A sea clutter suppression method based on singular value decomposition of fractional Fourier transform

Abstract

The present invention discloses a sea clutter suppression method based on singular value decomposition of a fractional Fourier transform. The method comprises the following steps: re-arranging a target echo signal and then performing phase demodulation; performing a fractional Fourier transform on the demodulated target echo signal to obtain a transformed target echo signal, and then performing an inverse Fourier transform to transform it back into the time domain; performing singular value decomposition on the target echo signal transformed back into the time domain and constructing a signal subspace matrix; projecting the target echo signal transformed back into the time domain into the signal subspace matrix to obtain a target echo signal with sea clutter suppressed; and finally performing a Fourier transform and an inverse fractional Fourier transform to obtain a target echo signal with sea clutter suppressed. The present invention overcomes the problem that existing traditional clutter suppression methods are unable to suppress sea clutter that overlaps with the target on a time-frequency diagram, thereby improving the detection capability of the radar.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and in particular relates to a sea clutter suppression method based on singular value decomposition of fractional Fourier transform. Background Art

[0002] When radar processes received signals, clutter components can adversely affect target signal detection. If not suppressed, accurate and effective target detection is impossible. In a real sea clutter environment, sea clutter interference is intense, complex, and subject to radar interference. The spectrum center frequency varies widely, often exhibiting non-Gaussian and non-stationary characteristics. Furthermore, low-speed targets on the sea surface have a small Doppler shift, significantly overlapping with strong and low-frequency clutter in the Doppler domain.

[0003] Although traditional clutter suppression methods such as MTI and MTD algorithms can filter clutter in the time or frequency domain, when detecting slow-moving targets, it is difficult to distinguish between the target and clutter signals when the target and zero-frequency clutter overlap significantly in the Doppler domain. Subspace-based algorithms, however, rely on signal characteristics to perform eigendecomposition of the echo signal matrix and separate the clutter subspace, thereby suppressing the clutter component in the signal and having a strong ability to extract weak target features, thereby highlighting the target. Sira et al. proposed a sea clutter suppression technique based on a subspace approach. This technique suppresses sea clutter by estimating the sea clutter subspace, and the choice of clutter subspace directly affects the suppression effect. Rafaat Khan et al. proposed a sea clutter suppression technique based on singular value decomposition. However, this algorithm has difficulty effectively suppressing sea clutter when the Bragg peak of sea clutter is not prominent.

[0004] To address the above issues, the prior art with publication number CN116224277A combines time-frequency spectrum energy distribution with singular value decomposition to effectively filter out sea clutter signals and protect the signal energy of low-speed targets. This effectively filters out interference signals while reducing the loss of valid signals, thereby improving the target signal-to-noise ratio (SNR). This avoids the problem of poor sea clutter suppression in strong sea clutter environments, where weak targets are easily suppressed as clutter. However, when targets and clutter overlap on the time-frequency graph, this prior art method has difficulty effectively separating them. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a sea clutter suppression method based on singular value decomposition of fractional Fourier transform:

[0006] The technical problem to be solved by the present invention is achieved by the following method, comprising the following steps:

[0007] Echo signal rearrangement step: rearrange the target echo signal into a fast and slow time dimension matrix according to the period;

[0008] Echo signal phase demodulation step: performing phase demodulation on the target echo signal rearranged into a fast and slow time dimension matrix according to the period to obtain a demodulated target echo signal;

[0009] Fractional Fourier transform step: performing a fractional Fourier transform on the demodulated target echo signal according to the optimal fractional order to obtain the target echo signal transformed into the optimal fractional order fractional domain;

[0010] Inverse Fourier transform step: performing inverse Fourier transform on the target echo signal transformed into the optimal fractional order fractional domain to obtain the target echo signal transformed back into the time domain;

[0011] Singular value decomposition clutter suppression steps: Perform singular value decomposition on the target echo signal transformed back to the time domain to obtain the singular value decomposition result of the target echo signal, select the large singular values ​​representing the clutter components to obtain a singular value set, and construct a signal subspace matrix orthogonal to the clutter subspace based on the singular value set; project the target echo signal transformed back to the time domain into the signal subspace matrix to obtain the target echo signal after clutter suppression;

[0012] Fourier transform step: Perform Fourier transform on the target echo signal after clutter suppression to obtain the target echo signal after clutter suppression transformed back to the fractional domain;

[0013] Inverse fractional Fourier transform step: performing inverse fractional Fourier transform on the clutter-suppressed target echo signal transformed back to the fractional domain in sequence according to the slow time dimension to obtain the target echo signal with clutter suppressed.

