A Wavelet Decomposition-Based SVD-FRFT Sea Clutter Suppression Method

Abstract

This invention relates to a wavelet decomposition-based SVD-FRFT sea clutter suppression method, belonging to the field of signal processing technology in radar systems. Specifically, this invention relates to a method for suppressing sea clutter in radar echoes based on wavelet transform, singular value decomposition, and fractional Fourier transform. On one hand, it adaptively selects an effective component matrix to represent the target subspace using a singular value energy ratio method. On the other hand, by combining discrete wavelet transform, it preserves both time and frequency domain information, distinguishes non-stationary components in the signal, and achieves accurate search for the optimal order of the target under lower signal-to-clutter ratios and higher sea states, effectively extracting the target signal.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology in radar systems, specifically relating to an SVD-FRFT sea clutter suppression method based on wavelet decomposition. Background Technology

[0002] During radar monitoring of the sea surface, the presence of sea clutter severely affects target signal detection. Sea clutter is formed by the superposition of backscattered echoes from numerous small scatterers on the sea surface. The electromagnetic scattering echoes from the sea surface are intense and easily form sea spikes. The Doppler frequencies of weak targets on the sea surface tend to fall within the Doppler spectrum of sea clutter, making the detection of weak targets against a strong sea clutter background a major challenge. Therefore, effectively suppressing sea clutter and reducing its impact on target signals is crucial for sea surface target detection.

[0003] The mathematical theories employed in sea clutter subspace decomposition and suppression methods include singular value decomposition (SVD) and eigenvalue decomposition (EVD). These methods suppress clutter by setting the singular or eigenvalues ​​corresponding to the clutter space to zero. However, both classical methods only suppress clutter when the Doppler frequencies differ significantly, making it difficult to adaptively determine the set of singular values ​​corresponding to the target subspace. Furthermore, EVD incurs substantial computational costs and is primarily applied to symmetric matrices, limiting its applicability. To better distinguish between sea clutter and target signals, some methods extend SVD to the FRFT domain to extract first-order components, resulting in a cleaner target signal. However, since pure sea clutter exhibits some aggregation characteristics even in the fractional-order domain, this method fails to find the optimal order for the target signal when the signal-to-clutter ratio is low, easily leading to the extraction of sea clutter signals while suppressing the target signal. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] The technical problem this invention aims to solve is that existing SVD-FRFT methods cannot find the optimal order of the target signal when the signal-to-clutter ratio is low, easily extracting sea clutter signals while suppressing the target signal, and cannot adaptively select the component matrix corresponding to the target during singular value decomposition. This invention provides an SVD-FRFT sea clutter suppression method based on wavelet transform, thereby achieving the search for the optimal order of the target signal and adaptive determination of the target subspace and effective target extraction under lower signal-to-clutter ratios and higher sea states.

[0006] (II) Technical Solution

[0007] To address the aforementioned technical problems, this invention provides an SVD-FRFT sea clutter suppression method based on wavelet decomposition, comprising the following steps:

[0008] (1) Acquire the echo signal to be processed, wherein the echo signal to be processed includes sea clutter, target signal and noise pollution;

[0009] (2) For the echo signal to be processed, perform wavelet transform decomposition to obtain the modulus maxima of wavelet coefficients, distinguish the target signal and sea clutter according to the modulus maxima characteristics, remove the modulus maxima of sea clutter, retain the wavelet coefficients corresponding to the target signal, and reconstruct the signal through the retained wavelet coefficients;

[0010] (3) Perform fractional Fourier transform to convert the wavelet transform reconstructed signal to the fractional domain, use the two-dimensional peak search method to obtain the optimal order corresponding to the target signal, and extract the signal under the optimal order.

[0011] (4) The extracted signal is transformed to the time domain by inverse Fourier transform, and singular value decomposition is performed on the time domain signal. The effective set of singular values ​​representing the target subspace is selected according to the singular value energy ratio. The signal after singular value decomposition is recovered by averaging the target subspace.

[0012] (5) The signal obtained after singular value decomposition is transformed into the fractional domain by Fourier transform, and the signal is then transformed into the fractional Fourier inverse transform to obtain the signal after sea clutter suppression. The signal is used to characterize the target signal after suppressing sea clutter and noise.

