A blind source separation method based on stiefel manifold optimization and information entropy criterion

Abstract

The application discloses a blind source separation method based on Stiefel manifold optimization and information entropy criterion, and relates to the technical field of radar signal processing. The specific implementation of the method comprises the following steps: collecting received signals of multiple samples, performing pre-whitening processing on the received signals by using a pre-whitening matrix to obtain preprocessed signals of the multiple samples; the preprocessed signals of the multiple samples are divided into multiple small sample sets; the small sample sets are used to solve the blind source separation based on the information entropy criterion according to the numbering order of the small sample sets to determine a target demixing matrix; and the antenna directional diagram of an array radar is calculated according to the target demixing matrix. The implementation can effectively separate target echo signals and interference signals from the received signals of the radar, saves the time resources of the radar, reduces the time cost consumed by the radar, greatly improves the solving efficiency of the blind source separation, realizes real-time anti-interference and interference signal filtering of the radar, and has strong robustness and real-time performance.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a blind source separation method based on Stiefel manifold optimization and information entropy criterion. Background Technology

[0002] Blind source separation refers to the process of separating target echo signals from interference signals when the radar source signal is unknown, thereby enabling the extraction and detection of target echoes. Various metrics exist for evaluating the independence of separated signals, with common ones including the JADE algorithm based on the fourth-order cumulant criterion and the Fast ICA method based on the higher-order moment criterion. The information entropy criterion, as one of the criteria for solving blind source separation methods, is considered the optimal metric for measuring the independence of separated signals.

[0003] Existing blind source separation algorithms based on the information entropy criterion approximate the probability density function of the separated signal using a Gaussian kernel, directly using the information entropy criterion as the objective function. However, since approximating the Gaussian function to estimate the Gaussian kernel requires the use of all samples, the computational load is quite large. Given the precious time resources of radar, this not only incurs high time costs but also fails to filter out interference signals from the received signal in real time. Summary of the Invention

[0004] In view of this, the present invention provides a blind source separation method based on Stiefel manifold optimization and information entropy criterion, which can effectively separate target echo signals and interference signals from radar received signals, save radar time resources, reduce radar time consumption costs, greatly improve the solution efficiency of blind source separation, realize real-time anti-interference of radar and filtering of interference signals, and has strong robustness and real-time performance.

[0005] The technical solution for implementing the present invention is as follows:

[0006] A blind source separation method based on Stiefel manifold optimization and information entropy criterion includes:

[0007] The received signals of multiple samples are collected, and the received signals are pre-whitened using a pre-whitening matrix to obtain pre-processed signals of multiple samples.

[0008] The preprocessed signals of the multiple samples are divided into multiple small sample sets;

[0009] According to the numbering order of the small sample set, the blind source separation solution based on the information entropy criterion is performed using the small sample set to determine the target unmixing matrix; wherein, the solution method is the Stiefel manifold optimization algorithm with variable step size;

[0010] Calculate the antenna pattern of the array radar based on the target unmixing matrix.

[0011] Optionally, the step of using a pre-whitening matrix to pre-whiten the received signal to obtain pre-processed signals of multiple samples includes:

[0012] The covariance matrix of the received signal X is estimated using the multiple samples, and the estimated value R is obtained. X :

[0013]

[0014] In the above formula, R X The eigenvalues ​​λ1≥λ2≥λ3≥…≥λ p ≥…≥λ n , where λ1~λ p Corresponding to the source signal S, λ p+1 ~λ n Corresponding to the noise signal N;

[0015] Using the estimated value R X The eigenvalue λ corresponding to the noise signal p+1 ~λ n Estimate the variance of the noise signal

[0016] For the estimated value R X Perform eigenvalue decomposition to obtain the estimated value R. X eigenvector u i ;

[0017] Using the feature vector u corresponding to the source signal i and the estimated value R X The eigenvalues ​​corresponding to the source signal are used to generate a solution vector.

[0018] The solution vector G and the variance of the noise signal and p-dimensional identity matrix I p The symmetric positive definite matrix formed Perform Cholesky decomposition to obtain the lower triangular matrix C;

[0019] The received signal X is pre-whitened using a pre-whitening matrix generated by the product of the inverse of the lower triangular matrix C and the solution vector G, resulting in a pre-processed signal of the received signal X.

