High-resolution subspace estimation method for array covariance matrix correction

Abstract

The invention discloses a high-resolution subspace estimation method for array covariance matrix correction, and the method comprises the steps: building a receiving signal model based on transmitting signals received by M array elements of an array antenna at a t moment; dividing the array antenna into a first sub-array and a second sub-array, respectively obtaining covariance matrixes of the two sub-arrays, performing characteristic decomposition, and dividing a signal space US into two signal sub-spaces; determining a rotation invariant factor matrix psi LS according to the two signal subspaces, and solving P eigenvalues of the psi LS to obtain P signal arrival angle estimated values; determining a probability density function of the L times of snapshots according to the received signal model and the first-order moment and the second-order moment of the received signal, and solving to obtain a maximum likelihood functional expression about a signal arrival angle as a target function; and reconstructing the US according to the estimated value of the signal angle of arrival, substituting the reconstructed signal space # imgabs0 # into a target function, minimizing the target function by using a particle swarm optimization algorithm, and performing high-resolution subspace estimation.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a high-resolution subspace estimation method for correcting an array covariance matrix. Background Art

[0002] With the development of signal processing technology, high-resolution subspace estimation has broad application prospects in multiple fields such as mobile communication, geological exploration, electronic or communication interference detection, etc.

[0003] In order to improve the estimation accuracy of traditional high-resolution subspace estimation methods, the estimation of the array sample covariance matrix can be improved. In the prior art, Y. Chen et al. proposed a method for estimating the covariance matrix from the perspective of minimum mean square error; at the same time, B. D. Carlson proposed the diagonal loading method, which improves the covariance matrix by scaling and shifting the eigenvalues of the array output covariance matrix while keeping the corresponding eigenvectors unchanged. However, the covariance matrices obtained by the above two methods do not change the signal and noise projection matrices corresponding to the sample data covariance matrix, so the effect is poor. Similarly, M. Shaghaghi et al. adopted a two-step method, which reduced subspace leakage and improved the high-resolution subspace estimation performance at low signal-to-noise ratio and with a small number of snapshots. However, the improvements achieved are minimal and cannot justify its complexity.

[0004] In recent years, those skilled in the art have also proposed a method for updating the covariance matrix based on pseudo-random spatial spectrum resampling, which includes resampling based on pseudo-noise and updating the covariance matrix using pseudo-noise recovery technology. The newly synthesized pseudo-noise will interfere with the previous noise, and this process will be repeated multiple times to obtain the final estimated angle. However, the improvement effect of this method is still not obvious, and the performance failure of the threshold space is closely related to the leakage of the subspace, that is, a part of the true signal subspace exists in the estimated noise subspace, so the effect is greatly reduced. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a high-resolution subspace estimation method for correcting an array covariance matrix. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] The present invention provides a high-resolution subspace estimation method for correcting an array covariance matrix, including:

[0007] Based on the transmitted signals received by M array elements of an array antenna at time t, a received signal model is established, where the transmitted signals are P far-field narrowband signals, and P < M;

[0008] Divide the array antenna into a first sub-array and a second sub-array, respectively obtain the covariance matrices of the first sub-array and the second sub-array and perform eigenvalue decomposition, and divide the signal space U S into two signal sub-spaces;

[0009] Determine the rotation invariant factor matrix Ψ according to the two signal sub-spaces LS , and solve the P eigenvalues of the rotation invariant factor matrix Ψ LS to obtain P signal arrival angle estimation values;

[0010] According to the received signal model, the first moment and the second moment of the received signal, determine the probability density function of L snapshots, and obtain the maximum likelihood function formula for the signal arrival angle by solving the probability density function, as the objective function;

[0011] Reconstruct the signal space U S according to the signal arrival angle estimation values, and substitute the reconstructed signal space into the objective function, and use the particle swarm optimization algorithm to minimize the objective function for high-resolution subspace estimation.

[0012] In an embodiment of the present invention, the received signal model is expressed as:

[0013] X(t) = A(θ)S(t) + N(t);

[0014] wherein, X(t) represents an M×1 dimensional received signal vector, A(θ) represents an M×P dimensional manifold matrix of the array antenna, S(t) represents a P×1 dimensional manifold matrix of the transmitted signal, N(t) represents an M×1 dimensional noise data vector of the received signal, and θ represents the signal arrival angle to be estimated.