[0014] Furthermore, in the echo signal rearrangement step, it also includes:

[0015] The target signal transmitted by the radar is phase modulated to obtain a modulated target signal, and the modulated target signal is received by the receiving end to obtain a target echo signal.

[0016] Furthermore, the target signal transmitted by the radar is phase modulated to obtain a modulated target signal, which is implemented as follows:

[0017]

[0018] Among them, S(t) is the modulated target signal, N is the number of sampling points, T r is the pulse repetition period, S1(t) is the target signal emitted by the radar, m and n are parameters ranging from 1 to N, t is the continuous time, and C1(m) is the phase coding signal.

[0019] Furthermore, the modulated target signal is received by the receiving end to obtain the target echo signal, which is achieved as follows:

[0020] X(l)=fs S(l)+Z b (l)+Z s (l)l=0,…,N-1

[0021]

[0022] Z b (l)=[z b1 (l),…,z bm (l),…,z bN (l)]

[0023] Z s (l)=[z s1 (l),…,z sm (l),…,z sN (l)]

[0024] Where X(l) represents the target echo signal, f s represents the Doppler vector of the target echo, f d represents the Doppler vector frequency, S(l) is the echo signal of the modulated target signal S(t), and Z b (l) represents the clutter of the lth range unit, Z s (l) represents the noise vector of the lth distance unit, and l represents a distance unit with a value range of 0 to N-1.

[0025] Furthermore, the echo signal rearrangement step is implemented as follows:

[0026]

[0027] Among them, the M×N-order matrix X is the target echo signal rearranged into a fast and slow time dimension matrix according to the period, and M is the number of pulses.

[0028] Furthermore, the echo signal phase demodulation step is implemented as follows:

[0029]

[0030] Where R(t) is the demodulated target echo signal, C2(m) is the demodulated signal, j is a complex number, and μ is the frequency modulation slope.

[0031] Furthermore, the optimal fractional order p is calculated as follows:

[0032]

[0033] Where B is the signal bandwidth and Fs is the signal sampling frequency.

[0034] Furthermore, in the singular value decomposition clutter suppression step, the target echo signal transformed back to the time domain is subjected to singular value decomposition to obtain the singular value decomposition result of the target echo signal matrix, which is implemented as follows:

[0035]

[0036] Among them, X c To transform the target echo signal back to the time domain, C, T, and N represent the singular value set of the clutter subspace, the singular value set of the target subspace, and the singular value set of the noise subspace, respectively. The superscript () H represents the conjugate transpose of the matrix, u i For X c The i-th left singular vector, v i For X c The i-th right singular vector of i is the i-th singular value, and u i >v i >λ i And they are arranged in descending order from largest to smallest.

[0037] Furthermore, in the singular value decomposition clutter suppression step, a signal subspace matrix orthogonal to the clutter subspace is constructed based on the singular value set, including:

[0038] The vector product of the singular vectors representing the clutter subspace is calculated based on the singular value set. The calculation formula is as follows:

[0039]

[0040] Among them, P c represents the singular vector-vector product;

[0041] The signal subspace matrix orthogonal to the clutter subspace is constructed based on the least squares method according to the vector product of the singular vectors. The calculation formula is as follows:

[0042]

[0043] in, is the signal subspace matrix, I represents the identity matrix, P c represents the singular vector-cross product.

[0044] Furthermore, in the singular value decomposition clutter suppression step, the target echo signal transformed back to the time domain is projected into the signal subspace matrix to obtain the target echo signal after clutter suppression, and the calculation formula is as follows:

[0045]

[0046] Among them, X rIndicates the target echo signal after clutter suppression. represents the signal subspace matrix, X c Represents the target echo signal transformed back to the time domain.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] This invention employs a sea clutter suppression method based on singular value decomposition (SVD) using a fractional Fourier transform. By combining SVD with SVD, the method effectively filters out sea clutter signals, while minimizing effective signal loss and improving the target's signal-to-noise ratio (SNR). This overcomes the inability of existing clutter suppression methods to suppress sea clutter that overlaps with the target on time-frequency plots, thereby enhancing radar detection capabilities.