[0020] Optionally, the step of segmenting the preprocessed signals of the plurality of samples into a plurality of small sample sets includes:

[0021] Preprocessed signals of T samples The data is segmented to obtain various small sample sets. M represents the number of small sample sets; V represents the number of preprocessed signals in each small sample set; v represents the number of the small sample set.

[0022] Optionally, determining the target unmixing matrix includes:

[0023] Use the vth smallest sample set as the current sample set;

[0024] On the current sample set, the probability density function of the separated signal is estimated using the unmixing matrix B: in,

[0025] The minimum value of the information entropy of the probability density function is taken as the objective function, and the orthogonal matrix of the unmixing matrix is ​​taken as the constraint condition.

[0026] The objective function is solved using the variable-step-size Stiefel manifold optimization algorithm. It is then determined whether the Riemann gradient on the Stiefel manifold is less than the convergence coefficient. If so, the objective unmixing matrix B is determined. * .

[0027] Optionally, the step of using the minimum value of the information entropy of the probability density function as the objective function and the orthogonality of the unmixing matrix as the constraint condition includes:

[0028] The separation signal is estimated using the unmixing matrix B. The information entropy of the probability density function is:

[0029]

[0030] The minimum value of the information entropy is taken as the objective function:

[0031]

[0032] The unmixing matrix B and its transpose B H The product is a p-dimensional identity matrix I. p As a constraint: B H B = I p .

[0033] Optionally, the objective function is solved using the variable-step-size Stiefel manifold optimization algorithm. It is then determined whether the Riemann gradient on the Stiefel manifold is less than the convergence coefficient. If so, the objective unmixing matrix is ​​determined, including:

[0034] Initialize the unmixing matrix B to obtain the initial unmixing matrix B0;

[0035] Determine if the update count k has reached the maximum iteration count K. If not, check the unmixing matrix B.k Riemann gradient on the corresponding Stiefel manifold Is it less than the preset convergence threshold ε?

[0036] If not, according to the unmixing matrix B k The geodesic equation values ​​are calculated using the geodesic equations on the Stiefel manifold. Determine the step size coefficient τ k Does it satisfy the Wolfe search condition F(γ)? k (τ k ))≤D k +ρ1τF′(γ k (0)), where D0=F(B0);

[0037] If so, demixing matrix B k The geodesic equation value γ k (τ k ) as the updated unmixing matrix B k+1 =γ k (τ k );

[0038] Based on the difference α between the unmixing matrices before and after the update k =B k+1 -B k The difference between the Riemann gradient on the Stiefel manifold corresponding to the unmixing matrix before and after the update. Determine the updated step size coefficient τ k+1 :

[0039] tr() calculates the trace of a matrix, and mod is the modulo function;

[0040] Using the updated coefficient η, the algorithm coefficients before and after the update, and the updated unmixing matrix B k+1 The corresponding objective function value F(B) k+1 ), determine the updated D k+1 =(ηQ k D k +F(B k+1 )) / Q k+1 ; where Q k+1 =ηQ k +1;

[0041] Update k to k+1, and obtain the updated unmixing matrix B. k+1 As the unmixing matrix B k Then, determine whether the number of updates k has reached the maximum number of iterations K.

[0042] Optionally, in the unmixing matrix B kRiemann gradient on the corresponding Stiefel manifold If the unmixing matrix B is less than the preset convergence threshold ε, k As the target unmixing matrix B * .

[0043] Optionally, the initialization of the unmixing matrix B to obtain the initial unmixing matrix B0 includes:

[0044] Determine if the previous small sample set is empty. If it is, then arbitrarily assign an orthogonal initial unmixing matrix B0; otherwise, use the target unmixing matrix B0 calculated from the previous small sample set. * Let B0 be the initial unmixing matrix for the current small sample set.

[0045] Optionally, in the step size coefficient τ k If the Wolfe search conditions are not met, reduce the step size coefficient τ. k The reduction factor is δ, and the step size factor after reduction is τ. k =δτ k .

