Radar intermittent sampling interference resisting method based on VMD and sparse Bayesian blind separation

Abstract

The invention discloses a radar intermittent sampling interference resisting method based on VMD and sparse Bayesian blind separation, and the method comprises the steps: determining an intermittent sampling forwarding interference signal based on a transmitting signal model and an echo signal model of a radar, so as to determine a mixed signal received by a receiver under the condition of a single channel; decomposing the mixed signal into P modal components by using a VMD algorithm; selecting a part of modal components from the P modal components and raising the dimension of the mixed signal to obtain a new mixed signal; estimating the number of source signals by using an entropy minimum source number estimation algorithm according to the new mixed signal; reconstructing a multi-channel signal by using the number of estimated source signals and the mixed signal; and recovering a source signal by using a multi-channel signal and a positive definite independent component analysis algorithm based on sparse Bayesian learning. The method can be used for resisting intermittent sampling interference of the linear frequency modulation pulse pressure radar in a complex electromagnetic environment, has good interference suppression capability, and can effectively suppress intermittent sampling interference and recover interfered radar frequency modulation signals.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to a radar anti-intermittent sampling interference method based on VMD (Variational Mode Decomposition) and sparse Bayesian blind separation. Background Art

[0002] In order to improve the target recognition and anti-interference capabilities, modern radars usually use pulse compression signals such as linear frequency modulation or phase coding to obtain high coherent processing gain and distance resolution, which greatly improves the ability to resist traditional suppression interference and incoherent interference. However, for pulse compression signal radar, active deceptive coherent interference of digital RF memory has appeared. For intermittent sampling forwarding interference, the interference signal and the source signal have strong coherence, and the anti-interference method in the airspace fails in this case. Under the premise of having certain prior knowledge, blind signal separation can recover the original signal from the observed signal in the case of unknown source signals and mixed systems, and is therefore widely used in bioengineering, speech signal processing and digital communications.

[0003] Usually, the anti-interference problem of intermittent sampling forwarding interference can be converted into a single-channel blind source separation problem, and the source signal can be separated using the blind source separation algorithm to achieve the effect of suppressing interference. At present, the blind source separation algorithm is based on second-order statistics, high-order statistics, non-stationarity and sparsity to achieve blind source separation. Underdetermined blind signal separation solves the problem that the number of source signals is greater than the number of observed signals. Since the estimated mixing matrix does not have a pseudo-inverse, it is more complicated than the well-determined and over-determined cases. In the actual radar anti-interference problem, the interference signal emitted by the jammer and the source signal are far apart. In many cases, the difference in the arrival direction of the signal is small, and the array signal processing method cannot be used. It can be considered to use a single-channel blind separation method to separate the source signal from the mixed signal received at the receiver.

[0004] In order to counter intermittent sampling interference, the electronic countermeasure methods in the prior art can be divided into two categories. The first category is the signal processing method, which utilizes the characteristics of interference in the time-frequency domain, extracts the parameters of the target echo and the interference signal through time-frequency analysis, and constructs a time-frequency filter based on the extracted parameters to achieve the suppression of intermittent sampling interference. However, constructing a time-frequency filter will cause the loss of echo signals, and the time-frequency filter cannot filter out all interference under specific interference parameters. In addition, the reconstruction of the source signal using time domain parameters depends on prior knowledge and is sensitive to noise, resulting in a serious decrease in anti-interference performance.

[0005] The second type of electronic countermeasure method is the waveform design method. In order to more actively counteract intermittent sampling interference, a specific waveform can be designed to achieve the purpose of interference suppression. For example, an orthogonal working waveform and protection waveform can be designed, and the waveform after interference matches the protection waveform to achieve interference suppression. Of course, it is also possible to construct a frequency hopping waveform or use a frequency step waveform and other waveform construction methods to suppress intermittent sampling forwarding interference. Complex waveform optimization design is difficult to cope with real-time complex interference scene changes. Some waveform design methods require pre-estimation of intermittent sampling forwarding interference parameters. If the parameter estimation is inaccurate, the designed waveform cannot effectively suppress interference. Summary of the invention

