A transient interference suppression method combined with sparse prior

Abstract

The application discloses a transient interference suppression method combined with a sparse prior, and comprises the following steps: S1, an echo signal model is established, each component of the echo signal is subjected to regularization constraint, and an equation constraint is performed through a discrete Fourier matrix to construct an objective function; S2, a peak value detection is used to estimate a Bragg frequency to determine a block position; S3, according to the objective function constructed in step S1, an equation constraint is eliminated through an augmented Lagrange function; S4, a regularization parameter of the objective function is initialized and set, and an iteration termination condition of an algorithm is set; S5, all variables to be solved are updated alternately until iteration convergence is achieved, a result after clutter components are removed is obtained, and transient interference suppression is realized. The application can effectively suppress transient interference, improve target signal-to-noise ratio loss, and further improve target detection performance of OTHR.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar detection, and more particularly, to a transient interference suppression method combined with sparse prior. BACKGROUND

[0002] Over-the-Horizon Radar (OTHR) uses the ionosphere to refract and reflect high frequency (3-30MHz) electromagnetic waves to detect targets beyond the horizon, with a detection range of 800-3000km. OTHR has the ability to continuously monitor remote areas early, which is difficult for conventional microwave radars to achieve. Due to its special propagation mechanism, OTHR is susceptible to transient interference from electromagnetic devices in the same frequency band, lightning pulses, and meteor trails. Transient interference, also known as "impulse noise", is a high-frequency interference signal with a duration (about 100-400ms) much shorter than the coherent integration time (CIT). Since the transient interference is not coherent with the radar transmit waveform, the accumulated energy covers almost the entire Doppler frequency domain. Taking lightning interference as an example, without any processing, lightning impulse noise can cause the radar receiver sensitivity to decrease by more than 10dB, and the output signal-to-noise ratio (SNR) to decrease by about 10-30dB. Therefore, transient interference suppression is one of the key technologies for improving the target detection performance of OTHR in adverse conditions. SUMMARY

[0003] The present application aims to provide a transient interference suppression method combined with sparse prior to overcome the shortcomings of the prior art.

[0004] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0005] A transient interference suppression method combined with sparse prior, comprising the following steps:

[0006] S1, establishing an echo signal model, performing regularization constraint on each component of the echo signal, and performing equation constraint through a discrete Fourier matrix to construct an objective function;

[0007] S2, estimating the Bragg frequency according to peak value detection to determine the block position;

[0008] S3, eliminating the equation constraint through an augmented Lagrange function according to the objective function constructed in step S1;

[0009] S4, initializing the regularization parameter of the objective function and setting the iteration termination condition of the algorithm;

[0010] S5, all variables to be solved are updated alternately until iteration converges, and the result after clutter component is removed is obtained, so as to realize transient interference suppression.

[0011] Further, the step S1 specifically comprises:

[0012] S10, setting that the slow time echo data of a certain distance unit contains M accumulated pulse numbers

[0013] S11, when there is transient interference, y is decomposed into the sum of target component, clutter component, transient interference component and noise component y(m) = s(m) + c(m) + o(m) + n(m), m = 1, …, M, wherein s, c, o and n represent the slow time domain components of target, clutter, transient interference and noise respectively;

[0014] The noise component obeys zero-mean complex Gaussian distribution, and is expressed as:

[0015]

[0016] In the formula, σ 2 is the internal noise variance;

[0017] The target component is expressed as:

[0018]

[0019] In the formula, a k is the amplitude of the kth target, f d,k is the Doppler frequency of the kth target, T r is the pulse repetition period, is the phase disturbance term caused by ionospheric pollution to the target component;

[0020] The clutter component is expressed as:

[0021]

[0022] In the formula, b c1 and b c2 respectively represent the amplitudes of positive and negative Bragg peaks of sea clutter, T r is the pulse repetition period, and are respectively the phase disturbance terms caused by ionosphere to the positive and negative Bragg peaks, f b1 and f b2 are respectively the positive and negative Bragg frequencies, and are expressed as:

[0023]

[0024] where g is the acceleration of gravity, θ is the angle between radar and sea surface, λ is the radar operating wavelength, and Δf = 2v s cosθ / λ is the Doppler shift caused by the sea current movement, where v s is the radial velocity of the sea current;

[0025] The transient interference component is:

[0026]

[0027] where has rect j (m) is a rectangular window function, defined as:

[0028]

[0029] where j represents the jth transient interference in the distance unit, and the length of the slow time unit that the transient interference lasts is M j,2 -M j,1 , satisfying 0≤M j,1 <M j,2 ≤M and M i,2 -M i,1 《M;

[0030] S12, separate the transient interference component in the slow time domain, and coherently accumulate the remaining signal component to obtain a corresponding Doppler domain component:

[0031] x = A (y - o) = A (s + c + n),

[0032] where is a normalized discrete Fourier matrix, and the (i, j)th element of the matrix is

[0033]

[0034] Sparse constraint is performed on the non-convex term l p norm, and an l2 norm is added as a noise reduction term to obtain an objective function:

[0035]

[0036] where μ1, μ2 and μ3 are regularization parameters, φ(x) is a block sparse regularization term, x is divided into G non-overlapping sub-blocks, and φ(x) is represented as:

[0037]

[0038] where is an index set, satisfying

[0039]

[0040] Further, the step S2 specifically comprises:

[0041] S20, set the Doppler frequency range of the clutter region as 2f b2 ~ 2f b1 , and combine the prior information to divide the clutter region into two sub-blocks with positive and negative Bragg peaks as boundaries, respectively denoted as and

[0042]

[0043] In the formula, and are the floor and ceiling symbols respectively;

[0044] S21, find the Doppler frequencies corresponding to the h peaks with the largest amplitudes, and take the mean value as the estimated value of the Bragg frequency f b1 or f b2

[0045]

[0046] In the formula, mean(·) is the mean value, findpeaks(v, h) is the index value of the first h peaks of the vector v, and the estimated value of Δf is:

[0047]

[0048] The joint Bragg frequency expression realizes the estimation of f b1 and f b2

[0049] Further, the step S3 specifically comprises:

[0050] S30, introduce new variables and Rewrite the objective function as:

[0051]

[0052] S31, eliminate the equality constraint by using the augmented Lagrange function, and obtain:

[0053]

[0054] In the formula, and are intermediate variables, and (·) H ​​is the Hermitian transpose, and ρ is the quadratic penalty coefficient. The separation of the slow time-domain transient interference component and the recovery of the clean spectrum defined as the Doppler spectrum corresponding to the target and sea clutter are achieved by minimizing the above formula;

[0055] S32, the optimal solution of each component is expressed as:

[0056]

[0057] Each variable is solved by ADMM alternately updated.

[0058] Further, the step S4 is specifically:

[0059] The initial variable x 0 , o 0 , w 0 , a 0 , and are set to The regularization parameter is set to μ1=1 / (3M), μ2=μ3=1 / (4M), and the initial value of the quadratic penalty coefficient is ρ0=10 -2 , the maximum value is ρ max =10 6 , the iteration step length τ=1.1, the iteration termination error ε=10 -6 , the step length κ=2, and the peak number h=5. When the following formula is satisfied, the iteration converges:

[0060]

[0061] In the formula, Further, the step S5 is specifically:

[0062] S50, update the variable x:

[0063]

[0064] In the formula, is a soft threshold operator, defined as

[0065]

[0066] In the formula, max{·} is the maximum function, is a sign function; S51, update the variable o:

[0067]

[0068] Wherein is:

[0069]

[0070] l p norm proximity operator The expression is:

[0071]

[0072] In the formula, beta and alpha are constants, and are defined as:

[0073]

[0074] Beta * The solving method is:

[0075]

[0076] The initial value is set as beta 0 E(beta, |v i |), and the iteration number is 10-20 times, so that the accuracy requirement of the algorithm can be met.

