Radar anti-intermittent sampling jamming method based on VMD and sparse bayesian blind source separation

Abstract

The application discloses a radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation, and comprises the following steps: based on a radar transmitting signal model and an echo signal model, determining an intermittent sampling retransmission interference signal to determine a mixed signal received by a receiver in a single-channel condition; using a VMD algorithm to decompose the mixed signal into P modal components; selecting part of the modal components from the P modal components and dimensionally upgrading the mixed signal to obtain a new mixed signal; according to the new mixed signal, using an entropy minimum source number estimation algorithm to estimate the number of source signals; using the estimated number of source signals and the mixed signal to reconstruct a multi-channel signal; using the multi-channel signal and a positive definite independent component analysis algorithm based on sparse Bayesian learning to recover the source signals. The application can be used for anti-intermittent sampling interference of a linear frequency modulation pulse pressure radar in a complex electromagnetic environment, has good interference suppression capacity, can effectively suppress intermittent sampling interference and recover a disturbed radar frequency modulation signal.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of signal processing, and particularly relates to a radar anti-intermittent sampling jamming method based on VMD (Variational Mode Decomposition) and sparse Bayesian blind separation. BACKGROUND

[0002] In order to improve the target recognition ability and anti-jamming ability, modern radars usually use pulse compression signals such as linear frequency modulation or phase coding to obtain high coherent processing gain and range resolution, which greatly improves the anti-jamming ability against traditional suppressive jamming and non-coherent jamming. However, for pulse compression signal radars, active deception coherent jamming of digital radio frequency memory appears, and the interference signal and the source signal have strong coherence for intermittent sampling and forwarding interference. The spatial anti-jamming method is invalid 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 signal and mixed system, and therefore is widely used in biological engineering, speech signal processing and digital communication.

[0003] Generally, the anti-interference problem of intermittent sampling and forwarding interference can be converted into a single-channel blind source separation problem, and the source signal is separated by using a blind source separation algorithm to achieve the effect of suppressing interference. At present, blind source separation algorithms are based on second-order statistics, high-order statistics, non-stationarity and sparsity to realize 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 complex than the overdetermined case. In the actual radar anti-jamming problem, the interference signal and the source signal emitted by the jammer are far apart, and in many cases the difference in the direction of arrival of the signals is small, so it is impossible to use array signal processing methods. The single-channel blind separation method can be considered to process the mixed signal received from the receiver to separate the source signal.

[0004] In order to counteract intermittent sampling interference, the electronic counter-countermeasure method in the prior art can be divided into two categories. The first category is a signal processing method, which uses the characteristics of the 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 according to the extracted parameters to realize the suppression of intermittent sampling interference. However, the construction of the time-frequency filter will cause the loss of the echo signal, and the time-frequency filter cannot completely filter out the interference under certain interference parameters. In addition, the use of time-domain parameters for source signal reconstruction depends on prior knowledge and is sensitive to noise, resulting in a serious decline in anti-interference performance.

[0005] The second type of electronic countermeasure method is a waveform design method. In order to more actively counter the intermittent sampling interference, a specific waveform can be designed to suppress the interference. For example, an orthogonal working waveform and a protection waveform can be designed. The interference waveform matches the protection waveform to achieve interference suppression. Of course, frequency hopping or frequency stepping waveform construction methods can also be used to suppress intermittent sampling and forwarding interference. Complex waveform optimization design is difficult to cope with real-time complex interference scenario changes. Some waveform design methods need to estimate the parameters of intermittent sampling and forwarding interference in advance. If the parameter estimation is not accurate, the designed waveform cannot effectively suppress the interference. SUMMARY

[0006] In order to solve the above problems existing in the prior art, the present application 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 application is solved by the following technical scheme:

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

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

[0009] The VMD algorithm is used to decompose the mixed signal into P modal components;

[0010] Some modal components are selected from the P modal components, and the mixed signal is upgraded to obtain a new mixed signal;

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

[0012] The estimated number of source signals and the mixed signal are used to reconstruct a multi-channel signal S';

[0013] The multi-channel signal S' and the positive definite independent component analysis algorithm based on sparse Bayesian learning are used to recover the source signal.