[0049] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Flowchart of a sea clutter suppression method based on singular value decomposition of fractional Fourier transform provided by an embodiment of the present invention;

[0051] Figure 2 This is the spectrum diagram before sea clutter suppression in the present invention;

[0052] Figure 3 (a) is the range-Doppler diagram before sea clutter suppression in the present invention;

[0053] Figure 3 (b) is a normalized amplitude diagram of range-velocity before sea clutter suppression in the present invention;

[0054] Figure 4 (a) Range-Doppler diagram of the suppression results of traditional singular value decomposition sea clutter suppression method;

[0055] Figure 4 (b) is the normalized amplitude diagram of range-velocity of the suppression result of the traditional singular value decomposition sea clutter suppression method;

[0056] Figure 5 (a) A range-Doppler diagram of the sea clutter suppression results of the sea clutter suppression method based on fractional Fourier transform singular value decomposition provided by the present invention;

[0057] Figure 5 (b) A normalized amplitude diagram of the range-velocity value of the sea clutter suppression result of the sea clutter suppression method based on the fractional Fourier transform singular value decomposition provided by the present invention;

[0058] Figure 6(a) Range-Doppler diagram of target detection results after sea clutter suppression using the singular value decomposition (SVD) sea clutter suppression method based on fractional Fourier transform provided by the present invention;

[0059] Figure 6 (b) is the normalized amplitude diagram of the range-speed target detection result after sea clutter suppression by the singular value decomposition method based on fractional Fourier transform provided by the present invention. DETAILED DESCRIPTION

[0060] The present invention will be further described below with reference to the accompanying drawings and examples, but the embodiments of the present invention are not limited thereto.

[0061] In order to overcome the problem that the existing traditional clutter suppression method cannot suppress the sea clutter overlapping with the target in the time-frequency diagram and improve the radar's detection capability of the target, the embodiment of the present invention provides a sea clutter suppression method based on singular value decomposition of fractional Fourier transform, such as Figure 1 As shown, the method includes the following steps:

[0062] Step 1: The signal transmitted by the radar is a linear frequency modulation signal. The target signal transmitted by the radar is phase modulated to obtain the modulated target signal. The implementation is as follows:

[0063]

[0064] Among them, S(t) is the modulated target signal, N is the number of sampling points, T r is the pulse repetition period, S1(t) is the target signal emitted by the radar, m and n are parameters ranging from 1 to N, t is the continuous time, and C1(m) is the phase coding signal.

[0065]

[0066] Among them, τ is the signal time width, B is the signal bandwidth, μ is the frequency modulation slope,

[0067] Where C1(m) is the phase coding signal, expressed as:

[0068]

[0069] in, is the frequency modulation slope.

[0070] The modulated target signal is received by the receiver to obtain the target echo signal. The implementation is as follows:

[0071] X(l)=f s S(l)+Z b (l)+Z s (l)l=0,…,N-1

[0072]

[0073] Z b (l)=[z b1 (l),…,z bm (l),…,z bN (l)]

[0074] Z s (l)=[z s1 (l),…,z sm (l),…,z sN (l)]

[0075] Where X(l) represents the target echo signal, f s represents the Doppler vector of the target echo, f d represents the Doppler vector frequency, S(l) is the echo signal of the modulated target signal S(t), and Z b (l) represents the clutter of the lth range unit, Z s (l) represents the noise vector of the lth distance unit, and l represents a distance unit with a value range of 0 to N-1.

[0076] The target echo signal is rearranged into a fast and slow time dimension matrix according to the period, which can be achieved as follows:

[0077]

[0078] Among them, the M×N-order matrix X is the target echo signal rearranged into a fast and slow time dimension matrix according to the period, and M is the number of pulses.