[0006] In order to solve the above problems existing in the prior art, the present invention provides a radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0007] The present invention provides a radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation, comprising:

[0008] Based on the radar's transmission signal model and echo signal model, determine the intermittent sampling forwarding interference signal to further determine the mixed signal received by the receiver in the single-channel case;

[0009] Decomposing the mixed signal into P modal components by using a variational mode decomposition (VMD) algorithm;

[0010] Selecting some modal components from the P modal components and upgrading the dimension of the mixed signal to obtain a new mixed signal;

[0011] According to the new mixed signal, the number of source signals is estimated using an entropy minimum source number estimation algorithm;

[0012] Reconstructing a multi-channel signal S′ using the estimated number of source signals and the mixed signal;

[0013] The source signal is restored using the multi-channel signal S′ and a positive definite independent component analysis algorithm based on sparse Bayesian learning.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] The present invention aims at the problem of anti-intermittent sampling interference of linear frequency modulation pulse compression radar, utilizes the sparsity of linear frequency modulation signal in frequency modulation frequency domain, and converts the problem of anti-intermittent sampling interference of linear frequency modulation into positive definite blind source separation problem in CFCR (Chirp Fourier Coefficient Ratio) domain for solution through independent component analysis blind source separation algorithm based on sparse Bayesian learning. The modal components obtained by VMD decomposition increase the dimension of the mixed signal, and the modal components after decomposition are screened by correlation analysis to construct a multi-channel signal. The received single-channel interfered signal can be converted into a virtual multi-channel signal, and then the reconstructed multi-channel signal is used as the input of sparse Bayesian independent component analysis blind separation algorithm, realizing the anti-intermittent sampling interference of frequency modulation signal in single channel. Therefore, the present invention can be used for anti-intermittent sampling interference of linear frequency modulation pulse compression radar in complex electromagnetic environment, has good interference suppression capability, can effectively suppress intermittent sampling interference and restore the interfered radar frequency modulation signal.

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation provided by an embodiment of the present invention;

[0018] Figure 2 Another flow chart of a radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation provided by an embodiment of the present invention;

[0019] Figure 3a is a schematic diagram of an undisturbed linear frequency modulation signal provided by an embodiment of the present invention;

[0020] Figure 3b yes Figure 3a The pulse compression result diagram of the linear frequency modulation signal without interference is shown;

[0021] Figure 4a is a schematic diagram of a linear frequency modulation signal after interference provided by an embodiment of the present invention;

[0022] Figure 4b yes Figure 4a The pulse pressure result diagram of the linear frequency modulation signal after interference is shown;

[0023] Figure 5a is a time-frequency spectrum diagram of an undisturbed linear frequency modulation signal provided by an embodiment of the present invention;

[0024] Figure 5b is a time-frequency spectrum diagram of a linear frequency modulation signal after interference provided by an embodiment of the present invention;

[0025] Figure 6a is a schematic diagram of a mixed signal after de-skewing provided by an embodiment of the present invention;

[0026] Figure 6b is a time-frequency spectrum diagram of a mixed signal after de-skewing provided by an embodiment of the present invention;

[0027] Figure 7a is a schematic diagram of each modal component obtained by VMD decomposition provided by an embodiment of the present invention;

[0028] Figure 7b yes Figure 7a Spectrum diagram of each modal component shown;

[0029] Figure 8 Schematic diagram of average information entropy for different numbers of estimation sources provided by an embodiment of the present invention;

[0030] Figure 9a is a schematic diagram of a source signal after separation provided by an embodiment of the present invention;

[0031] Figure 9b yes Figure 9a Schematic diagram of pulse pressure results of source signal after separation;

[0032] Fig.10 It is the time-frequency spectrum diagram of the source signal after separation shown in FIG9. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0034] Figure 1-2 Flow chart of the radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation provided by an embodiment of the present invention. Figure 1 and Figure 2 The embodiment of the present invention provides a radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation, comprising:

[0035] S1. Based on the radar transmission signal model and echo signal model, determine the intermittent sampling forwarding interference signal to further determine the mixed signal received by the receiver in the single-channel case;