[0077] S52, update the variable w:

[0078] The solving problem of the variable w is smooth and convex, and the solution is:

[0079]

[0080] S53, update the variable a:

[0081]

[0082] Decompose into G sub-problems for solving, and there are:

[0083]

[0084] Among them:

[0085]

[0086] S54, update the variable lambda1:

[0087]

[0088] S55, update the variable lambda2:

[0089]

[0090] In the formula, tau is an iteration step, and satisfies The above variables are alternately updated until the iteration converges, so that the signal component after removing the transient interference is obtained, and the transient suppression is realized. Compared with the prior art, the advantages of the present application are that: the present application utilizes the sparse prior of the slow time domain transient interference component, the overlapping block sparse prior of the Doppler domain sea clutter and the target component, and the l1 norm, lp The norm, the block sparse regularization term and the l2 norm are constrained, and the solution is obtained through an optimization algorithm framework, so that the transient interference can be effectively suppressed, the signal-to-noise ratio (SNR) loss of the target can be improved, and then the target detection performance of the OTHR can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0091] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0092] Figure 1 is a flow chart of the transient interference suppression method of the present application combined with sparse prior.

[0093] Figure 2 The schematic diagram is constructed for the target function.

[0094] Figure 3 The algorithm execution flow chart is constructed for the present application.

[0095] Figure 4 The transient interference suppression result in the range-doppler domain under the OTHR measured data.

[0096] Figure 5 The transient interference suppression result comparison in the range-doppler domain under the OTHR measured data.

[0097] Figure 6 The OTHR transient interference suppression performance comparison and analysis. DETAILED DESCRIPTION

[0098] The preferred embodiments of the present application will be described in detail below with reference to the drawings, so that the advantages and characteristics of the present application can be more easily understood by those skilled in the art, and the protection scope of the present application can be more clearly and definitely defined.

[0099] Referring to Figure 1 The present embodiment discloses a transient interference suppression method combined with sparse prior, which comprises the following steps.

[0100] Step S1, an echo signal model is established, each component of the echo signal is regularized, and the equation is constrained through a discrete Fourier matrix, so as to construct a target function.

[0101] Step S2, the Bragg frequency is estimated according to peak detection, so as to determine the block position.

[0102] Step S3, according to the objective function constructed in step S1, eliminate the equality constraints by augmented Lagrange function.

[0103] Step S4, initialize the regularization parameter of the objective function, set the iteration termination condition of the algorithm.

[0104] Step S5, update all variables alternately until the iteration converges, get the result after removing the clutter component, and realize the transient interference suppression.

[0105] Specifically, the step S1 specifically includes:

[0106] Step S10, set the slow-time echo data of a certain range cell to contain M accumulated pulse numbers

[0107] Step S11, when there is transient interference, y is decomposed into the sum of target component, clutter component, transient interference component and noise component y(m)=s(m)+c(m)+o(m)+n(m), m=1,…,M, wherein s, c, o and n represent the slow-time components of target, clutter, transient interference and noise respectively.

[0108] The noise component obeys zero-mean complex Gaussian distribution, which is expressed as:

[0109]

[0110] In the formula, σ 2 is the internal noise variance;

[0111] The target component is expressed as:

[0112]

[0113] In the formula, a k is the amplitude of the kth target, f d,k is the Doppler frequency of the kth target, T r is the pulse repetition period, is the phase disturbance term caused by ionospheric pollution to the target component.

[0114] The clutter component is expressed as:

[0115]

[0116] In the formula, b c1 and b c2 represent the amplitudes of the positive and negative Bragg peaks of sea clutter respectively, T r is the pulse repetition period, and are the phase disturbance terms caused by the ionosphere to the positive and negative Bragg peaks respectively, f b1and f b2 These are the positive and negative Bragg frequencies, respectively, expressed as:

[0117]

[0118] In the formula, g is the acceleration due to gravity, θ is the angle between the radar and the sea surface, λ is the radar's operating wavelength, and Δf = 2v s cosθ / λ is the Doppler frequency shift caused by ocean currents, where v s The radial velocity of the ocean current.