[0079] Step 2: Phase demodulate the target echo signal that is rearranged into a fast and slow time dimension matrix according to the period to obtain the demodulated target echo signal, which is implemented as follows:

[0080]

[0081] Where R(t) is the demodulated target echo signal, C2(m) is the demodulated signal, j is a complex number, μ is the frequency modulation slope, And the demodulated signal C2(m) is the conjugate signal of the phase-encoded signal C1(m), C(m)*C.(m)=1

[0082] After demodulation, the target signal emitted by the radar is restored to a single-frequency signal, and its delay and Doppler information remain unchanged, while the C2(m)Z of the clutter part is b (t-nT r ) and C2(m)Z s (t-nT r) is equivalent to expanding the clutter, so that the originally concentrated clutter components are dispersed in the frequency domain, and the clutter signal exhibits linear frequency modulation characteristics. At this time, there is a difference between the clutter signal and the target echo signal in the slow time dimension.

[0083] Step 3: Perform a fractional Fourier transform on the demodulated target echo signal according to the optimal fractional order to obtain the target echo signal transformed into the optimal fractional order fractional domain. The specific steps are:

[0084] Performing a Fourier transform on a single-frequency signal in the time domain will cause the signal to appear as an impulse function in the frequency domain, thus achieving energy concentration. Similarly, performing a fractional Fourier transform (FRFT) on the demodulated target echo signal at a specific fractional order can make the signal appear as an impulse function in the fractional Fourier domain, thus achieving energy concentration. However, fractional Fourier transforms of different fractional orders have different energy concentration effects on the same target echo signal. Improper selection of the fractional order will result in unsatisfactory energy concentration effects. Therefore, it is necessary to determine an optimal fractional order for fractional Fourier transform through peak search. The calculation formula for the optimal fractional order p is as follows:

[0085]

[0086] Where B is the signal bandwidth and Fs is the signal sampling frequency.

[0087] After performing a fractional Fourier transform on a linear frequency modulation signal at the optimal fractional order, it appears as a pulse with concentrated energy in the fractional domain. However, the Fourier transform of a single-frequency signal achieves optimal energy concentration when the fractional order is 1, with the energy being more dispersed in the remaining fractions. Therefore, performing phase demodulation on the target echo signal followed by a fractional Fourier transform can make the energy difference between the target and clutter more pronounced at the fractional order. While the target and clutter frequencies are typically mixed and difficult to decompose using singular value decomposition (SVD) for subspace decomposition, transforming to the fractional Fourier transform domain allows for greater distinction between the two, enabling direct use of SVD for clutter suppression.

[0088] Step 4: Perform an inverse Fourier transform (IFFT) on the target echo signal transformed into the optimal fractional-order fractional domain to obtain a target echo signal transformed back into the time domain.

[0089] Singular value decomposition is a clutter suppression method for time domain signals, so it is necessary to transform the target echo signal in the fractional domain back to the time domain before performing clutter suppression.

[0090] Step 5: Construct a signal subspace matrix based on the target echo signal transformed back to the time domain, and project the target echo signal transformed back to the time domain into the signal subspace matrix to obtain the target echo signal after suppressing sea clutter. The specific steps are:

[0091] Perform singular value decomposition on the target echo signal transformed back to the time domain to obtain the singular value decomposition result of the target echo signal. The implementation is as follows:

[0092]

[0093] Among them, X c To transform the target echo signal back to the time domain, C, T, and N represent the singular value set of the clutter subspace, the singular value set of the target subspace, and the singular value set of the noise subspace, respectively. The superscript () H represents the conjugate transpose of the matrix, u i For X c The i-th left singular vector, v i For X c The i-th right singular vector of i is the i-th singular value, and u i >v i >λ i And they are arranged in descending order from largest to smallest.

[0094] The vector product of the singular vectors representing the sea clutter subspace is calculated based on the singular value set. The calculation formula is as follows:

[0095]

[0096] Among them, P c represents the singular vector-cross product.

[0097] The signal subspace matrix orthogonal to the clutter subspace is constructed based on the least squares method according to the vector product of the singular vectors. The calculation formula is as follows:

[0098]

[0099] in, is the signal subspace matrix, I represents the identity matrix, P c represents the singular vector-cross product.

[0100] Project the target echo signal transformed back to the time domain into the signal subspace matrix to obtain the target echo signal after suppressing sea clutter. The calculation formula is as follows:

[0101]

[0102] Among them, X r Indicates the target echo signal after suppressing sea clutter. represents the signal subspace matrix, X c Represents the target echo signal transformed back to the time domain.

[0103] Step 6: Perform Fourier transform (FFT) on the target echo signal after suppressing sea clutter to obtain the target echo signal after suppressing sea clutter transformed back into the fractional domain.