[0046] Optionally, based on the target unmixing matrix B * The antenna pattern of the array radar is calculated, including:

[0047] Using the solved target unmixing matrix B * Determine the separation signal

[0048] With the target unmixing matrix B * The antenna pattern of the array radar with weights is as follows:

[0049] F(θ) = |(B * ) H Wa(θ)|;

[0050] In the above formula, a(θ) is the steering vector of the array radar, expressed as a(θ)=[1,e jκdsinθ ,…,e jκ(n-1)dsinθ ] H θ is the angle of the antenna pattern; j is the imaginary unit; d is the element spacing of the array radar; and κ is the preset antenna coefficient.

[0051] Beneficial effects:

[0052] (1) This invention greatly reduces the computation time by dividing the preprocessed signal into small samples and estimating the probability density function in real time, which has good real-time performance and is conducive to engineering implementation.

[0053] (2) The present invention uses the Stiefel manifold optimization algorithm with variable step size to solve the problem, ensuring the orthogonality of the unmixed matrix. The algorithm has good convergence and robustness.

[0054] (3) When the present invention is applied to the received signal of the array radar, the received signal is first preprocessed and divided into a small sample set. Then, the Stiefel manifold optimization method is used on the small sample set to solve the blind source separation problem based on the information entropy criterion, determine the target unmixing matrix, and obtain the separated signal including the target echo signal and the interference signal, and the antenna pattern of the array radar with the target unmixing matrix as the weight, so as to achieve the purpose of anti-interference of the array radar.

[0055] (4) The blind source separation method of the present invention can effectively solve the problem of active interference, especially the case of mixed main lobe interference and side lobe interference. The radar signal processing has the advantages of strong real-time performance, high robustness and fast solution speed. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the main process of the blind source separation method based on Stiefel manifold optimization and information entropy criterion according to an embodiment of the present invention;

[0057] Figure 2 This is a schematic diagram of the target echo signal and interference signal in the simulated source signal according to an embodiment of the present invention;

[0058] Figure 3 This is a schematic diagram of a simulated noise signal according to an embodiment of the present invention;

[0059] Figure 4 This is a schematic diagram of a simulated received signal according to an embodiment of the present invention;

[0060] Figure 5 This is a schematic diagram of the solution results of solving the simulated received signal using the blind source separation method based on Stiefel manifold optimization and information entropy criterion of the present invention according to an embodiment of the present invention;

[0061] Figure 6 This is a schematic diagram of the radiation pattern of the array radar anti-jamming antenna corresponding to the solution result obtained from simulation according to an embodiment of the present invention;

[0062] Figure 7 This is a schematic diagram of the solution results obtained by solving the simulated received signal using the traditional JADE blind source separation algorithm;

[0063] Figure 8 This is a schematic diagram showing the solution results of solving the simulated received signal using the traditional FastICA blind source separation algorithm. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0065] The JADE algorithm is a fast solution algorithm for blind source separation problems based on the fourth-order cumulant criterion.

[0066] The FastICA algorithm is a fast solution algorithm for blind source separation problems based on the higher-order moment criterion.

[0067] Stiefel manifold optimization algorithms are a class of methods for solving optimization problems on manifolds. Unlike traditional optimization methods, these methods can preserve the manifold structure well during the solution process.

[0068] Figure 1 This is a schematic diagram of the main process of the blind source separation method based on Stiefel manifold optimization and information entropy criterion according to an embodiment of the present invention, as shown below. Figure 1 As shown, the blind source separation method based on Stiefel manifold optimization and information entropy criterion of the present invention includes the following steps:

[0069] Step 1: Collect the received signals of multiple samples, and use a pre-whitening matrix to pre-whiten the received signals to obtain the pre-processed signals of multiple samples.