[0036] S2, using variational mode decomposition (VMD) algorithm, decompose the mixed signal into P modal components;

[0037] S3, selecting some modal components from the P modal components and upgrading the dimension of the mixed signal to obtain a new mixed signal;

[0038] S4, estimating the number of source signals using an entropy minimum source number estimation algorithm according to the new mixed signal;

[0039] S5, reconstructing the multi-channel signal S′ using the estimated number of source signals and the mixed signal;

[0040] S6. Restore the source signal by using the multi-channel signal S′ and a positive definite independent component analysis algorithm based on sparse Bayesian learning.

[0041] Optionally, in step S1, based on the radar transmission signal model and the echo signal model, determining the intermittent sampling forwarding interference signal to further determine the mixed signal received by the receiver in the single-channel case includes:

[0042] S101. Construct the radar transmission signal model:

[0043]

[0044] In the formula, f0 represents the center frequency of the transmitted signal, the transmitted signal is a linear frequency modulation signal, j is an imaginary unit, K represents the frequency modulation slope, t represents time, T p Represents the signal pulse width, and rect represents the rectangular function.

[0045] S102. Determine the radar echo signal model based on the transmission signal model:

[0046]

[0047] Wherein, time delay Δt=2R / c, c represents the speed of light, R represents the distance from the preset reference point to the radar, and A represents the amplitude of the echo signal.

[0048] S103: Determine the intermittent sampling forwarding interference signal according to the transmission signal model and the echo signal model:

[0049]

[0050] In the formula, n represents the number of extensions and the number of sampling pulses. T m represents the sampling period, [·] represents the rounding operation, τ m Indicates the sampling pulse width, represents the Kronecker product, Δτ(n)=t-2R j / c-nT m -t0,R j represents the distance between the jammer and the radar, and t0 represents the internal delay of the jammer.

[0051] S104, intermittent sampling and forwarding interference intercepts, stores and forwards radar signals, samples the radar's transmission signal at a lower sampling rate, and uses the matched filtering characteristics of the transmission signal to obtain pulse compression gain, and forwards it after amplitude and phase modulation to generate coherent interference, thereby achieving suppression and deception interference. According to the echo signal model and the intermittent sampling and forwarding interference signal, determine the mixed signal received by the receiver in the single-channel case:

[0052] Y(t)=s r (t)+ηs j (t)+ξ(t);

[0053] Where η represents the weighting coefficient of the intermittent sampling forwarding interference signal, and ξ(t) represents the noise.

[0054] Optionally, in step S2, the step of decomposing the mixed signal Y(t) into P modal components using a variational mode decomposition (VMD) algorithm includes:

[0055] S201, set the number of iterations q = 1, initialize the number of modes P, the first convergence threshold ε1, the maximum number of iterations Q1, the penalty factor β, and the pth modal component at the qth iteration Modal Components Center frequency and the Lagrangian operator λ q , p=1,2,…,P, q=1,2,…,Q1;

[0056] S202, respectively update the modal components Modal Components Center frequency and the Lagrangian operator λ q :

[0057]

[0058]

[0059] In the formula, represents the i-th modal component at the q-th iteration, represents the updated i-th modal component at the q+1th iteration, Indicates updated The center frequency, λ q+1 represents the updated Lagrangian operator at the q+1th iteration, ω represents the frequency variable, is the frequency domain representation of the mixed signal;

[0060] S203, when satisfy and and When the frequency difference of is less than the first preset threshold, P modal components are obtained; otherwise, and λ q+1 As and λ q , and after setting the number of iterations q = q + 1, return to update the modal components respectively Modal Components Center frequency and the Lagrangian operator λ q steps.

[0061] In step S3, the step of selecting some modal components from the P modal components and upgrading the dimension of the mixed signal to obtain a new mixed signal includes:

[0062] S301, from P modal components, select the first G modal components whose cumulative contribution rates exceed a second preset threshold;

[0063] S302 , using the selected G modal components to upgrade the dimension of the mixed signal Y(t) to form a new mixed signal S.