[0119] The transient disturbance component is:

[0120]

[0121] In the formula, have rect j (m) is a rectangular window function, defined as:

[0122]

[0123] In the formula, j represents the j-th transient disturbance at this distance cell, and its duration is a slow time cell of length M. j,2 -M j,1 , satisfying 0≤M j,1 <M j,2 ≤M and M i,2 -M i,1 <<M.

[0124] S12. Separate the transient interference components in the slow time domain and perform coherent accumulation on the remaining signal components to obtain the corresponding Doppler domain components:

[0125] x = A(yo) = A(s+c+n),

[0126] In the formula, The normalized discrete Fourier matrix has the following element as its (i,j)th element:

[0127]

[0128] With non-convex term l p By applying sparsity constraints using the norm and adding the L2 norm as a noise reduction term, we obtain the objective function:

[0129]

[0130] In the formula, μ1, μ2, and μ3 are regularization parameters, and φ(x) is a block sparsity regularization term that divides x into G non-overlapping sub-blocks. φ(x) is expressed as:

[0131]

[0132] wherein, is a set of indices satisfying

[0133]

[0134] Specifically, the step S2 specifically comprises:

[0135] Step S20, set the Doppler frequency range of the clutter region as 2f b2 ~ 2f b1 , and combine the prior information to divide the clutter region into two sub-blocks with positive and negative Bragg peaks as boundaries, respectively denoted as and

[0136]

[0137] wherein, and are the floor and ceiling symbols respectively.

[0138] Step S21, find the Doppler frequencies corresponding to the h peaks with the largest amplitudes, and take the mean value as the estimation of the Bragg frequency f b1 or f b2

[0139]

[0140] wherein, mean(·) is the mean value, findpeaks(v, h) is the index value of the first h peaks of the vector v, and the estimation of Δf is:

[0141]

[0142] The joint Bragg frequency expression realizes the estimation of f b1 and f b2

[0143] Specifically, the step S3 specifically comprises:

[0144] Step S30, introduce new variables and and rewrite the objective function as:

[0145]

[0146] s.t.A(y-o)-x-w=0,a-x=0

[0147] Step S31, eliminate the equality constraints by the augmented Lagrange function, to obtain: ​​

[0148]

[0149] wherein, and are intermediate variables, (·) H is the Hermitian transpose, and ρ is a quadratic penalty coefficient, by minimizing the above formula, the slow time-domain transient interference component is separated and the pure spectrum is recovered, and the pure spectrum is defined as the Doppler spectrum corresponding to the target and sea clutter.

[0150] Step S32, the optimization solution of each component is represented as:

[0151]

[0152] Each variable is solved by ADMM alternately updated.

[0153] Specifically, the step S4 is specifically:

[0154] The initial variable x 0 , o 0 , w 0 , a 0 , and are set to The regularization parameter is set to μ1=1 / (3M), μ2=μ3=1 / (4M), and the initial value of the quadratic penalty coefficient is ρ0=10 -2 , the maximum value is ρ max =10 6 , the iteration step length τ=1.1, and the iteration termination error ε=10 -6 , the step length κ=2, and the peak number h=5

[0155] When the following formula is satisfied, the iteration converges:

[0156]

[0157] wherein, Specifically, the step S5 is specifically:

[0158] Step S50, update the variable x:

[0159]

[0160] wherein, is a soft threshold operator, defined as

[0161]

[0162] wherein, max{·} is a maximum function, is a sign function;

[0163] Step S51, update variable o:

[0164]

[0165] where is:

[0166]

[0167] l p Norm proximity operator The expression of is:

[0168]

[0169] In the formula, β and α are constants, defined as:

[0170]

[0171] β * The solution method of is:

[0172]

[0173] The initial value is set to β 0 ∈(β, |v i |), and the iteration number is 10-20 times, which can meet the accuracy requirement of the algorithm.

