[0045] Where, is the radar signal echo vector under the i-th observation.

[0046] ②To X c Each line Construct the Hankel matrix one by one:

[0047] Here, L = m + k - 1, m ≤ k, and the closer m and k are, the better the signal processing effect. Therefore, when L is an even number, m = L / 2, k = L / 2 + 1; when L is an odd number, m = (L + 1) / 2, k = (L + 1) / 2.

[0048] ③ X i Perform singular value decomposition

[0049] 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 the matrix. i and v i The matrix X i The i-th left singular value column vector and right singular value column vector of , δ i is the i-th singular value in descending order.

[0050] ④ From the perspective of considering the overall distribution of singular values, in order to more accurately distinguish sea clutter signals from target echo signals, the definition of singular value index ratio is proposed.

[0051] Among them, in order to more accurately distinguish the target echo and clutter, b m The ratio of is more obvious, k is a positive integer, and its value depends on the multiple ratio of the clutter energy to the target signal energy. ε is a positive number, and its value changes with the input signal-to-noise ratio. i ∈D, q is the number of sets in D, m is the value obtained when the loop first satisfies the above formula, at this time we think that the set The signal recovered by the singular values ​​in is the target signal.

[0052] After multiple experimental analyses, the input signal-to-noise ratio SCNR_IN is used as the independent variable. is a function of the dependent variable and obeys the Gaussian distribution, that is:

[0053] a, b, and c are constants. Through a large number of experimental analyses, the values ​​of a, b, and c are in the range of 0.5-1, 5-10, and 6-10. In the present invention, the best effect is achieved when a, b, and c are 0.8012, 9.29, and 9.378, respectively.

[0054] ⑤ After determining the singular value set D1 that represents the target subspace, the target signal is restored by matrix reconstruction, that is,

[0055] Step 3: Double delay line cancellation is performed to further suppress clutter.

[0056] After pulse compression and singular value decomposition, most of the noise in the echo signal is removed, but there is still interference from residual clutter. To further suppress the interference of clutter without affecting the signal, the MTI double delay line cancellation algorithm is applied to the recovered target signal. The impulse response of the MTI double delay line cancellation algorithm is: h(t) = δ(t) - 2δ(tT) + δ(t-2T)

[0057] Where δ(t) represents the impulse response and T is the period of the target signal.

[0058] To verify the performance of the SVD-MTI algorithm under different input SNRs, we tested the suppression effects of the OP algorithm, OP-SVD algorithm, SVD-FRFT algorithm, and SVD-MTI algorithm at different input SNRs before testing. The results are shown in Table 2. It can be seen that the SVD-MTI algorithm is consistently effective within an input SNR range of -30dB to 5dB, while the other three algorithms are not as widely applicable as the SVD-MTI algorithm and are not as effective. The OP algorithm only achieves primary clutter suppression in the orthogonal subspace, so its clutter suppression effect is less significant than the method of the present invention. Although the SVD-FRFT algorithm achieves signal energy aggregation at the optimal order, it still cannot detect target signals when the radar echo SNR is low. The OP-SVD algorithm relies on the correlation between the unit under test and its neighboring units, and its suppression effect is not significant.

[0059] This embodiment rearranges the target echo signal after pulse compression into a matrix of fast and slow time dimensions according to periodicity and performs periodic singular value decomposition. It then constructs a relationship between the threshold of the singular value corresponding to the signal and the input signal-to-noise ratio (SNR). The threshold is used to determine the singular value exponent ratio, enabling adaptive differentiation between sea clutter and target signals. Finally, dual delay line cancellation is performed on the reconstructed target signal, suppressing clutter while minimizing target signal loss. The proposed method minimizes target signal loss while suppressing clutter, and can still suppress most clutter and accurately detect signals at an input SNR of -30dB.