[0070] In this embodiment of the invention, the received signal model of the array radar is shown in equation (1) below:

[0071] X = AS + N (1)

[0072] In the above formula, X is the received signal actually received by the array radar, a known quantity, with a matrix dimension of n×1; A is the array radar steering vector matrix, a known quantity used to represent the arrangement of radar antennas, A is a full-rank complex matrix with a matrix dimension of n×p; S is the source signal emitted by the signal source, an unknown quantity, with a matrix dimension of p×1; N is the noise signal, an unknown quantity, with a matrix dimension of n×1. To facilitate the subsequent solution of the source signal S and the noise signal N, it is assumed that the source signal S is a zero-mean, unit covariance, statistically independent random vector, and that S has at most one Gaussian component.

[0073] In this embodiment of the invention, since the covariance matrix of the received signal X is usually not an identity matrix, that is, the elements of the received signal X are linearly correlated, in order to remove the influence of the correlation between the elements, the received signal X is pre-whitened to transform the covariance matrix of the received signal X into an identity matrix. Specifically:

[0074] Assume that the mean of the noise signal N is zero and the covariance matrix of the noise signal N satisfies the form shown in equation (2):

[0075]

[0076] In the above formula, I is the variance of the noise signal N; n It is an n-dimensional identity matrix.

[0077] Step 11: Estimate the covariance matrix of the received signal X using T samples to obtain the estimated value R. X .

[0078] In this embodiment of the invention, the estimated value R of the covariance matrix of X is... X As shown in equation (3):

[0079]

[0080] In the above formula, R X The eigenvalues ​​λ1≥λ2≥λ3≥…≥λ p ≥…≥λ n , where λ1~λ p Corresponding to the source signal S, λ p+1 ~λ n This corresponds to the noise signal N.

[0081] Step 12, using the estimated value R X The variance of the noise signal is estimated by taking the eigenvalues ​​corresponding to the noise signal.

[0082] In this embodiment of the invention, the variance of the noise signal N R can be used to correspond to the noise signal N X The average value of the eigenvalues ​​is represented as shown in equation (4) below:

[0083]

[0084] Step 13, for the estimated value R X Perform eigenvalue decomposition to obtain the estimated value R. X eigenvector u i .

[0085] In this embodiment of the invention, the estimated value R X eigenvector u i The matrix dimension is n×1.

[0086] Step 14, using the eigenvector u corresponding to the source signal i and the estimated value R X The eigenvalues ​​corresponding to the source signal are used to generate the solution vector G.

[0087] In this embodiment of the invention, a solution vector is introduced.

[0088] Step 15, calculate the variance of the solution vector G and the noise signal. and p-dimensional identity matrix I p The symmetric positive definite matrix formed is subjected to Cholesky decomposition to obtain a lower triangular matrix C.

[0089] In this embodiment of the invention, due to Since it is a symmetric positive definite matrix, therefore, for Performing Cholesky decomposition yields a lower triangular matrix C with p×p dimensions.

[0090] Step 16: The received signal X is pre-whitened using a pre-whitening matrix generated by the product of the inverse of the lower triangular matrix C and the solution vector G, to obtain the pre-processed signal of the received signal X.

[0091] In this embodiment of the invention, the pre-whitening matrix W is W = C. -1 G, based on the relationship between the received signal, the source signal, and the noise signal, determines the preprocessed signal of the received signal X. As shown in equation (5):

[0092]

[0093] In the above formula, The matrix dimension is p×p.

[0094] Step 2: Divide the preprocessed signals of the T samples into multiple small sample sets.

[0095] In this embodiment of the invention, the preprocessed signals of T samples are... The samples are segmented to obtain the various small sample sets Π, as shown in equation (6) below:

[0096]

[0097] In the above formula, M represents the number of small sample sets; V represents the number of preprocessed signals in each small sample set; and v represents the number of the small sample set, for example, v = 1 represents the first small sample set. v=2 represents the second small sample set. And so on.

[0098] For ease of narration, The i-th element in is denoted as

[0099] Step 3: According to the numbering order of the small sample sets, perform blind source separation solution based on the information entropy criterion on the small sample sets in sequence to determine the target unmixing matrix; wherein, the solution method is the Stiefel manifold optimization algorithm with variable step size.

[0100] In this embodiment of the invention, according to a small sample set The numbering order is used to process each small sample set sequentially. Solving blind source separation problems based on the information entropy criterion using the Stiefel manifold optimization algorithm with variable step size includes:

[0101] Step 31: Take the vth small sample set as the current sample set.