[0174] Step S52, update variable w:

[0175] The solution problem of variable w is smooth and convex, and the solution is:

[0176]

[0177] Step S53, update variable a:

[0178]

[0179] Decompose into G sub-problems for solution, and there are:

[0180]

[0181] Where:

[0182]

[0183] Step S54, update variable λ1:

[0184]

[0185] Step S55, update variable λ2:

[0186]

[0187] In the formula, τ is an iteration step length, and satisfies

[0188] The above variables are alternately updated until the iteration converges, to obtain the signal component after eliminating the transient interference, and realize transient suppression.

[0189] Figure 2 A schematic diagram is constructed for the target function. Figure 2 Firstly, each echo signal component in the simulation data is shown; then, according to the prior information of each component in the simulation data, the corresponding regularization constraint is constructed; finally, the target function is constructed in combination with the equality constraint.

[0190] Figure 3 The algorithm flow proposed in the application. Given the input slow-time signal y and the discrete Fourier matrix A, under the parameter initialization setting, the algorithm is executed, to obtain the pure Doppler spectrum x after suppressing the transient interference, and the transient interference component o that is eliminated, so that the transient interference suppression is realized.

[0191] Figure 4 The transient interference suppression result in the distance slow-time domain under the OTHR measured data is shown. Figure 4 (a) is the measured OTHR distance slow-time data with transient interference, and the transient interference component and the remaining signal component are separated by performing transient interference suppression processing on the data. Figure 4 (b) is the distance slow-time data after LPOBS transient interference suppression. Figure 4 (c) is the separated transient interference component. It can be known that LPOBS can effectively suppress the transient interference component in the measured data and restore the original data.

[0192] Figure 5 The transient interference suppression result in the distance Doppler domain under the OTHR measured data is shown. Three known real targets are labeled in the figure, and Huber smoothing, RPCA-SVT, L1L1 and MCD are existing transient interference suppression methods. Figure 5 (a) is the RD map without transient interference suppression, Figure 5 (b)-(f) are RD maps after various transient interference suppressions. In Figure 5 In (a), the transient interference component causes three targets to be submerged. Huber smoothing and RPCA-SVT can suppress the transient interference to a certain extent, but there is still residual transient interference component, and the effect is not ideal. The RD maps obtained by L1L1, MCD and LPOBS are relatively clear, and the targets are more obvious.

[0193] Figure 6A comparative analysis of the transient interference suppression performance of OTHR methods is presented. First, the reconstruction accuracy of all transient interference suppression methods is analyzed. The ICNR of the transient interference is set to 10 dB. A transient interference is injected into the entire range-slow-time matrix, and its length (number of slow-time units) is varied. Curves showing the NMSE of various methods as a function of the transient interference length are obtained, as shown below. Figure 6 As shown in (a). In Figure 6 In (a), Huber smoothing has the lowest NMSE when the transient interference length is 5, while MCD has the lowest NMSE when the transient interference length is greater than 90. LPOBS has the lowest NMSE when the transient interference length is 10-85. Overall, LPOBS has the highest reconstruction accuracy among all methods, while Smoothing and RPCA-SVT have the lowest. Next, the output SNR of various methods is analyzed; a higher output SNR indicates better detection performance. With a transient interference length of 30 slow time units and an ICNR of 10 dB, the target's input SCNR is varied, and the curves showing the change in output SNR with input SCNR are obtained, as shown below. Figure 6 As shown in (b). In Figure 6 In (b), LPOBS achieves the highest output SNR when the input SCNR is below -50dB, while MCD achieves the highest output SNR when the SCNR is above -50dB. This is because MCD reduces the amplitude of low-SCNR targets during noise reduction. It's important to note that an SNR of 13dB is sufficient for target detection; higher SNRs are meaningless, making SNR improvement more crucial for low-SCNR targets. Overall, LPOBS demonstrates the best SNR improvement, followed by MCD, while Smoothing and RPCA-SVT perform poorly.