[0013] (III) Beneficial Effects

[0014] This invention proposes a wavelet transform-based SVD-FRFT sea clutter suppression method, specifically involving a radar echo sea clutter suppression method based on wavelet transform, singular value decomposition, and fractional Fourier transform. On the one hand, it achieves adaptive selection of effective component matrices to characterize the target subspace by using a singular value energy ratio method. On the other hand, by combining discrete wavelet transform, it preserves both time and frequency domain information, distinguishes non-stationary components in the signal, and achieves accurate search for the optimal order of the target under lower signal-to-clutter ratios and higher sea states, effectively extracting the target signal. Attached Figure Description

[0015] Figure 1 A flowchart of a wavelet transform-based SVD-FRFT sea clutter suppression method provided by the present invention;

[0016] Figure 2 Time-frequency analysis diagrams before and after processing under sea state 3-4 provided by this invention;

[0017] Figure 3 Time-frequency analysis diagrams before and after processing under sea state level 2 low, provided by this invention;

[0018] Figure 4The time-frequency analysis diagrams before and after processing under sea state level 5 provided by this invention. Detailed Implementation

[0019] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0020] Existing SVD-FRFT methods fail to find the optimal order of the target signal at low signal-to-clutter ratios, easily extracting sea clutter signals while suppressing the target signal. Furthermore, they cannot adaptively select the component matrix corresponding to the target during singular value decomposition. This invention provides an SVD-FRFT sea clutter suppression method based on wavelet transform. It performs discrete wavelet decomposition to remove clutter before fractional Fourier transform to improve the signal-to-clutter ratio, and adaptively determines the target subspace using singular value energy ratios. This enables the search for the optimal order of the target signal and the adaptive determination of the target subspace, effectively extracting the target, even at lower signal-to-clutter ratios and higher sea states.

[0021] This invention discloses a wavelet transform-based SVD-FRFT sea clutter suppression method. Based on discrete wavelet decomposition theory, it uses discrete wavelet transform for clutter removal, suppressing a portion of the sea clutter and improving the signal-to-clutter ratio. The processed signal is then subjected to fractional Fourier transform. Utilizing the different aggregation characteristics of the target and sea clutter in the fractional domain, the optimal order signal containing the target can be accurately searched in the FRFT domain. The signal is then converted to the time domain via inverse Fourier transform. Since the target signal energy is greater than the sea clutter energy at the optimal order, the target subspace is obtained after SVD decomposition using a singular value energy ratio method. After selecting the target subspace, the signal is recovered using the averaging method, and a Fourier transform is performed to convert the signal to the FRFT domain. Finally, the sea clutter-suppressed signal is obtained through fractional Fourier transform, and time-frequency analysis is performed to verify whether the target has been extracted. This method effectively suppresses sea clutter and extracts target information under low signal-to-clutter ratio and high sea state conditions.

[0022] like Figure 1 As shown in the figure, the SVD-FRFT sea clutter suppression method based on wavelet transform provided in this embodiment specifically includes the following steps:

[0023] S101. Obtain the echo signal to be processed, wherein the echo signal to be processed includes sea clutter, target signal and noise pollution.

[0024] Optionally, acquiring the echo signal to be processed involves adding a simulated linear frequency modulated (LFM) target signal to the sea clutter in the radar's actual sea detection dataset, and ensuring that the sea clutter signal strength is much greater than the target signal strength in the echo signal to be processed, i.e., extracting the effective signal against a strong sea clutter background.

[0025] S102. For the echo signal to be processed, perform wavelet transform decomposition to obtain the modulus maxima of wavelet coefficients. Based on the modulus maxima characteristics, distinguish between the target signal and sea clutter. Remove the modulus maxima of sea clutter and retain the wavelet coefficients corresponding to the target signal. Reconstruct the signal using the retained wavelet coefficients.

[0026] The positive and negative signs of the Lieschmann exponent are used to determine the target signal and sea clutter, and the modulus maxima of the sea clutter are removed. The position of the modulus maxima of each decomposition scale is determined according to the relationship between the number of sampling points of the discrete wavelet decomposition scale. The wavelet coefficients corresponding to the target signal in each decomposition scale are retained, and the signal is reconstructed by the retained wavelet coefficients.