[0102] In this embodiment of the invention, As the current sample set.

[0103] Step 32: On the current sample set, establish the unmixing matrix B and the separation signal Y. (v) The relationship between probability density functions.

[0104] In this embodiment of the invention, on the current sample set, a demixing matrix X and a separation signal are established. The relationship between their probability density functions is shown in equation (7) below:

[0105]

[0106] In the above formula, b i h is the i-th column vector of B; M For window coefficients,

[0107] Step 33: Use the information entropy of the probability density function as the objective function and the orthogonal matrix of the unmixing matrix as the constraint condition.

[0108] In this embodiment of the invention, the signal Y is separated. (v) The information entropy of the probability density function is shown in equation (8) below:

[0109]

[0110] Using information entropy as the objective function, the unmixing matrix B and its transpose B H The product of these is the identity matrix, which serves as a constraint, as shown in equation (9) below:

[0111]

[0112] Step 34: Solve the objective function using the Stiefel manifold optimization algorithm with variable step size, and determine whether the Riemann gradient on the Stiefel manifold is less than the convergence coefficient. If yes, proceed to step 35; otherwise, proceed to step 36.

[0113] In this embodiment of the invention, when solving the unmixing matrix B using the Stiefel manifold optimization algorithm with a variable step size, the unmixing matrix is ​​first initialized for each small sample set. It is then determined whether the Riemann gradient on the Stiefel manifold is less than a preset convergence threshold. If so, the solution is completed and the target unmixing matrix is ​​obtained. If not, the unmixing matrix, step size coefficients, and algorithm coefficients are updated according to the step size update strategy of the Stiefel manifold optimization algorithm. The updated unmixing matrix, step size coefficients, and algorithm coefficients are used to make another judgment until the maximum number of iterations of the algorithm is reached, and then the judgment is continued for the next small sample set.

[0114] Step 341: Initialize the unmixing matrix B to obtain the initial unmixing matrix B0.

[0115] In this embodiment of the invention, the algorithm parameters of the Stiefel manifold optimization algorithm include the unmixing matrix B, step size coefficient τ, update number k, maximum number of iterations K, update coefficient -ρ1, shrinkage coefficient δ, update coefficient -η, convergence coefficient ε, and algorithm coefficient Q. Among them, the maximum number of iterations K, update coefficient -ρ1, shrinkage coefficient δ, update coefficient -η, and convergence coefficient ε are preset: ρ1,δ,η,ε∈(0,1).

[0116] During the initialization of the Stiefel manifold optimization algorithm, the initial values ​​of the algorithm parameters—the unmixing matrix B, the step size coefficient τ, the number of updates k, and the algorithm coefficients Q—are given. Specifically:

[0117] Determine if the previous small sample set is empty. If it is, arbitrarily assign an orthogonal initial unmixing matrix B0. If not, use the target unmixing matrix finally calculated from the previous small sample set as the initial unmixing matrix for the current small sample set, denoted as B0. The initial step size coefficient τ0 > 0, the number of iterations k = 0, and the algorithm coefficient Q0 = 1.

[0118] Step 342: Determine whether the update count k has reached the maximum iteration count K. If yes, proceed to step 36; otherwise, proceed to step 343.

[0119] Step 343, determine the unmixing matrix B k Riemann gradient on the corresponding Stiefel manifold Is it less than the preset convergence threshold ε? If yes, proceed to step 35; otherwise, proceed to step 344.

[0120] In this embodiment of the invention, the determination is made. Whether it holds true, for example, when k = 0, determine... Does it hold true? When k = 1, determine... Whether it is true or not, and so on.

[0121] Step 344, based on the unmixing matrix B k γ is calculated using the geodesic equation on the Stiefel manifold. k (τ k Determine the step size coefficient τ. k Does the Wolfe search criteria meet? If yes, proceed to step 345; otherwise, proceed to step 349.

[0122] In this embodiment of the invention, the geodesic equation on the Stiefel manifold is shown in equation (10):

[0123]

[0124] According to equation (10), calculate the geodesic equation value γ. k (τ k Substitute into equation (9) to calculate the geodesic equation value γ. k (τ k The corresponding objective function value F(γ) k (τ k Does it satisfy the Wolfe search criteria, as shown in equation (11) below?