[0194] Table 1 below compares the computation time of OTHR transient interference suppression methods. The data includes 100 distance units and 512 slow time units. Experimental conditions were: Intel eight-core processor, 16GB memory, and MATLAB (2021b) software. RPCA-SVT and IALM process vectors into matrices, significantly increasing computational complexity and resulting in the longest runtime, making them largely unsuitable for real-time OTHR detection. CS, Smoothing, L1L1, and LPOBS (the proposed method) have runtimes on the same order of magnitude, remaining within 5 seconds, far shorter than other algorithms. CS and Smoothing are two-step methods (two-step methods include localization and suppression steps; the time here refers only to the suppression time). If interference localization processing is considered, the runtime of two-step methods may increase further. The proposed LPOBS is the shortest runtime method among one-step methods (one-step methods do not require localization).

[0195] Table 1. Comparison of operation time of OTHR transient interference suppression method

[0196]

[0197] The present application utilizes the sparse prior of slow time domain transient interference component, the overlapping block sparse prior of Doppler domain sea clutter and target component, and the l1 norm, l p norm, block sparse regularization term and l2 norm to constrain, and solves through an optimization algorithm framework, which can effectively suppress transient interference, improve the Signal-to-Noise Ratio (SNR) loss of target, and further improve the target detection performance of OTHR.

[0198] Although the embodiments of the present application are described in combination with the drawings, various modifications or changes can be made by the patent owner within the scope of the appended claims, as long as they do not exceed the protection scope described in the claims of the present application, and should be within the protection scope of the present application.

Claims

1. A method for transient interference suppression incorporating a sparse prior, characterized by, The method comprises the following steps; S1, an echo signal model is established, a sparse prior of a slow time domain transient interference component is used, an overlapping block sparse prior of a Doppler domain sea clutter and a target component is used, l1 norm, l p norm, a block sparse term and l2 norm are used for regularization constraint, and an equation constraint is performed through a discrete Fourier matrix, so as to construct a target function; S2, estimating the Bragg frequency according to the peak value detection to determine the block position; S3, eliminating the equality constraint by using the augmented Lagrange function according to the objective function constructed in step S1; S4, initializing the regularization parameter of the objective function and setting the iteration termination condition of the algorithm; S5, updating all variables to be solved alternately until the iteration converges, obtaining the result after removing the clutter component, and realizing the transient interference suppression.