[0027] S103. Perform fractional Fourier transform to convert the wavelet transform reconstructed signal to the fractional domain, use the two-dimensional peak search method to obtain the optimal order corresponding to the target signal, and extract the signal at the optimal order.

[0028] S104. The extracted signal is transformed to the time domain by inverse Fourier transform. Singular value decomposition is performed on the time domain signal. The effective set of singular values ​​representing the target subspace is selected according to the singular value energy ratio. The signal after singular value decomposition is recovered by averaging the target subspace.

[0029] Optionally, this embodiment provides a subspace selection method based on singular value energy ratio, including: any selection method that places the singular value energy ratio into a mathematical expression with a known trend of change, such as the logarithmic part or base part of a logarithmic function, power function, etc.; selecting the target subspace and using the averaging method to recover the signal; or selecting the sea clutter subspace, in which case the component projected in the sea clutter subspace needs to be subtracted before recovering the signal.

[0030] S105. The signal obtained after singular value decomposition is transformed into the fractional domain by Fourier transform, and the signal is then transformed into the fractional domain by inverse fractional Fourier transform to obtain the signal after sea clutter suppression. The signal is used to characterize the target signal after suppressing sea clutter and noise.

[0031] In one possible implementation, step S102 involves performing wavelet transform decomposition on the echo signal to be processed to obtain the modulus maxima of the wavelet coefficients, distinguishing the target signal from sea clutter based on the modulus maxima characteristics, removing the modulus maxima of the sea clutter, retaining the wavelet coefficients corresponding to the target signal, and reconstructing the signal using the retained wavelet coefficients, including:

[0032] For the echo signal to be processed, a discrete wavelet transform is performed. Starting from the maximum decomposition scale, the modulus maxima of the wavelet coefficients are selected. After determining the modulus maxima of the maximum decomposition scale, the modulus maxima of the target signal and sea clutter are distinguished by the Lie index.

[0033] The sea clutter modulus maxima are removed using the Lee index. For each reduction in the decomposition scale using wavelet transform, the number of sampling points doubles. Based on this positional relationship, the modulus maxima of the next scale are found, and so on. Finally, the wavelet coefficients corresponding to the target modulus maxima are retained, and the signal is reconstructed using the retained wavelet coefficients.

[0034] In one possible implementation, the echo signal to be processed is subjected to a discrete wavelet transform, which is a discretization of the continuous scale parameter 'a' and the continuous translation parameter 'b'. During this process, 'a' only takes positive values, and the expansion step size 'a0' is a fixed value. The discretization formulas for the continuous scale parameter 'a' and the continuous translation parameter 'b' are typically defined as follows: For a0≠1, j∈Z, the corresponding discrete wavelet function is:

[0035]

[0036] Discrete wavelet transform is

[0037]

[0038] Discretized wavelet transform coefficients are

[0039]

[0040] Its reconstruction formula is

[0041]

[0042] Here, C is a constant whose value is independent of the signal.

[0043] After wavelet transform, the signal will be decomposed into smooth components c. j (j = 1, 2, ..., m) and coefficient components d j (j=1,2,…,m), where m is the maximum decomposition scale. The smaller the decomposition scale, the more information it contains, and the closer it is to the original signal. As the wavelet decomposition scale increases, the coefficient components can compensate for the high-frequency components lost by the smoothing components.

[0044] This embodiment uses the modulus maxima method to perform discrete wavelet transform for clutter removal. Take any point (a0, b0) above, and if in the neighborhood of b0 there is...

[0045]

[0046] If established, it is called Let be the modulus maxima of the wavelet coefficients at scale a0. After wavelet transform, the modulus maxima of the wavelet coefficients vary with scale a and are determined by the Lipschitz exponent, which characterizes the local singularity of the signal.

[0047]

[0048] Where m is a constant, the wavelet modulus maxima of the signal increase as the scale a increases during the wavelet transform. Generally, the target signal L > 0, while for white noise L ≤ 0, thus the target signal and noise are distinguished by the Lieberthal index. Sea clutter signals can be considered as a combination of first-order and second-order sea clutter and noise. First-order sea clutter can be described as the sum of multiple single-frequency signals, while second-order sea clutter and noise are considered as white noise following a Gaussian distribution. In the process of calculating L at each decomposition scale, a0, as the base of the logarithmic function, cannot be 1. Therefore, when the decomposition scale is 1, the sign of L is not filtered, and a hard thresholding method is directly used to retain larger amplitude values. The threshold T = C·A / J, where C is a constant and A is the maximum amplitude of the signal at the largest scale.