[0064] In this embodiment, the cumulative contribution rate of the first G modal components can be expressed as:

[0065]

[0066] In the formula, u g represents the g-th modal component.

[0067] Exemplarily, the new mixed signal composed of the first G modal components whose cumulative contribution rates exceed the second preset threshold and the mixed signal Y(t) is expressed as S=[Y(t); u1, u2, ..., u G ].

[0068] In step S4, the step of estimating the number of source signals using an entropy minimum source number estimation algorithm according to the new mixed signal includes:

[0069] S401, based on the new mixed signal S, using the FastICA algorithm to determine the estimated source signal Y under different numbers of estimated sources o , the estimated number of sources o = 2, 3,…, O, where O represents the total number of estimated sources.

[0070] S402, using Gaussian mixture model to fit each estimated source signal Y o The probability density of Where M represents the number of Gaussian mixture components, π m represents the weight of the mth Gaussian mixture component, and the hyperparameter Θ m ={μ m , σ m2}, Indicates that the mean of the mth Gaussian mixture component is μ m , the variance is σ m 2 When the source signal Y is estimated o Gaussian distribution.

[0071] S403, after obtaining the target distribution samples through independent Metropolis sampling, combine the estimated source signals Y o The probability density f(Y o ) to estimate information entropy.

[0072] According to the law of large numbers, when the sample size is large enough, the sample mean tends to the expectation. Using Metropolis sampling, we can obtain The random sample is then calculated to estimate the expectation of the sample mean, thus avoiding complex integral calculation problems.

[0073] Assume that the target distribution is p(x), select an initial point x0, sample candidate samples x′ from the proposed distribution q(x′|x), and calculate the acceptance probability:

[0074]

[0075] Generate a uniform distribution u~U(0,1), if u<α receive candidate sample x i+1 = x′, otherwise refuse to keep the current sample x i+1 =x i The sample distribution obtained by sampling is

[0076] S404, selecting the number of estimated source signals corresponding to the minimum average information entropy represents the average information entropy.

[0077] Based on independent Metropolis sampling, we obtain random samples that obey the GMM fitting distribution, calculate the sample mean, and estimate the information entropy:

[0078]

[0079] Select the number of estimated source signals corresponding to the minimum average information entropy. The number of estimated source signals at this time is the required number of source signals:

[0080]

[0081] In step S5, the step of reconstructing the multi-channel signal S′ by using the estimated number of source signals and the mixed signal includes:

[0082] According to the estimated number of source signals The multi-channel signal S' is reconstructed based on the new mixed signal S.

[0083] It should be noted that in step S5, if the estimated number of source signals is less than the new mixed signal S = [Y(t); u1, u2, ..., u G ], then from S = [Y(t); u1,u2,…,u G ] by removing the corresponding number of modal components.

[0084] In step S6, the step of restoring the source signal by using the multi-channel signal S′ and a positive independent component analysis algorithm based on sparse Bayesian learning includes:

[0085] S601, according to the multi-channel signal S', determine the instantaneous model of the source signal as: Y = ΦX + Ξ; wherein,

[0086] Ξ represents the noise matrix, Φ is the dictionary matrix, represents the mixing matrix;

[0087] S602, perform column operations on the instantaneous model to obtain: Among them, y v represents the column vector obtained by column transformation of Y, T represents transpose, s v represents the column vector obtained by column transformation of the multi-channel signal S′, ξ v represents the column vector obtained by column transformation of the noise matrix Ξ;

[0088] S603, initialize the maximum number of iterations Q2, the second convergence threshold ε2, and the hyperparameters: Γ, α, σ 2 , and parameters a, b, c, d, where the hyperparameter Γ is a diagonal matrix with γ as the diagonal element;

[0089] S604, set the number of iterations q′=1;

[0090] S605, calculate s v The mean μ (q′) and the covariance matrix in,

[0091]

[0092] S606, calculate s v The maximum a posteriori probability estimate And estimate the source signal L1 represents the number of columns of the dictionary matrix, L2 represents the dimension of the mixing matrix, It means converting a column vector of dimension L1L2×1 into a matrix of dimension L1×L2:

[0093] S607, when the source signal satisfy Or the number of iterations q′ reaches the maximum number of iterations Q2; if so, then As the recovered source signal;

[0094] Otherwise, let q′=q′+1 and update Γ respectively. (q′) , α (q′) 、(σ (q′) ) -2 , Then return to calculate s v The mean μ (q′) and the covariance matrix steps.