2. The method of claim 1, wherein, The step S1 specifically comprises: S10, set the slow time echo data of a certain distance unit contains M accumulation pulse numbers S11, when the transient interference exists, y is decomposed into the sum of the target component, the clutter component, the transient interference component and the noise component, that is, y(m) = s(m) + c(m) + o(m) + n(m), m = 1, …, M, wherein s, c, o and n represent the slow time domain components of the target, the clutter, the transient interference and the noise respectively; The noise component obeys the zero-mean complex Gaussian distribution and is expressed as: n(m) ~ CN(0, σ 2 ) where σ2 2 is the internal noise variance; The target component is expressed as: where a k is the amplitude of the kth target, f d,k is the Doppler frequency of the kth target, T r is the pulse repetition period, is the phase perturbation term caused by ionospheric contamination on the target component; The clutter component is expressed as: In the formula, b c1 and b c2 respectively represent the amplitudes of the positive and negative Bragg peaks, T r is the pulse repetition period, and are the phase perturbation terms caused by the ionosphere to the positive and negative Bragg peaks, f b1 and f b2 are the positive and negative Bragg frequencies, and are expressed as: where g is the acceleration of gravity, θ is the angle between the radar and the sea surface, λ is the radar operating wavelength, and Δf = 2v s cosθ / λ is the Doppler shift caused by the sea current movement, where v s is the radial velocity of the sea current; The transient interference component is: wherein there are rect j (m) is a rectangular window function defined as: where j represents the jth transient disturbance of the distance unit, which lasts for M slow time unit lengths j,2 -M j,1 , satisfying 0≤M j,1 <M j,2 ≤M and M i,2 -M i,1 <<M; S12, the transient interference component is separated in the slow time domain, and the remaining signal components are coherently accumulated to obtain the corresponding Doppler domain components: x = A(y-o) = A(s+c+n), wherein is the normalized discrete Fourier matrix whose (i,j)th element is Sparse constraint is added by non-convex term l p The l2 norm is added as a denoising term to obtain the objective function: wherein μ1, μ2, and μ3 are regularization parameters, φ(x) is a block-sparse regularization term, x is divided into G non-overlapping sub-blocks, and φ(x) is expressed as: In the formula, B g (g = 1,..., G) is a set of indexes, satisfying 3. The method of claim 2, wherein, The step S2 specifically comprises: S20, set the Doppler frequency range of the clutter area as 2f b2 ~ 2f b1 , combine the prior information, and divide the clutter area into two sub-blocks B g(c) and B g(c)+1 with positive and negative Bragg peaks as boundaries, respectively. |B g | = K, (g≠ g(c), g≠ g(c) + 1), wherein and are the floor and ceiling functions, respectively. S21, find the Doppler frequencies corresponding to the h peak values with the largest amplitudes, and average them as the Bragg frequency f b1 or f b2 estimate In the formula, mean(·) is the mean value, findpeaks(v, h) is the index value of the first h peaks of the vector v, and the estimated value of Δf is: In the equation, the joint Bragg frequency expression achieves the estimation of f b1 and f b2 .

4. The method of claim 3, wherein, The step S3 specifically comprises: S30, introduce new variable and Rewrite the objective function as: s.t.A(y-o)-x-w = 0, a-x = 0 S31, the equality constraint is eliminated by using the augmented Lagrange function, and the following formula is obtained: wherein and are intermediate variables, (·) H is the Hermitian transpose, and ρ is a quadratic penalty coefficient, by minimizing the above equation to separate the slow time-domain transient interference component and recover the pure spectrum, which is defined as the Doppler spectrum corresponding to the target and sea clutter. S32, the optimal solution of each component is expressed as: Each variable is solved alternately by using the ADMM.

5. The method of claim 4, wherein, The step S4 specifically comprises: The initial variable x 0 , o 0 , w 0 , a 0 , and are set to The regularization parameter is set to μ1=1 / (3M), μ2=μ3=1 / (4M), and the initial value of the quadratic penalty coefficient is ρ0=10 -2 , the maximum value is ρ max =10 6 , the iteration step size τ=1.1, and the iteration termination error ε=10 -6 , the step size κ=2, and the peak number h=5 When the following formula is satisfied, the iteration converges: max{||A(y-o k+1 )-x k+1 -w k+1 || ∞ ,||a k+1 -x k+1 || ∞} < ε In the formulae, 6. The method of claim 1, wherein, The step S5 specifically comprises: S50, updating the variable x: wherein is a soft threshold operator defined as where max{·} is the max function, is the sign function; S51, updating the variable o: wherein is: l p norm proximity operator is given by In the formula, β and α are constants and are defined as: β * The solution method is: The initial value is set as β 0 ∈(β,|v i |), and the iteration number is 10-20 times, which can meet the accuracy requirement of the algorithm. S52, updating the variable w: The solving problem of the variable w is smooth and convex, and the solution is: S53, updating the variable a: The decomposition is solved by G sub-problems, and the following formula is obtained: Wherein: S54, updating the variable λ1: S55, updating the variable λ2: where τ is the iteration step size, satisfying The above variables are updated alternately until the iteration converges, the signal component after removing the transient interference is obtained, and the transient suppression is realized.

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