[0014] Compared with the prior art, the present application has the following advantages:

[0015] This invention addresses the problem of intermittent sampling interference in linear frequency modulated (LFM) pulse compression radar. Leveraging the sparsity of the LFM signal in the frequency modulation domain, it transforms the LFM interference problem into a positive definite blind source separation problem in the CFCR (Chirp Fourier Coefficient Ratio) domain by employing a blind source separation algorithm based on sparse Bayesian learning and independent component analysis. The mixed signal is augmented by modal components obtained through VMD decomposition, and correlation analysis is used to filter the decomposed modal components to construct a multi-channel signal. This converts the received single-channel interfered signal into a virtual multi-channel signal, which is then used as input to the sparse Bayesian independent component analysis blind source separation algorithm, achieving interference resistance for the LFM signal in the single-channel case. Therefore, this invention can be used for intermittent sampling interference in LFM pulse compression radar under complex electromagnetic environments, exhibiting excellent interference suppression capabilities and effectively suppressing intermittent sampling interference while recovering the interfered radar LFM signal.

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

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

[0018] Figure 2 This is another flowchart of the radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation provided in the embodiments of the present invention;

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

[0020] Figure 3b yes Figure 3a The diagram shows the pulse compression result of the undisturbed linear frequency modulated signal.

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

[0022] Figure 4b yes Figure 4a The diagram shows the pulse compression result of the linear frequency modulated signal after interference.

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

[0024] Figure 5b This is the time-frequency spectrum diagram of the linear frequency modulated signal after interference provided in the embodiments of the present invention;

[0025] Figure 6a is a mixed signal diagram after deskewing provided by an embodiment of the present application;

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

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

[0028] Figure 7b is a spectrum diagram of each modal component shown in Figure 7a

[0029] Figure 8 is an average information entropy diagram of different estimated source numbers provided by an embodiment of the present application;

[0030] Figure 9a is a diagram of the separated source signal provided by an embodiment of the present application;

[0031] Figure 9b is a diagram of the separated source signal shown in Figure 9a

[0032] Figure 10 is a time-frequency spectrum diagram of the separated source signal shown in FIG. 9. DETAILED DESCRIPTION

[0033] The present application will be further described in detail below in combination with specific embodiments, but the embodiments of the present application are not limited thereto.

[0034] Figures 1-2 is a flowchart of a radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation provided by an embodiment of the present application. Please refer to Figure 1 and Figure 2 An embodiment of the present application provides a radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation, comprising:

[0035] S1, based on a radar transmitting signal model and a return signal model, determining an intermittent sampling retransmission interference signal, to further determine a mixed signal received by a receiver in a single-channel case;

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

[0037] S3, selecting part of the P modal components and dimensioning the mixed signal to obtain a new mixed signal;

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

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

[0040] S6, recovering the source signals by using the multi-channel signal S' and the positive definite independent component analysis algorithm based on sparse Bayesian learning.

[0041] Optionally, in step S1, based on the radar's transmitting signal model and echo signal model, the intermittent sampling and retransmission jamming signal is determined, and the step of further determining the mixed signal received by the receiver in the single-channel case comprises:

[0042] S101, constructing the radar's transmitting signal model:

[0043]

[0044] In the formula, 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, and rect represents a rectangular function.

[0045] S102, determining the radar's echo signal model based on the transmitting signal model:

[0046]

[0047] In the formula, the 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, determining the intermittent sampling and retransmission jamming signal according to the transmitting signal model and the echo signal model:

[0049]

[0050] In the formula, n represents the number of extensions, the number of sampling pulses T m represents the sampling period, [·] represents the rounding operation, τ m represents 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, the intermittent sampling and forwarding interference samples the radar transmitting signal at a low sampling rate by intercepting, storing and forwarding the radar signal, and utilizes the matched filtering characteristic of the transmitting signal to obtain pulse compression gain, and after amplitude and phase modulation, the transmitting signal is forwarded to generate coherent interference, so as to realize suppression and deception interference. According to the echo signal model and the intermittent sampling and forwarding interference signal, the mixed signal received by the receiver in a single channel is determined:

[0052] Y (t) = s r (t) + ηs j (t) + ξ (t) ;

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

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

[0055] S201, let the iteration number q=1, initialize the modal number P, the first convergence threshold ε1, the maximum iteration number Q1, the penalty factor β, the pth modal component of the qth iteration modal component center frequency and Lagrange operator λ q , p=1, 2, …, P, q=1, 2, …, Q1;

[0056] S202, respectively update the center frequency modal component of the modal component and the Lagrange operator λ q :

[0057]

[0058]

[0059] In the formula, represents the ith modal component of the qth iteration, represents the updated ith modal component of the q+1th iteration, represents the updated center frequency of the modal component , λ q+1 represents the updated Lagrange operator of the q+1th iteration, ω represents a frequency variable, is a frequency domain representation of the mixed signal;

[0060] S203, when satisfies and and the frequency difference of the P modal components is less than the first preset threshold, obtaining the P modal components; otherwise, obtaining the P modal components and λ q+1 respectively as and λ q , and letting the iteration number q=q+1, returning to updating the modal components respectively. the center frequency of the modal component and the Lagrange operator λ q .