[0095] Update the hyperparameter Γ according to the following formulas: (q′) , α (q′) 、(σ (q′) ) -2 ,

[0096]

[0097] In the formula, α represents the inverse of the variance of the prior distribution of the source signal in the sparse Bayesian model,

[0098] Tr(·) represents trace, s I 、s J denote the Ith and Jth elements of s respectively, I′=J+L(I+1), J′=P+L(V+1), E represents expectation, μ (q′) (I′) , μ (q′) (J′) Respectively represent μ (q′) The I′ and J′ elements in S (I,J) , S (V,P) Represent the elements in S located at the Ith Jth column and the Vth row and Pth column respectively.

[0099] The radar anti-intermittent interference method based on VMD and sparse Bayesian blind separation provided by the present invention is further illustrated by simulation experiments below.

[0100] Specifically, the parameters of the radar linear frequency modulation signal in the simulation experiment are shown in Table 1:

[0101] Table 1 Radar and target motion parameters

[0102]

[0103]

[0104] The jammer slice width is 0.25μs. When the signal-to-noise ratio is 20dB and the signal-to-interference ratio is 10dB, the undisturbed linear frequency modulation signal and its pulse compression results are as follows: Figure 3a , 3b shown.

[0105] Add intermittent sampling direct forwarding interference to the linear frequency modulation signal and add 20dB noise. The linear frequency modulation signal and its pulse compression results after interference are as follows Figure 4a , 4b shown.

[0106] Perform short time Fourier transform (STFT) on the linear frequency modulation signal before interference and after interference and noise pollution, and obtain the time-frequency spectrum of the signal before and after interference as shown in the figure. Figure 5a , 5b shown.

[0107] In order to ensure the sparsity of the input matrix of the sparse Bayesian independent component analysis blind source separation algorithm, the mixed signal is de-skewed. The time domain and time-frequency spectrum of the mixed signal after de-skew are as follows: Figure 6a , 6b shown.

[0108] The mixed signal after de-skewing is decomposed by VMD algorithm. The modal components and the spectrum of each modal component are obtained as shown in the figure. Figure 7a , 7b shown.

[0109] The decomposed modal components and mixed signals are subjected to correlation analysis. The decomposed modal components are screened by correlation analysis to construct a multi-channel signal, and the received single-channel interfered signal is converted into a virtual multi-channel signal. Then, the information entropy is calculated under different numbers of estimated sources using the information entropy minimum algorithm. 40 experiments are conducted and the average information entropy is taken to reduce random errors. The average information entropy results for different numbers of estimated sources are shown in Figure 2. Figure 8 As shown. Figure 8 It can be seen that in the 40 information entropy calculations, the average information entropy is the smallest when the estimated number of sources is 2, so it can be considered that the number of source signals is 2.

[0110] According to the number of source signals obtained by the information entropy minimum algorithm, the modal components obtained by decomposition are selected to reconstruct the multi-channel signal. This multi-channel signal is used as the input of the sparse Bayesian independent component analysis blind source separation algorithm. The time domain and pulse pressure results of the separated source signal are as follows: Figure 9a , 9b shown.

[0111] Perform STFT analysis on the separated signal to obtain the time-frequency spectrum as follows Fig.10 As shown in FIG9-10, it can be seen that for the linear frequency modulation signal that is interfered by intermittent sampling and direct forwarding, the original linear frequency modulation signal is obtained after separation by the method provided by the present invention. The mean square error between the separated linear frequency modulation signal and the original linear frequency modulation signal is 0.0188, and the similarity coefficient is 0.9104.