[0060] In summary, an improved singular value decomposition sea clutter suppression algorithm (abbreviated as SVD-MTI algorithm) is proposed. The method includes: first, rearranging the target echo signal after pulse compression into a fast and slow time dimension matrix according to the period, and performing periodic singular value decomposition; then constructing the relationship between the threshold of the singular value corresponding to the signal and the input signal-to-clutter plus noise ratio (Signal to Clutter Plus Noise Ratio, SCNR), using the threshold to judge the singular value exponent ratio to achieve adaptive distinction between sea clutter and target signal; finally, performing double delay line cancellation on the reconstructed target signal. The method of the present application can adapt to the changes in the signal-to-noise ratio of the target echo sequence, and while suppressing the sea clutter, it also ensures that the loss of the target signal is minimized.

Claims

1. An improved singular value decomposition sea clutter suppression algorithm, characterized in that: Here are the steps: Step 1: After pulse compression of the echo sequence received by the radar, the echo signal is rearranged into a fast and slow time dimension matrix according to the period, with one row representing one period; Step 2: Based on the obtained matrix, construct the Hankel matrix according to the fast time dimension and perform singular value decomposition. Adaptively select the singular values ​​according to the ratio of the singular value energy index and separate the target and clutter. Then, perform reconstruction operation on the selected singular values ​​to recover the signal. Step 3: Perform double delay line cancellation on the recovered signal to further suppress clutter.

2. The improved singular value decomposition sea clutter suppression algorithm according to claim 1, characterized in that: Step 1 specifically includes: (1) The radar transmitter transmits a linear frequency modulation signal, t is the time of transmitting the signal, n is the number of transmitting cycles, and the radar pulse width is T p , the pulse repetition period is T r , the frequency modulation bandwidth is B, and the frequency modulation rate is defined as μ=B / T p , the carrier frequency is f c , j is an imaginary unit, then the radar's transmission signal S in the nth transmission cycle is n (t) is: (2) Assuming that at t = 0, the distance of the target relative to the radar is R0, and the speed of the uniform motion is v, 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 of a single target in the nth cycle can be obtained e (t) is: Where c(t) is the clutter and n(t) is the Gaussian white noise generated by the receiver; (3) The obtained echo signal x e (t) is rearranged into a fast and slow time dimension echo matrix according to the period, and the matrix fast time dimension pulse is compressed to obtain Among them, X c is an N×L echo data matrix, where N is the number of pulse accumulations, L is the number of distance units, j is the imaginary unit, and w d is the Doppler frequency of the echo signal.

3. The improved singular value decomposition sea clutter suppression algorithm according to claim 1, characterized in that: Step 2 specifically includes: (1) The radar signal after pulse compression is in is the radar signal echo vector under the i-th observation; (2) To X c Each line Construct the Hankel matrix one by one: Among them, L=m+k-1, m≤k, and when m and k are closer, the better the signal processing effect is; when L is an even number, m=L / 2, k=L / 2+1; when L is an odd number, m=(L+1) / 2, k=(L+1) / 2. i Perform singular value decomposition: 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 the matrix. i and v i They are respectively the matrix X i The i-th left singular value column vector and right singular value column vector of , δ i is the i-th singular value in descending order; (3) In order to more accurately distinguish sea clutter signals from target echo signals, the definition of the singular value index ratio is proposed as follows: Where k is a positive integer whose value depends on the ratio of the clutter energy to the target signal energy; ε is a positive number whose value changes with the input signal-to-noise ratio; σ i ∈D, q is the number of sets in D, m is the value obtained when the loop first satisfies the above formula, at this time we think that the set The signal recovered by the singular values ​​in is the target signal; Taking the input signal-to-noise ratio SCNR_IN as the independent variable, is a function of the dependent variable and obeys the Gaussian distribution, that is: Among them: a, b, c are constants. Through a large number of experimental analyses, the values ​​of a, b, and c are in the range of 0.5~1, 5~10, and 6~10; (4) After determining the singular value set D1 that represents the target subspace, the target signal is restored by matrix reconstruction, that is, 4. The improved singular value decomposition sea clutter suppression algorithm according to claim 1, characterized in that: Step 3 specifically includes: performing the MTI double delay line cancellation algorithm on the recovered target signal, and its impulse response h(t) is: h(t)=δ(t)-2δ(tT)+δ(t-2T) Where δ(t) represents the impulse response and T is the period of the target signal.

Images