[0061] In step S3, the step of selecting part of the P modal components and dimensionally upgrading the mixed signal to obtain a new mixed signal, comprises:

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

[0063] S302, dimensionally upgrading the mixed signal Y(t) using the selected G modal components 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] wherein, u g represents the gth modal component.

[0067] Exemplarily, the new mixed signal formed by 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 the entropy minimum source number estimation algorithm according to the new mixed signal, comprises:

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

[0070] S402, using a Gaussian mixture model to fit the probability density o of each estimated source signal Y wherein, 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}, The mean of the m-th Gaussian mixture component is μ. m The variance is σ m 2 At that time, estimate the source signal Y o The Gaussian distribution.

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

[0072] According to the law of large numbers, when the sample size is sufficiently large, the sample mean tends to the expected value. Metropolis sampling is used to obtain the result that follows this principle. We obtain a random sample and then calculate the sample mean to estimate the expectation, thus avoiding the problem of complex integral calculation.

[0073] Assuming the target distribution is p(x), we choose an initial point x0, sample candidate samples x′ from the proposal distribution q(x′|x), and calculate the acceptance probability:

[0074]

[0075] Generate a uniform distribution u ~ U(0,1), and accept candidate samples x if u < α. i+1 =x′, otherwise reject keeping the current sample x i+1 =x i The sample distribution obtained from the sampling is as follows:

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

[0077] Random samples conforming to a GMM-fitted distribution are obtained from independent Metropolis sampling. The sample mean is calculated to estimate the information entropy:

[0078]

[0079] Choose the number of estimated source signals that corresponds to the minimum average information entropy; this number of estimated source signals is the required number of source signals.

[0080]

[0081] Step S5, which involves reconstructing the multi-channel signal S′ using the estimated number of source signals and the mixed signal, includes:

[0082] Based on the estimated number of source signals The multi-channel signal S′ is obtained by reconstructing 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] in step S3, ... G The number of columns is then determined from S = [Y(t); u1, u2, ..., u]. G The corresponding number of modal components can be removed from the [image / data].

[0084] Step S6, which involves recovering the source signal using the multi-channel signal S′ and a positive definite independent component analysis algorithm based on sparse Bayesian learning, includes:

[0085] S601. Based on the multi-channel signal S′, the instantaneous model of the source signal is determined as: Y=ΦX+Ξ; where,

[0086] Ξ represents the noise matrix, and Φ is the dictionary matrix. Represents a mixture matrix;

[0087] S602. Perform column operations on the instantaneous model to obtain: Among them, y v This represents the column vector obtained by column transformation of Y. T represents transpose, s v ξ represents the column vector obtained by column transformation of the multi-channel signal S′. v This 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 its diagonal element;

[0089] S604. Let the iteration number q′ = 1;

[0090] S605, Calculate s v mean μ (q′) Covariance Matrix in,

[0091]

[0092] S606, Calculate s v Maximum posterior probability estimation And estimate the source signal L1 represents the number of columns in the dictionary matrix, and L2 represents the dimension of the mixture matrix. This means transforming a column vector of dimension L1L2×1 into a matrix of dimension L1×L2:

[0093] S607、when the source signal satisfies or the iteration number q' reaches the maximum iteration number Q2; if yes, as the recovered source signal;

[0094] otherwise, let q'=q'+1, and update respectively (q′) , alpha (q′) , (sigma (q′) ) -2 , and then return to the step of calculating the mean value mu v and the covariance matrix (q′) of s .

[0095] The hyperparameters (q′) , alpha (q′) , (sigma (q′) ) -2 ,

[0096]

[0097] where alpha represents the reciprocal of the variance of the prior distribution of the source signal in the sparse Bayesian model,

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

[0099] The radar anti-intermittent jamming method based on VMD and sparse Bayesian blind separation provided by the present application is further described through a simulation experiment.

[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 0.25 μs, and under the conditions of a signal-to-noise ratio of 20 dB and a signal-to-jamming ratio of 10 dB, the linear frequency modulation signal not interfered and its pulse compression result are shown in Figure 3a 、 3b .

[0105] The intermittent sampling direct forwarding interference is added to the linear frequency modulation signal, and 20 dB noise is added, and the linear frequency modulation signal after interference and its pulse compression result are shown in Figure 4a 、 4b .