[0112] It can be seen from the above embodiments that the beneficial effects of the present invention are:

[0113] The present invention aims at the problem of anti-intermittent sampling interference of linear frequency modulation pulse compression radar, utilizes the sparsity of linear frequency modulation signal in frequency modulation frequency domain, and converts the problem of anti-intermittent sampling interference of linear frequency modulation into positive definite blind source separation problem in CFCR (Chirp Fourier Coefficient Ratio) domain for solution through independent component analysis blind source separation algorithm based on sparse Bayesian learning. The modal components obtained by VMD decomposition increase the dimension of the mixed signal, and the modal components after decomposition are screened by correlation analysis to construct a multi-channel signal. The received single-channel interfered signal can be converted into a virtual multi-channel signal, and then the reconstructed multi-channel signal is used as the input of sparse Bayesian independent component analysis blind separation algorithm, realizing the anti-intermittent sampling interference of frequency modulation signal in single channel. Therefore, the present invention can be used for anti-intermittent sampling interference of linear frequency modulation pulse compression radar in complex electromagnetic environment, has good interference suppression capability, can effectively suppress intermittent sampling interference and restore the interfered radar frequency modulation signal.

[0114] In the description of the present invention, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification.

[0115] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation, characterized in that: include: Based on the radar's transmission signal model and echo signal model, determine the intermittent sampling forwarding interference signal to further determine the mixed signal received by the receiver in the single-channel case; Decomposing the mixed signal into P modal components by using a variational mode decomposition (VMD) algorithm; Selecting some modal components from the P modal components and upgrading the dimension of the mixed signal to obtain a new mixed signal; According to the new mixed signal, the number of source signals is estimated using an entropy minimum source number estimation algorithm; Reconstructing a multi-channel signal S′ using the estimated number of source signals and the mixed signal; The source signal is restored using the multi-channel signal S′ and a positive definite independent component analysis algorithm based on sparse Bayesian learning.

2. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 1 is characterized in that: The steps of determining the intermittent sampling forwarding interference signal based on the radar transmission signal model and the echo signal model to further determine the mixed signal received by the receiver in the single-channel case include: Construct the radar's transmission signal model: Wherein, f0 represents the center frequency of the transmitting signal, the transmitting signal is a linear frequency modulation signal, j is an imaginary unit, K represents the frequency modulation slope, t represents time, T p Represents the signal pulse width, rect represents the rectangular function; Based on the transmission signal model, the echo signal model of the radar is determined: Wherein, time delay Δt=2R / c, c represents the speed of light, R represents the distance from the preset reference point to the radar, and A represents the amplitude of the echo signal; Determine the intermittent sampling forwarding interference signal according to the transmission signal model and the echo signal model: In the formula, n represents the number of extensions and the number of sampling pulses. T m represents the sampling period, represents the rounding operation, τ m Indicates the sampling pulse width, represents the Kronecker product, Δτ(n)=t-2R j / c-nT m -t0,R j represents the distance between the jammer and the radar, and t0 represents the internal delay of the jammer; According to the echo signal model and the intermittent sampling forwarding interference signal, a mixed signal received by the receiver in a single-channel case is determined: Y(t)=s r (t)+ηs j (t)+ξ(t); Where η represents the weighting coefficient of the intermittent sampling forwarding interference signal, and ξ(t) represents the noise.

3. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 2 is characterized in that: The steps of decomposing the mixed signal Y(t) into P modal components by using the variational mode decomposition (VMD) algorithm include: Let the number of iterations q = 1, initialize the number of modes P, the first convergence threshold ε1, the maximum number of iterations Q1, the penalty factor β, and the pth modal component at the qth iteration Modal Components Center frequency and the Lagrangian operator λ q , p=1,2,...,P, q=1,2,...,Q1; Update the modal components separately Modal Components Center frequency and the Lagrangian operator λ q : In the formula, represents the i-th modal component at the q-th iteration, represents the updated i-th modal component at the q+1th iteration, Indicates updated The center frequency, λ q+1 represents the updated Lagrangian operator at the q+1th iteration, ω represents the frequency variable, is a frequency domain representation of the mixed signal; when satisfy and and When the frequency difference of is less than the first preset threshold, P modal components are obtained; otherwise, and λ q+1 As and λ q , and after the number of iterations q = q + 1, return to the update mode components respectively Modal Components Center frequency and the Lagrangian operator λ q steps.

4. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 1 is characterized in that: The step of selecting some modal components from the P modal components and upgrading the dimension of the mixed signal to obtain a new mixed signal includes: From the P modal components, select the first G modal components whose cumulative contribution rates exceed a second preset threshold; The mixed signal Y(t) is dimensionally upgraded using the selected G modal components to form a new mixed signal S.

5. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 4 is characterized in that: The cumulative contribution rate of the first G modal components is expressed as: In the formula, u g represents the g-th modal component.

6. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 3 is characterized in that: The step of estimating the number of source signals using an entropy minimum source number estimation algorithm according to the new mixed signal comprises: Based on the new mixed signal S, the estimated source signal Y under different numbers of estimated sources is determined using the FastICA algorithm o , the estimated number of sources o = 2, 3, ..., O, O represents the total number of estimated sources; Use Gaussian mixture model to fit each estimated source signal Y o The probability density of Where M represents the number of Gaussian mixture components, π m represents the weight of the mth Gaussian mixture component, and the hyperparameter Θ m ={μ m , σ m 2 }, Indicates that the mean of the mth Gaussian mixture component is μ m , the variance is σ m 2 When the source signal Y is estimated o Gaussian distribution of After obtaining the target distribution samples through independent Metropolis sampling, the estimated source signals Y o The probability density f(Y o ) Estimate information entropy; Select the number of estimated source signals corresponding to the minimum average information entropy represents the average information entropy.

7. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 6 is characterized in that: The step of reconstructing the multi-channel signal S′ by using the estimated number of source signals and the mixed signal comprises: According to the estimated number of source signals Based on the new mixed signal S, a multi-channel signal S' is reconstructed.

8. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 7 is characterized in that: The steps of restoring the source signal by using the multi-channel signal S′ and the positive definite independent component analysis algorithm based on sparse Bayesian learning include: According to the multi-channel signal S', the instantaneous model of the source signal is determined as: Y = ΦX + Ξ; where, Ξ represents the noise matrix, Φ is the dictionary matrix, represents the mixing matrix; Performing column operations on the instantaneous model, we obtain: Among them, y v represents the column vector obtained by column transformation of Y, T represents transpose, s v represents the column vector obtained by column transformation of the multi-channel signal S′, ξ v represents the column vector obtained by column transformation of the noise matrix Ξ; Initialize the maximum number of iterations Q2, the second convergence threshold ε2, and hyperparameters: Γ, α, σ 2 , and parameters a, b, c, d, where the hyperparameter Γ is a diagonal matrix with γ as the diagonal element; Let the number of iterations q′ = 1; Calculate v The mean μ (q′) and the covariance matrix in, Calculate v The maximum a posteriori probability estimate And estimate the source signal L1 represents the number of columns of the dictionary matrix, L2 represents the dimension of the mixing matrix, It means converting a column vector of dimension L1L2×1 into a matrix of dimension L1×L2: When the source signal satisfy Or the number of iterations q′ reaches the maximum number of iterations Q2; if so, then As the recovered source signal; Otherwise, let q′=q′+1 and update Γ respectively. (q′) , α (q′) 、(σ (q′) ) -2 , Then return to calculate s v The mean μ (q′) and the covariance matrix steps.

9. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 8 is characterized in that: Update the hyperparameter Γ according to the following formulas: (q′) , α (q′) 、(σ (q′) ) -2 , In the formula, α represents the inverse of the variance of the prior distribution of the source signal in the sparse Bayesian model, Tr(·) represents trace, s I 、s J denote the Ith and Jth elements of s respectively, I′=J+L(I+1), J′=P+L(V+1), E represents expectation, μ (q′) (I′) , μ (q′) (J′) Respectively represent μ (q′) The I′ and J′ elements in S (I，J) , S (V，P) Represent the elements in S located at the Ith Jth column and the Vth row and Pth column respectively.

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