[0125] F(γ k (τ k ))≤D k +ρ1τF′(γ k (0)) (11)

[0126] Where, D0 = F(B0).

[0127] Step 345, unmix matrix B k The geodesic equation value γ k (τ k ) as the updated unmixing matrix B k+1 =γ k (τ k ).

[0128] Step 346: Determine the updated step size coefficient τ based on the difference between the unmixed matrices before and after the update, and the difference between the unmixed matrices before and after the update and the Riemann gradients on the corresponding Stiefel manifolds. k+1 .

[0129] In this embodiment of the invention, the difference α between the unmixed matrices before and after the update is... k For α k =B k+1 -Bk Unmixed matrix B before update k The corresponding Riemann gradient on the Stiefel manifold is Updated unmixing matrix B k+1 The corresponding Riemann gradient on the Stiefel manifold is The difference between the Riemann gradients on the Stiefel manifold corresponding to the unmixing matrices before and after the update is: Accordingly, the updated step size coefficient τ k+1 As shown in equation (12):

[0130]

[0131] In the above formula, tr() means to find the trace of the matrix; mod is the remainder function, k≡1mod 2 means that the remainder when k is divided by 2 is 1; k≡0mod 2 means that the remainder when k is divided by 2 is 0.

[0132] Step 347: Use the updated coefficients η, the algorithm coefficients before and after the update, and the updated unmixing matrix B. k+1 The corresponding objective function value F(B) k+1 ), determine the updated D k+1 .

[0133] Step 3471, by updating coefficient η and the previous algorithm coefficient Q. k Calculate the updated algorithm coefficients Q. k+1 As shown in equation (13):

[0134] Q k+1 =ηQ k +1 (13)

[0135] Step 3472, based on the algorithm coefficients before and after the update and the updated unmixing matrix B k+1 The corresponding objective function value F(B) k+1 ), determine the updated D k+1 As shown in equation (14):

[0136] D k+1 =(ηQ k D k +F(B k+1 )) / Q k+1 (14)

[0137] Step 348, update k to k+1, the updated unmixing matrix B k+1 As the unmixing matrix B k Proceed to step 342.

[0138] Step 349, reduce the step size coefficient τ kProceed to step 344.

[0139] In this embodiment of the invention, the step size coefficient τ k If the Wolfe search conditions are not met, reduce the step size coefficient τ. k The reduction factor is δ, which makes τ k =δτ k , will δτ k As a new step size coefficient.

[0140] Step 35: Determine the target unmixing matrix.

[0141] In this embodiment of the invention, in the unmixing matrix B k Riemann gradient on the corresponding Stiefel manifold If the unmixing matrix B is less than the preset convergence threshold ε, that is, the unmixing matrix B... k Riemann gradient on the corresponding Stiefel manifold In the case of convergence, the unmixing matrix B k As the target unmixing matrix B * .

[0142] Step 36: Use the next small sample set as the current sample set, and proceed to step 31.

[0143] In this embodiment of the invention, if the solution result of the current sample set does not converge, the next small sample set is used as the current sample set for further judgment, that is, v is updated to v+1, until all small sample sets have been traversed.

[0144] Step 4, based on the target unmixing matrix B * Calculate the antenna pattern of the array radar.

[0145] In this embodiment of the invention, the solved target unmixing matrix B is used. * Determine the separation signal Y * As shown in equation (15):

[0146]

[0147] Accordingly, with the target unmixing matrix B * The antenna pattern of the array radar with weights is shown in equation (16) below:

[0148] F(θ)=(B * ) H Wa(θ)| (16)

[0149] In the above formula, a(θ) is the steering vector of the array radar, expressed as a(θ)=[1,e jκdsinθ ,…,e jκ(n-1)dsinθ ]H θ is the angle of the antenna pattern; j is the imaginary unit; d is the element spacing of the array radar; and κ is the preset antenna coefficient. The resulting antenna pattern can achieve the purpose of anti-jamming for the array radar.