[0049] For each decomposition scale, the modulus maxima corresponding to the sea clutter are removed according to the Lieschmann exponent. For each decomposition scale reduced by the wavelet transform, the number of sampling points is doubled. Based on this positional relationship, the modulus maxima of the next scale are found, and so on. Finally, the wavelet coefficients corresponding to the target modulus maxima at each decomposition scale are retained, and the signal is reconstructed using the retained wavelet coefficients.

[0050] In one possible implementation, step S103 performs a fractional Fourier transform on the wavelet transform reconstructed signal to convert it to the fractional domain. The fractional Fourier transform can be viewed as rotating the signal counterclockwise around the origin by an arbitrary angle in the time-frequency domain, decomposing the signal onto a set of linear frequency-modulated orthogonal bases in the fractional domain. The p-order FRFT of the signal x(t) has...

[0051]

[0052] Where p is the transform order of the FRFT, F p Denotes a fractional operator, K p (t,u) is the kernel function of FRFT.

[0053]

[0054] in n is an integer, α is the rotation angle, and the relationship α = pπ / 2, p ≠ 2n exists. Specifically, when p = 0, X0(u) is its antiderivative x(t); when p = 1, X1(u) is the Fourier transform of x(t), then X... -1 (u) is the inverse Fourier transform of x(t).

[0055] For the target signal is a linear frequency modulated signal

[0056] x(t)=exp[jπ(2f c t+μt2 )]t∈[-T / 2,T / 2]

[0057] Among them, f c Let α be the center frequency of the linear frequency modulated (LFM) signal, μ be the modulation slope, and T be the signal's duration. The frequency of an LFM signal varies with time, and its spectrum resembles a rectangular window. When α = cot -1 When (-μ), performing a fractional Fourier transform on the linear frequency modulated signal yields...

[0058] X p (u)=A α exp(jπu 2 cotα)δ[2π(f c -ucscα)]

[0059] Since the transform basis of the fractional Fourier transform is composed of a set of linear frequency modulated signals, the orthogonal basis corresponding to different frequency modulation slopes can be obtained by rotating by an angle α. When it is the same as the linear frequency modulated signal, the linear frequency modulated signal forms an impulse function in this set of basis, which shows the best energy accumulation at the optimal fractional order.

[0060] In one possible implementation, step S103 uses a two-dimensional peak search method to obtain the optimal order corresponding to the target signal and extracts the signal at the optimal order. The received echo signal containing the target is processed by multiple different orders using a fractional Fourier transform, and the resulting output constitutes a dataset of signal energy in the pu two-dimensional plane. In this dataset, the peak value represents the optimal energy concentration at a specific transform order. The coordinates corresponding to the maximum energy value in the dataset are found in the two-dimensional plane.

[0061]

[0062] Where p0 is the optimal fractional order of the target, and the signal corresponding to this order is the echo signal containing the target.

[0063] In one possible implementation, step S104 involves performing an inverse Fourier transform on the extracted signal to the time domain and then performing singular value decomposition (SVD) on the time-domain signal. The data processed by the fractional Fourier transform is transformed back to the time domain using another Fourier transform to obtain x'(n). A Hankel matrix is ​​constructed on x'(n) and SVD is performed on it. The decomposed signal is divided into two parts based on the magnitude of the singular values: one part consists of the main target signal and a large amount of sea clutter, and the other part consists of a portion of the target signal, a small amount of sea clutter, and noise components. Since the interference of sea clutter on the signal is much greater than that of noise, the influence of noise is ignored when discussing sea clutter. A Hankel matrix is ​​constructed on x'(n).

[0064]

[0065] Where m = N - L + 1, m ≤ L, the larger L is, the more detailed the signal space is, and the better the target signal and clutter signal are separated, but the corresponding computational load will also increase. The closer m and L are, the better the processing results will be. That is, when N is even, take L = N / 2 + 1, m = N / 2; when N is odd, take L = (N+1) / 2, m = (N+1) / 2. SVD decomposition of H yields...