[0104] Step 7: Perform inverse fractional Fourier transform (IFRFT) on the target echo signal after sea clutter suppression that has been transformed back to the fractional domain in the slow time dimension to obtain the target echo signal after sea clutter suppression.

[0105] This invention employs a sea clutter suppression method based on singular value decomposition (SVD) using a fractional Fourier transform. By combining the SVD with the fractional Fourier transform (FFT), the method effectively filters out sea clutter signals, while minimizing effective signal loss and improving the target's signal-to-noise ratio (SNR). This overcomes the inability of existing clutter suppression methods to suppress sea clutter that overlaps with the target on time-frequency plots, thereby enhancing the radar's detection capabilities.

[0106] Figure 2 This is the spectrum diagram before sea clutter suppression in the present invention. It can be seen that the clutter and target overlap on the time-frequency diagram before suppression and cannot be effectively distinguished.

[0107] Figure 3 (a) is the range-Doppler diagram before sea clutter suppression in the present invention. In order to obtain the target velocity information intuitively, its Doppler frequency is converted to velocity to obtain the normalized amplitude of the range-velocity diagram, as shown in Fig. Figure 3 (b) shown.

[0108] Figure 4 (a) is the range-Doppler diagram of the traditional singular value decomposition sea clutter suppression method. Figure 4 (b) is the normalized amplitude diagram of the range-velocity suppression result of the traditional singular value decomposition sea clutter suppression method. It can be seen that when the target and clutter overlap on the time-frequency diagram, the traditional singular value decomposition algorithm is difficult to effectively separate the target from the clutter.

[0109] Figure 5 (a) is a range-Doppler diagram of the sea clutter suppression result of the sea clutter suppression method based on fractional Fourier transform provided by the present invention, Figure 5 (b) is a normalized amplitude diagram of the sea clutter suppression result of the sea clutter suppression method based on fractional Fourier transform singular value decomposition provided by the present invention. It can be seen that after using the method of the present invention, the sea clutter component is greatly reduced and well suppressed, and the target component can be highlighted. In addition, the sea clutter suppression effect of the method of the present invention is significantly better than that of the traditional singular value decomposition method.

[0110] Figure 6(a) is a range-Doppler diagram of target detection results after sea clutter suppression using the singular value decomposition (SVD) sea clutter suppression method based on fractional Fourier transform provided by the present invention, Figure 6 (b) is a normalized amplitude diagram of the distance-velocity of the target detection result after sea clutter suppression using the singular value decomposition (SVD) method based on fractional Fourier transform provided by the present invention. It can be seen that the obtained target distance and velocity information are very close to the initially set parameter values, indicating that after sea clutter suppression using the method of the present invention, the output signal-to-noise ratio is improved, facilitating subsequent target detection and other processing.

[0111] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A sea clutter suppression method based on singular value decomposition of fractional Fourier transform, characterized in that: The following steps are involved: Echo signal rearrangement step: rearrange the target echo signal into a fast and slow time dimension matrix according to the period; The echo signal phase demodulation step: performing phase demodulation on the target echo signal rearranged into a fast and slow time dimension matrix according to the period to obtain a demodulated target echo signal; Fractional Fourier transform step: performing a fractional Fourier transform on the demodulated target echo signal according to an optimal fractional order to obtain a target echo signal transformed into a fractional domain of the optimal fractional order; Inverse Fourier transform step: performing inverse Fourier transform on the target echo signal transformed into the optimal fractional-order fractional domain to obtain the target echo signal transformed back into the time domain; Singular value decomposition clutter suppression step: performing singular value decomposition on the target echo signal transformed back to the time domain to obtain a singular value decomposition result of the target echo signal, selecting large singular values ​​representing clutter components to obtain a singular value set, and constructing a signal subspace matrix orthogonal to the clutter subspace based on the singular value set; projecting the target echo signal transformed back to the time domain into the signal subspace matrix to obtain a target echo signal after clutter suppression; Fourier transform step: performing Fourier transform on the target echo signal after clutter suppression to obtain the target echo signal after clutter suppression transformed back into the fractional domain; Inverse fractional Fourier transform step: performing inverse fractional Fourier transform on the clutter-suppressed target echo signal transformed back to the fractional domain in sequence according to the slow time dimension to obtain the target echo signal with clutter suppressed.