[0106] The linear frequency modulation signal before being interfered and the signal after being interfered and contaminated by noise are respectively subjected to short time Fourier transform (STFT), and the time-frequency spectrograms of the signals before and after interference are shown in Figure 5a 、 5b .

[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 subjected to deskewing processing, and the time domain and time-frequency spectrum of the mixed signal after deskewing are shown in Figure 6a 、 6b .

[0108] The mixed signal after deskewing processing is subjected to VMD algorithm decomposition, the mixed signal is subjected to VMD decomposition, and the frequency spectrograms of each modal component and each modal component are shown in Figure 7a 、 7b .

[0109] The correlation analysis is performed on each modal component and the mixed signal obtained by decomposition, the modal components after decomposition are selected by using correlation analysis to construct a multi-channel signal, and the single-channel interfered signal received is converted into a virtual multi-channel signal. Then, by using the information entropy minimum algorithm, the information entropy under different estimated source numbers is calculated, 40 experiments are performed, and the average value of the obtained information entropy is taken to reduce random error, and the average information entropy results of different estimated source numbers are shown in Figure 8 . It can be seen from Figure 8 that in 40 information entropy calculations, the average information entropy is minimum when the estimated source number is 2, and therefore it can be considered that the source signal number is 2.

[0110] The modal components obtained by decomposition are selected according to the source signal number obtained by the information entropy minimum algorithm, a multi-channel signal is reconstructed, and this multi-channel signal is taken as the input of the sparse Bayesian independent component analysis blind source separation algorithm, and the time domain and pulse compression results of the separated source signals are shown in Figure 9a 、 9b respectively.

[0111] The time spectrum obtained by performing STFT analysis on the separated signal is as follows: Figure 10 As shown in Figures 9-10, it can be seen that after the linear frequency modulated signal is interfered with by intermittent sampling and direct forwarding, the original linear frequency modulated signal is obtained after separation by the method provided by this invention. The mean square error between the separated linear frequency modulated signal and the original linear frequency modulated signal is 0.0188, and the similarity coefficient is 0.9104.

[0112] As can be seen from the above embodiments, the beneficial effects of the present invention are as follows:

[0113] This invention addresses the problem of intermittent sampling interference in linear frequency modulated (LFM) pulse compression radar. Leveraging the sparsity of the LFM signal in the frequency modulation domain, it transforms the LFM interference problem into a positive definite blind source separation problem in the CFCR (Chirp Fourier Coefficient Ratio) domain by employing a blind source separation algorithm based on sparse Bayesian learning and independent component analysis. The mixed signal is augmented by modal components obtained through VMD decomposition, and correlation analysis is used to filter the decomposed modal components to construct a multi-channel signal. This converts the received single-channel interfered signal into a virtual multi-channel signal, which is then used as input to the sparse Bayesian independent component analysis blind source separation algorithm, achieving interference resistance for the LFM signal in the single-channel case. Therefore, this invention can be used for intermittent sampling interference in LFM pulse compression radar under complex electromagnetic environments, exhibiting excellent interference suppression capabilities and effectively suppressing intermittent sampling interference while recovering the interfered radar LFM signal.

[0114] In the description of this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0115] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection 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 transmitted signal model and echo signal model, the intermittent sampling and forwarding interference signal is determined, so as to further determine the mixed signal received by the receiver in the case of single channel; The mixed signal is decomposed into its components using the Variational Mode Decomposition (VMD) algorithm. P One modal component; From the above P Selecting some modal components from the modal components and upsizing the mixed signal yields a new mixed signal; Based on the new mixed signal, the number of source signals is estimated using the entropy minimum source number estimation algorithm; The multi-channel signal is reconstructed using the estimated number of source signals and the mixed signal. ; Utilizing multi-channel signals And a positive definite independent component analysis algorithm based on sparse Bayesian learning is used to recover the source signal.

2. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 1, characterized in that, Based on the radar's transmitted signal model and echo signal model, the steps for determining the intermittent sampling and forwarding interference signal, and further determining the mixed signal received by the receiver in the single-channel case, include: Construct a radar transmission signal model: ； In the formula, This indicates the center frequency of the transmitted signal, which is a linear frequency modulated (LFM) signal. The imaginary unit, K Indicates the frequency modulation slope. Indicates time, Indicates the signal pulse width. Represents a rectangular function; Based on the transmitted signal model, the radar echo signal model is determined: ； In the formula, time delay , Represents the speed of light. This indicates the distance from the preset reference point to the radar. Indicates the amplitude of the echo signal; Based on the transmitted signal model and the echo signal model, the intermittent sampling and forwarding interference signal is determined as follows: ； In the formula, Indicates the number of extensions and the number of sampling pulses. , Indicates the sampling period. This represents the integer operation. Indicates the sampling pulse width. Indicates the Kronecker product. , This indicates the distance between the jammer and the radar. This indicates the internal delay of the jammer; Based on the echo signal model and the intermittent sampling and forwarding interference signal, the mixed signal received by the receiver in the single-channel case is determined as follows: ； In the formula, The weighting coefficients represent the intermittent sampling and forwarding interference signals. Indicates noise.

3. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 2, characterized in that, Using the Variational Mode Decomposition (VMD) algorithm, the mixed signal is... Decomposed into P The steps for each modal component include: Let the number of iterations Initialize the number of modes P First convergence threshold Maximum number of iterations Punishment factor , No. The first iteration Modal components Modal components center frequency and Lagrange operators , , ; Update the modal components separately Modal components center frequency and Lagrange operators : In the formula, Indicates the first The first iteration One modal component, Indicates the updated result of the first... The first iteration One modal component, Indicates the result of the update The center frequency, Indicates the updated result of the first... Lagrange operators in the next iteration Represents frequency variables. This is the frequency domain representation of the mixed signal; when satisfy ,and and When the frequency difference is less than the first preset threshold, we get P One modal component; conversely, then... , and As respectively , and And let the number of iterations Then, return to the section on updating modal components respectively. Modal components center frequency and Lagrange operators The steps.

4. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 1, characterized in that, From the above P The steps of selecting a subset of modal components from the modal components and upscaling the mixed signal to obtain a new mixed signal include: From the above P Of the modal components, select the first one. G Modal components whose cumulative contribution rate exceeds the second preset threshold; Using the selected G Each modal component affects the mixed signal. Upgrading to higher dimensions to form new mixed signals S .

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

6. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 3, characterized in that, The step of estimating the number of source signals using the entropy minimum source number estimation algorithm based on the new mixed signal includes: Based on the new mixed signal S The FastICA algorithm is used to determine the estimated source signals under different numbers of estimated sources. Estimate the number of sources , This indicates the estimated total number of sources; Fitting each estimated source signal using a Gaussian mixture model probability density ,in, Indicates the number of Gaussian mixture components. Indicates the first The weights of the Gaussian mixture components, and the hyperparameters , Indicates the first The mean of the Gaussian mixture components is variance is At that time, estimate the source signal Gaussian distribution; After obtaining the target distribution samples through independent Metropolis sampling, they are combined with the estimated source signals. probability density Estimate information entropy; Select the estimated number of source signals corresponding to the minimum average information entropy. , This 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, characterized in that, The multi-channel signal is reconstructed using the estimated number of source signals and the mixed signal. The steps include: Based on the estimated number of source signals In the new mixed signal S Based on the reconstruction, multi-channel signals are obtained. .

8. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 7, characterized in that, Utilizing multi-channel signals The steps for recovering the source signal using a positive definite independent component analysis algorithm based on sparse Bayesian learning include: Based on multi-channel signals The instantaneous model of the source signal is determined as follows: ;in, , Represents the noise matrix. It is a dictionary matrix. Represents a mixture matrix; Performing columnar operations on the instantaneous model yields: ,in, Indicates to The column vector obtained through column transformation, , Indicates transpose. Indicates multi-channel signal The column vector obtained through column transformation, Representing the noise matrix The column vector obtained through column transformation; Initialize maximum number of iterations Second convergence threshold Hyperparameters: and parameters Among them, hyperparameters Therefore A diagonal matrix with diagonal elements; Let the number of iterations ; calculate mean Covariance Matrix ,in, , ; calculate Maximum posterior probability estimation And estimate the source signal , This represents the number of columns in the dictionary matrix. The dimension of the mixture matrix is ​​represented. This indicates that the dimension is The column vector is converted to dimension The matrix: ; When the source signal satisfy or number of iterations Reaching the maximum number of iterations If so, then As the recovered source signal; Conversely, then let and update them respectively Return to calculation mean Covariance Matrix The steps.

9. The radar anti-intermittent sampling interference method based on VMD and sparse Bayesian blind separation according to claim 8, characterized in that, Update the hyperparameters according to the following formulas respectively. : ； In the formula, This represents the reciprocal of the variance of the prior distribution of the source signal in the sparse Bayesian model. , , , Indicates trace, , They represent the first and second digits of s, respectively. I , J One element, , , Expressing expectations, , They represent The first in , One element, , They represent The middle is located in the first I No. J Column and the V Line 1 P The elements of the column.

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