[0066]

[0067] Where Λ is the singular value matrix, σ i Let u be the i-th singular value of matrix H after descending order. i Let v be the left singular column vector corresponding to the i-th singular value. i Let Λ' be the right singular column vector corresponding to the i-th singular value, U and V be m×m and n×n unitary matrices respectively, S be the singular value matrix, and C and T represent sets, where C represents the singular value set of the sea clutter and noise subspace, and T represents the singular value set of the target subspace. After obtaining Λ' by preserving the singular values ​​of the target subspace, the Hankel matrix can be recovered.

[0068]

[0069] In one possible implementation, the effective set of singular values ​​representing the target subspace is selected based on the singular value energy ratio. The energy of the Hankel matrix H constructed from the time series x'(n) is defined as the square of its Frobenius norm, i.e.

[0070]

[0071] Singular values ​​are invariant and matrices U and V are both unitary matrices; therefore, the F-norm of matrix H is unitarily invariant, which can be obtained by formula:

[0072]

[0073] Among them, S=diag(σ1,σ2,…,σ q ), q=min(m,n). Therefore, the energy of matrix H is equal to the sum of squares of the singular values. The energy distribution of the singular values ​​represents the contribution of each singular value to the total energy. Therefore, effective singular values ​​can be selected based on the energy distribution of the singular values. Hence, the singular value energy ratio is defined as...

[0074]

[0075] Among them, b kThe value ranges from 0 to 1, representing the cumulative energy percentage of the first k singular values. Typically, an energy threshold ε is chosen, ranging from 0 to 1. Addition stops when the accumulated energy exceeds or equals the chosen threshold. k is the number of the first k singular values ​​that satisfy the threshold condition. The set B = {σ1, σ2, ..., σ...} k} is the set of valid singular values ​​that characterize the target subspace, and the signal recovered from it is the target signal.

[0076] In one possible implementation, step S104 utilizes the target subspace and the averaging method to recover the singular value decomposition (SVD) signal. Since the elements of each secondary diagonal in the Hankel matrix are equal, and the value of the nth point of the time series x(n) is the element of the nth diagonal, the value of y(n) can be obtained by averaging the elements on the secondary diagonal, thus recovering the SVD signal time series.

[0077]

[0078] Among them, a n Let n be the number of elements on the secondary diagonal of the nth dimension.

[0079] Optionally, the target subspace selection method and signal recovery based on the singular value energy ratio can be achieved by selecting the singular value energy ratio by placing it into a mathematical expression with a known trend, such as as the logarithmic part or base of a logarithmic function or power function; selecting the target subspace to recover the signal; or selecting the sea clutter subspace, in which case the component projected onto the sea clutter subspace needs to be subtracted before recovering the signal.

[0080] In one possible implementation, step S105 transforms the signal obtained after singular value decomposition into the fractional domain using a Fourier transform, and then performs an inverse fractional Fourier transform on the signal to obtain the sea clutter-suppressed signal. Taking the negative of the optimal order and performing the inverse fractional Fourier transform yields its inverse transform, and the formula for the inverse fractional Fourier transform is as follows:

[0081]

[0082] Where y'(t) is the target signal after sea clutter suppression.

[0083] In MATLAB, partial radar data from the publicly shared radar sea-penetration data in the *Journal of Radar* was used for experiments. A shore-based X-band solid-state fully coherent radar was used to obtain radar measurement data and marine meteorological and hydrological data under different conditions. Table 1 shows some technical parameters of the X-band experimental radar. The echo signal was processed using the method of this invention. Table 2 shows the results compared with other methods, with results implemented under sea states 3-4, 2, and 5 as follows. Figure 2 , Figure 3 as well as Figure 4 .

[0084] Table 2 shows the optimal order search results of SVD-FRFT and the method described in this embodiment under different signal-to-clutter ratios. It can be seen that the SVD-FRFT sea clutter suppression method based on wavelet transform described in this embodiment can find the optimal order of the target signal under a lower signal-to-clutter ratio.