2. The sea clutter suppression method based on fractional Fourier transform singular value decomposition according to claim 1 is characterized in that: The echo signal rearrangement step further includes: The target signal transmitted by the radar is phase modulated to obtain a modulated target signal, and the modulated target signal is received by a receiving end to obtain a target echo signal.

3. The sea clutter suppression method based on fractional Fourier transform singular value decomposition according to claim 2 is characterized in that: The target signal transmitted by the radar is phase modulated to obtain the modulated target signal, which is implemented as follows: Among them, S(t) is the modulated target signal, N is the number of sampling points, T r is the pulse repetition period, S1(t) is the target signal emitted by the radar, m and n are parameters ranging from 1 to N, t is the continuous time, and C1(m) is the phase coding signal.

4. The sea clutter suppression method based on singular value decomposition of fractional Fourier transform according to claim 2 is characterized in that: The modulated target signal is received by the receiving end to obtain a target echo signal, which is achieved as follows: X(l)=f s S(l)+Z b (l)+Z s (l) l=0,…,N-1 Z b (l)=[z b1 (l),…,z bm (l),…,z bN (l)] Z s (l)=[z s1 (l),…,z sm (l),…,z sN (l)] Where X(l) represents the target echo signal, f s represents the Doppler vector of the target echo, f d represents the Doppler vector frequency, S(l) is the echo signal of the modulated target signal S(t), and Z b (l) represents the clutter of the lth range unit, Z s (l) represents the noise vector of the lth distance unit, and l represents a distance unit with a value range of 0 to N-1.

5. The sea clutter suppression method based on fractional Fourier transform singular value decomposition according to claim 1 is characterized in that: The echo signal rearrangement step is implemented as follows: Among them, the M×N-order matrix X is the target echo signal rearranged into a fast and slow time dimension matrix according to the period, and M is the number of pulses.

6. The sea clutter suppression method based on fractional Fourier transform singular value decomposition according to claim 1 is characterized in that: The echo signal phase demodulation step is implemented as follows: Where R(t) is the demodulated target echo signal, C2(m) is the demodulated signal, j is a complex number, and μ is the frequency modulation slope.

7. The sea clutter suppression method based on singular value decomposition of fractional Fourier transform according to claim 1 is characterized in that: The optimal fractional order p is calculated as follows: Where B is the signal bandwidth and Fs is the signal sampling frequency.

8. The sea clutter suppression method based on fractional Fourier transform singular value decomposition according to claim 1 is characterized in that: In the singular value decomposition clutter suppression step, singular value decomposition is performed on the target echo signal transformed back to the time domain to obtain a singular value decomposition result of the target echo signal matrix, which is implemented as follows: Among them, X c To transform the target echo signal back to the time domain, C, T, and N represent the singular value set of the clutter subspace, the singular value set of the target subspace, and the singular value set of the noise subspace, respectively. The superscript () H represents the conjugate transpose of the matrix, u i For X c The i-th left singular vector, v i For X c The i-th right singular vector of i is the i-th singular value, and u i >v i >λ i And they are arranged in descending order from largest to smallest.

9. The sea clutter suppression method based on fractional Fourier transform singular value decomposition according to claim 1 is characterized in that: In the singular value decomposition clutter suppression step, constructing a signal subspace matrix orthogonal to the clutter subspace based on the singular value set includes: The vector product of the singular vectors representing the clutter subspace is calculated based on the singular value set, and the calculation formula is as follows: Among them, P c represents the singular vector-vector product; A signal subspace matrix orthogonal to the clutter subspace is constructed based on the least squares method according to the singular vector vector product. The calculation formula is as follows: in, is the signal subspace matrix, I represents the identity matrix, P c represents the singular vector-cross product.

10. The sea clutter suppression method based on fractional Fourier transform singular value decomposition according to claim 1, characterized in that: In the singular value decomposition clutter suppression step, the target echo signal transformed back to the time domain is projected into the signal subspace matrix to obtain the target echo signal after clutter suppression. The calculation formula is as follows: Among them, X r Indicates the target echo signal after clutter suppression. represents the signal subspace matrix, X c Represents the target echo signal transformed back to the time domain.

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