[0150] In this embodiment of the invention, when applying the blind source separation method based on Stiefel manifold optimization and information entropy criterion of the present invention, the simulation conditions for the verification experiment are shown in Table 1 below:

[0151] Table 1

[0152]

[0153] In the table above, the array radar's receiving antennas are arranged in a 16-equal-spaced linear array, with each antenna receiving 3 signals. For example... Figure 2 As shown, the source signal consists of a target echo signal and two types of interference signals. The target echo signal is a chirp signal incident at 0° angle, interference signal 1 is a single-tone interference signal incident at 30° angle, and interference signal 2 is a noise amplitude-modulated interference signal incident at -3° angle. Interference signal 1 is injected from the sidelobe of the array radar, and interference signal 2 is injected from the main lobe of the array radar. Figure 3 As shown, the noise signal is Gaussian white noise. The received signal X is generated by mixing the noise signal N with the source signal S, which is linearly mixed by the steering vector matrix A. Figure 4 As shown, the number of received signals X is 3.

[0154] Furthermore, the blind source separation method based on Stiefel manifold optimization and information entropy criterion of this invention is used to solve the target unmixing matrix B. * The separated target echo signal and interference signal are obtained as follows: Figure 5 As shown, separation channel 1 corresponds to the separated single-tone interference signal, separation channel 2 corresponds to the separated target echo signal, and separation channel 3 corresponds to the separated amplitude modulation noise interference signal. From Figure 5 As can be seen from this, the blind source separation method of the present invention can effectively and accurately separate the target echo signal and the interference signal in the received signal.

[0155] Furthermore, using the solved target unmixing matrix B * Calculate the corresponding antenna pattern, such as Figure 6 As shown, a strong gain is formed in the direction of the target echo, and the two deepest nulls are formed in the two interference directions, indicating that the present invention can effectively suppress sidelobe interference signals and main lobe interference signals.

[0156] In an embodiment of the present invention, Figure 7 The separation result is from the traditional JADE blind source separation algorithm. Figure 8The separation results of the traditional FastICA blind source separation algorithm are shown below. Figure 7 and Figure 8 It can be seen that the present invention and the FastICA blind source separation algorithm can correctly separate the target echo signal and the interference signal, while the JADE blind source separation algorithm has a poor separation effect. Table 2 compares the solution time of the present invention with the traditional JADE blind source separation algorithm and the FastICA blind source separation algorithm. As can be seen from Table 2, the solution time required by the present invention and the JADE blind source separation algorithm is similar, while the FastICA blind source separation algorithm takes significantly longer. Considering both the separation effect and the solution time, the present invention has a significant advantage over the traditional JADE blind source separation algorithm and the FastICA blind source separation algorithm.

[0157] Table 2

[0158]

[0159] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A blind source separation method based on Stiefel manifold optimization and information entropy criterion, characterized in that, include: The received signals of multiple samples are collected, and the received signals are pre-whitened using a pre-whitening matrix to obtain pre-processed signals of multiple samples. The preprocessed signals of the multiple samples are divided into multiple small sample sets; According to the numbering order of the small sample set, the blind source separation solution based on the information entropy criterion is performed using the small sample set to determine the target unmixing matrix; wherein, the solution method is the Stiefel manifold optimization algorithm with variable step size; Calculate the antenna pattern of the array radar based on the target unmixing matrix; The determination of the target unmixing matrix includes: The first A small set of samples is used as the current sample set; On the current sample set, using the unmixing matrix Estimate the probability density function of the separated signal: ,in, ; in, This indicates the number of samples in the small sample set. Indicates the first The first small sample signal One element, for The Column vectors; The minimum value of the information entropy of the probability density function is taken as the objective function, and the orthogonal matrix of the unmixing matrix is ​​taken as the constraint condition. The objective function is solved using the Stiefel manifold optimization algorithm with varying step size. The Riemann gradient on the Stiefel manifold is then determined to be less than the convergence coefficient. If so, the objective unmixing matrix is ​​determined. ; The step of using the minimum value of the information entropy of the probability density function as the objective function and the orthogonality of the unmixing matrix as the constraint condition includes: Using the demixing matrix Estimate the separation signal The information entropy of the probability density function is: ; The minimum value of the information entropy is taken as the objective function: ； The demixing matrix Its transpose The product is 3D unit array As a constraint: .