[0085] Figure 2 The time-frequency analysis diagrams provided by this invention for sea states 3-4 before and after processing show that a linear frequency modulated simulated target signal is added to the sea clutter, with a signal-to-clutter ratio of -14dB, an initial target velocity of v = 200m / s, and an acceleration of a = 8m / s². 2 The initial Doppler frequency of the target is 60Hz. After FRFT, the optimal order is found to be 1.012, which is the optimal order of the target signal. The wavelet basis function is selected as db5, the decomposition scale is 5, and the output signal-to-clutter ratio is 10.84dB. It can be seen that the wavelet transform-based SVD-FRFT sea clutter suppression method described in this embodiment can effectively extract the target signal.

[0086] Figure 3 The time-frequency analysis diagrams before and after processing under sea state 2 provided by the present invention are shown. With the simulation target signal parameters being the same as those under sea states 3-4, it can be seen that the wavelet transform-based SVD-FRFT sea clutter suppression method described in this embodiment can effectively extract the target signal under low sea states.

[0087] Figure 4 The time-frequency analysis diagrams before and after processing under sea state 5 provided by the present invention are shown. With the initial Doppler frequency of the simulated target signal set to -80Hz, it can be seen that the SVD-FRFT sea clutter suppression method based on wavelet transform described in this embodiment can still effectively extract target information under higher sea states.

[0088] Table 1

[0089]

[0090] Table 2

[0091]

[0092]

[0093] This invention incorporates a linear frequency modulated simulated target signal into measured sea clutter. Table 1 shows some technical parameters of the X-band experimental radar from which the measured sea clutter originated. The initial velocity of the simulated target was set to ν = 200 m / s, and the acceleration was α = 8 m / s². 2With the initial Doppler function of the target being db5, the decomposition scale number being 5, and the input signal-to-clutter ratio (SCR) set to -12dB to -23dB, it can be seen that the wavelet transform-based SVD-FRFT sea clutter suppression method described in this invention can effectively extract the target signal. Table 2 compares the optimal order search results of the conventional singular value decomposition and fractional Fourier transform (SVD-FRFT) methods and the method described in this invention under different SCRs. It can be seen that the wavelet transform-based SVD-FRFT sea clutter suppression method described in this invention can still search for the optimal order of the target signal even at a low SCR of -22dB. The method described in this invention performs discrete wavelet transform decomposition to remove clutter before fractional Fourier transform, thereby improving the signal-to-clutter ratio and enabling the processing of echo signals under lower input signal-to-clutter ratio conditions. Applying SVD to the FRFT domain can further remove sea clutter by utilizing the aggregation characteristics of the target signal, realizing the extraction of target signals whose Doppler frequencies are submerged in the Doppler spectrum of sea clutter. The method based on singular value energy ratio simultaneously achieves adaptive partitioning of clutter and target singular values.

[0094] This embodiment discloses a wavelet transform-based SVD-FRFT sea clutter suppression method. Discrete wavelet transform decomposition before fractional Fourier transform improves the signal-to-clutter ratio (SNR). Applying SVD to the FRFT domain utilizes the convergence characteristics of the target signal to further remove sea clutter, enabling the processing of echo signals at a lower SNR. It can extract target signals whose Doppler frequencies fall within the sea clutter Doppler spectrum. Adaptive partitioning is achieved in target subspace selection using a singular value energy ratio-based method.

[0095] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A wavelet-decomposition-based SVD-FRFT sea clutter suppression method, characterized in that, The method comprises the following steps: (1) obtaining a to-be-processed echo signal, wherein the to-be-processed echo signal contains sea clutter, target signals and noise pollution; (2) performing wavelet transform decomposition on the to-be-processed echo signal to obtain wavelet coefficient modulus maxima, distinguishing the target signals and the sea clutter according to modulus maxima characteristics, removing the sea clutter modulus maxima, retaining the wavelet coefficients corresponding to the target signals, and reconstructing the signals through the retained wavelet coefficients; (3) performing fractional Fourier transform on the signals reconstructed by the wavelet transform to convert the signals to a fractional order domain, obtaining the optimal order corresponding to the target signals by using a two-dimensional search peak value method, and extracting the signals under the optimal order; (4) converting the extracted signals to the time domain through inverse Fourier transform, performing singular value decomposition on the time domain signals, selecting an effective singular value set representing a target subspace according to a singular value energy ratio, and restoring the signals after the singular value decomposition by using an average method in the target subspace; (5) performing Fourier transform on the signals obtained after the singular value decomposition to convert the signals to the fractional order domain, performing fractional inverse Fourier transform on the signals again to obtain signals after sea clutter suppression, and the signals are used to represent the target signals after the sea clutter and noise are suppressed. Step (2) specifically comprises: performing discrete wavelet transform on the to-be-processed echo signal, selecting wavelet coefficient modulus maxima from the maximum decomposition scale, determining the modulus maxima of the maximum decomposition scale, and distinguishing the modulus maxima of the target signals and the sea clutter by using the Lee index; removing the sea clutter modulus maxima according to the Lee index, increasing the sampling point number by one time for each decomposition scale of the wavelet transform, finding the modulus maxima of the next scale according to the position relationship, and finally retaining the wavelet coefficients corresponding to the target modulus maxima and reconstructing the signals by using the retained wavelet coefficients. The discrete wavelet transform of the echo signal to be processed is a discrete processing of continuous scale parameters and continuous translation parameters In this process, only positive values are taken, and the extension step is a fixed value, defining the continuous scale parameters and the continuous translation parameters The discrete formula is The corresponding discrete wavelet function is The discrete wavelet transform is The discrete wavelet transform coefficient is The reconstruction formula is wherein is a constant, the value of which is independent of the signal; After wavelet transform, the signal will be decomposed into smooth component , j = 1, 2,..., m and coefficient component , j = 1, 2,..., m, wherein is the maximum decomposition scale; the smaller the decomposition scale is, the more information contained, and the closer to the original signal, and with the increase of the wavelet decomposition scale, the coefficient component can compensate the lost high frequency part of the smooth component; Using the modulus maxima method for discrete wavelet transform clutter removal: In Take any point above ,exist If there are in the neighborhood If true, then call to extend the step size The modulus maxima of the wavelet coefficients; after the wavelet transform, the modulus maxima of the wavelet coefficients vary with the successive scale parameter and are determined by the Lipschitz exponent, which characterizes the local singularity of the signal, i.e. wherein, is a constant, the wavelet modulus maxima of the signal increases as the continuous scale parameter increases during the wavelet transform process, the target signal , while the white noise , so that the target signal is distinguished from the noise by the Lee index; the sea clutter signal is a combination of the first-order, second-order sea clutter and noise; wherein the first-order sea clutter is described as the accumulation of multiple single-frequency signals, while the second-order sea clutter and noise are considered as white noise following a Gaussian distribution; during the calculation of at each decomposition scale, the sign of the logarithmic function base part cannot be 1, so in the case of the decomposition scale being 1, the positive and negative of are not screened, and the hard threshold method is directly used to retain the maximum amplitude value, the threshold , is a constant, is the maximum amplitude value of the signal at the maximum scale; For each decomposition scale, the modulus maxima corresponding to the sea clutter is removed according to the Lee index, the sampling point number is increased by one time for each decomposition scale of the wavelet transform, the modulus maxima of the next scale is found according to the position relationship, and finally the wavelet coefficients corresponding to the target modulus maxima at each decomposition scale are retained, and the signals are reconstructed by using the retained wavelet coefficients.

2. The method of claim 1, wherein, Step (1) of obtaining the to-be-processed echo signal is a process of adding a simulated linear frequency modulation signal target to the sea clutter in the radar sea detection measured data set and extracting effective signals in a strong sea clutter background. In the to-be-processed echo signal, the sea clutter signal strength is greater than the target signal strength to a certain extent.

3. The method of claim 1, wherein, In step (2), the positive and negative nature of the Lee index is used to judge the target signals and the sea clutter, and the sea clutter modulus maxima is removed. The modulus maxima position of each decomposition scale is determined according to the relationship of the sampling point number of the discrete wavelet decomposition scale, the wavelet coefficients corresponding to the target signals in each decomposition scale are retained, and the signals are reconstructed by using the retained wavelet coefficients.

4. The method of claim 1, wherein, In step (4), the subspace selection method based on the singular value energy ratio comprises: any selection method of putting the singular value energy ratio into a mathematical expression with a known change trend; selecting the target subspace to restore the signals by using the average method; or selecting the sea clutter subspace, then subtracting the component projected in the sea clutter subspace to restore the signals.