2. The method as described in claim 1, characterized in that, The process of pre-whitening the received signal using a pre-whitening matrix to obtain pre-processed signals of multiple samples includes: Estimating the received signal using the multiple samples The covariance matrix is ​​used to obtain the estimated value. : ； In the above formula, The various eigenvalues ,in, Corresponding to the source signal , Corresponding to noise signal ; Using the estimated value Eigenvalues ​​corresponding to noise signals Estimate the variance of the noise signal : ; For the estimated value Perform eigenvalue decomposition to obtain the estimated value. eigenvectors ; Using the feature vector corresponding to the source signal and the estimated value The eigenvalues ​​corresponding to the source signal are used to generate the solution vector. ; For the solution vector The variance of the noise signal and 3D unit array The symmetric positive definite matrix formed Perform Cholesky decomposition to obtain the lower triangular matrix. ; Through the lower triangular matrix The inverse matrix and the solution vector The pre-whitening matrix generated by the product is used for the received signal. Pre-whitening processing is performed to obtain the received signal. Preprocessed signal .

3. The method as described in claim 2, characterized in that, The step of dividing the preprocessed signals of the multiple samples into multiple small sample sets includes: right Preprocessed signal of each sample The data is segmented to obtain various small sample sets. , Indicates the number of samples in the small sample set; This indicates the number of preprocessed signals in each small sample set; Indicates the number of the small sample set.

4. The method as described in claim 1, characterized in that, The objective function is solved using the variable-step-size Stiefel manifold optimization algorithm. The process involves determining whether the Riemann gradient on the Stiefel manifold is less than the convergence coefficient. If so, the objective unmixing matrix is ​​determined, including: For the unmixing matrix Initialization is performed to obtain the initial unmixing matrix. ; Determine the number of updates Has the maximum number of iterations been reached? If not, determine the unmixing matrix. Riemann gradient on the corresponding Stiefel manifold Is it less than the preset convergence threshold? ; If not, according to the unmixing matrix The geodesic equation values ​​are calculated using the geodesic equations on the Stiefel manifold. Determine the step size coefficient Does it meet Wolfe's search criteria? ,in, ; If so, the unmixing matrix geodesic equation value As the updated demixing matrix ; Based on the difference between the unmixing matrices before and after the update The difference between the Riemann gradient on the Stiefel manifold corresponding to the unmixing matrix before and after the update. Determine the updated step size coefficient : , This indicates finding the trace of a matrix. For the remainder function; Using update coefficient two Algorithm coefficients before and after update and the updated unmixing matrix Corresponding objective function value Confirm the updated ;in, ; Will Updated to Updated unmixing matrix As the demixing matrix Execute the aforementioned update count determination Has the maximum number of iterations been reached? .

5. The method as described in claim 4, characterized in that, In the unmixing matrix Riemann gradient on the corresponding Stiefel manifold Less than the preset convergence threshold In the case of unmixing the matrix As the target unmixing matrix .

6. The method as described in claim 5, characterized in that, The demixing matrix Initialization is performed to obtain the initial unmixing matrix. ,include: Determine if the previous small sample set is empty; if so, then arbitrarily give an orthogonal initial unmixing matrix. If not, use the target unmixing matrix finally calculated from the previous small sample set. The initial unmixing matrix for the current small sample set is denoted as... .

7. The method as described in claim 4, characterized in that, In the step size coefficient If the Wolfe search conditions are not met, reduce the step size coefficient. The reduction factor is The reduced step size coefficient .

8. The method as described in claim 1, characterized in that, The target unmixing matrix The antenna pattern of the array radar is calculated, including: Using the solved target unmixing matrix Determine the separation signal ; With the target unmixing matrix The antenna pattern of the array radar with weights is as follows: ； In the above formula, The steering vector of the array radar is expressed as follows: , The angle of the antenna pattern; The imaginary unit, The element spacing of the array radar. This is the preset antenna coefficient.

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