5. The method of claim 1, wherein, Step (3) when the wavelet transform reconstructed signal is converted to the fractional order domain by fractional Fourier transform, the fractional Fourier transform is regarded as rotating the original point counterclockwise by any angle in the time-frequency domain, and the signal is decomposed on a set of linear frequency modulation orthogonal bases in the fractional order domain The order FRFT has wherein is the transform order of the FRFT, denotes a fractional order operator, is the kernel function of the FRFT wherein , is an integer, is a rotation angle, and there is a relationship ; when , is its original function ; when , is the Fourier transform of , then is the inverse Fourier transform of ; For the target signal being a linear frequency modulation signal wherein is the center frequency of the chirp signal, is the chirp rate, is the time width of the signal; the frequency of the chirp signal varies with time when the fractional Fourier transform of the chirp signal is given by The orthogonal bases corresponding to different frequency modulation slopes pass through a rotation angle It is obtained that when the same as the linear frequency modulation signal, the linear frequency modulation signal forms an impulse function in the corresponding set of orthogonal bases, which shows the best energy concentration on the optimal fractional order.

6. The method of claim 5, wherein, Step (3) uses two-dimensional search peak value method to obtain the optimal order corresponding to the target signal, and extracts the signal under the optimal order. The received echo signal containing the target is processed by fractional Fourier transform with multiple different orders, and the output constitutes the energy of the signal The data set of two-dimensional plane, in which the peak represents the best energy concentration under a certain transform order, and the coordinates corresponding to the maximum energy value in the data set are found in the two-dimensional plane, that is wherein, The best fractional order of the target is found, and the signal corresponding to the order is the echo signal containing the target.

7. The method of claim 6, wherein, Step (4) inverse Fourier transform the extracted signal to the time domain, and perform singular value decomposition on the time domain signal. The data processed by the fractional Fourier transform is converted to the time domain by the Fourier transform to obtain singular value decomposition is performed on the Hankel matrix constructed therefrom. The complete space is divided into two parts according to the size of the singular value after decomposition, one part is the majority target signal and a large amount of sea clutter, and the other part is a small part of the target signal, a small amount of sea clutter and noise components. Hankel matrix wherein , when is even, take ; when is odd, , perform SVD decomposition on to get wherein, is a singular value matrix, is a matrix arranged in descending order is the first singular value of is the left singular column vector corresponding to the first singular value, is the right singular column vector corresponding to the first singular value, and are unitary matrices of and respectively, diagonal matrix is a singular value matrix, C and T represent sets, C represents a singular value set of a sea clutter and noise subspace, and T represents a singular value set of a target subspace; singular values of the target subspace are reserved to obtain after which the Hankel matrix is recovered According to the singular value energy ratio, an effective singular value set representing the target subspace is selected, and a time series Hankel matrix constructed The energy is defined as the square of the Frobenius norm, that is, matrix and are unitary matrices, so that the F-norm of the matrix is unitary invariant, leading to the equation wherein, Thus, the energy of the matrix is equal to the sum of the squares of the singular values, the energy distribution of the singular values represents the contribution of each singular value to the total energy, and therefore the effective singular values are selected according to the energy distribution of the singular values, and the definition of the singular value energy ratio is wherein, is the energy accumulation ratio of the first k singular values, and k is an integer between 1 and N, N is the number of singular values, and is an energy threshold value, and k is an integer between 1 and N, N is the number of singular values, and is the number of singular values that satisfy the threshold condition, and k is an integer between 1 and N, N is the number of singular values, and is the set of singular values that satisfy the threshold condition, and k is an integer between 1 and N, N is the number of singular values, and is the set of singular values that represent the target subspace, and k is an integer between 1 and N, N is the number of singular values, and is the recovered signal that represents the target signal.

8. The method of claim 7, wherein, In step (4), the average method is used to recover the signal after singular value decomposition by using the target subspace. The elements of each secondary diagonal line in the Hankel matrix are equal, and the value of the time series The first dimensional diagonal line is the value of the time series The value of the first dimensional diagonal line is the value of the time series wherein, is the the number of elements on the minor diagonal.

9. The method of claim 8, wherein, In step (5), the signal obtained after singular value decomposition is converted into a fractional order domain through Fourier transform, and the sea clutter suppressed signal is obtained again through inverse fractional Fourier transform of the signal.

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