[0015] In an embodiment of the present invention, the steps of determining the rotation invariant factor matrix Ψ LS according to the two signal sub-spaces, and solving the P eigenvalues of the rotation invariant factor matrix Ψ LS to obtain P signal arrival angle estimation values include:

[0016] Determine the rotation invariant factor matrix Ψ LS according to the two signal sub-spaces:

[0017]

[0018] wherein, U S1 and U S2 respectively represent the signal sub-space of the first sub-array and the signal sub-space of the second sub-array, represents the pseudo-inverse of the matrix;

[0019] For the rotation-invariant factor matrix ψ LS Perform eigenvalue decomposition, and determine the P eigenvalues obtained as P signal arrival angle estimates

[0020] In an embodiment of the present invention, according to the received signal model, the first moment and the second moment of the received signal, determining the probability density function of L snapshots, and obtaining the maximum likelihood function formula for the signal arrival angle by solving the probability density function as the objective function, includes:

[0021] According to the received signal model, the first moment and the second moment of the received signal, determine the probability density function of L snapshots:

[0022]

[0023] where I represents the identity matrix, x i represents the received signal vector of the i-th snapshot, σ 2 represents the noise power, s i represents the transmitted signal vector of the i-th snapshot;

[0024] Take the negative logarithm of the probability density function to obtain the maximum likelihood function formula for the signal arrival angle and use it as the objective function.

[0025] In an embodiment of the present invention, the objective function is expressed as:

[0026]

[0027] where tr represents the trace of the matrix, P A represents the projection matrix of the signal space U S and R X represents the covariance matrix of the received signal vector X.

[0028] In an embodiment of the present invention, according to the signal arrival angle estimates, reconstruct the signal space U S and substitute the reconstructed signal space into the objective function, and use the particle swarm optimization algorithm to minimize the objective function to perform high-resolution subspace estimation, including:

[0029] Based on the P signal arrival angle estimates, reconstruct the manifold matrix of the array antenna:

[0030]

[0031] where respectively represent the 1st, 2nd,..., P-th signal arrival angle estimates, and represents the steering vector;

[0032] According to the reconstructed array antenna manifold matrix Reconstruct the signal space

[0033]

[0034] Wherein, H represents the conjugate transpose;

[0035] Substitute the reconstructed signal space into the objective function:

[0036]

[0037] By using the particle swarm algorithm to determine the optimal diagonal complex matrix to perform complex weighting processing on the covariance matrix R of the received signal vector X X to obtain a high-resolution subspace estimation result.

[0038] In an embodiment of the present invention, the step of using the particle swarm algorithm to determine the optimal diagonal complex matrix to perform complex weighting processing on the covariance matrix R of the received signal vector X X includes:

[0039] Initialize and generate two diagonal complex matrices L and G with dimensions of M×M, and the diagonal complex matrices L and G are identity matrices;

[0040] Take each element on the diagonal of the diagonal complex matrices L and G as particles, and use the particle swarm optimization algorithm to sequentially determine 2M diagonal elements in the diagonal complex matrices L and G to generate the optimal diagonal complex matrices L′ and G′;

[0041] Use the optimal diagonal complex matrices L′ and G′ to correct the covariance matrix R X to obtain the corrected covariance matrix

[0042] Perform eigenvalue decomposition on the corrected covariance matrix to obtain the corrected signal space

[0043] According to the ESPRIT algorithm and the corrected signal space re-estimate to obtain P signal arrival angle estimation values

[0044] In an embodiment of the present invention, each diagonal element is sequentially determined according to the following steps:

[0045] Define the number of iterations iter = 1, the population size as N, and randomly initialize the velocity and position of each particle in the population, the individual best position of each particle, and the global best position of each particle;

[0046] Calculate the fitness function value corresponding to the position of each particle at the iter-th iteration;

[0047] If the fitness function value of the k-th particle at the iter-th iteration is less than the fitness function value corresponding to its individual best position at the (iter - 1)-th iteration, then update the fitness function value corresponding to the individual best position of the k-th particle;

[0048] If the fitness function value corresponding to the individual best position of the current k-th particle is less than the fitness function value corresponding to the global best position of each particle, then take the individual best position of the current k-th particle as the current global best position;

[0049] Update the velocity and position of the k-th particle;

[0050] Judge whether the number of iterations iter is greater than or equal to the preset number of iterations T max ; If not, let iter = iter + 1, and return to the step of calculating the fitness function value corresponding to the position of each particle at the iter-th iteration; otherwise, output the current global best position as the diagonal element.

[0051] In an embodiment of the present invention, the corrected covariance matrix

[0052] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0053] The present invention provides a high-resolution subspace estimation method for correcting the array covariance matrix, uses the maximum likelihood algorithm to obtain the maximum likelihood function formula related to the signal arrival angle, and takes it as the objective function, and then defines two diagonal complex matrices as the weighted matrices of the covariance matrix R of the received signal vector X X to further use the particle swarm optimization algorithm to make the objective function converge to the minimum value while minimizing the RMSE value, so as to update the value of each element on the diagonal complex matrix, thereby correcting the covariance matrix R X and re-estimate P signal arrival angle estimation values Therefore, the accuracy of the signal subspace is improved, thereby improving the quality of subsequent high-resolution subspace estimation.

[0054] The following will further describe the present invention in detail with reference to the drawings and embodiments. Description of the Drawings

[0055] Figure 1 It is a flowchart of the high-resolution subspace estimation method for correcting the array covariance matrix provided by an embodiment of the present invention;

[0056] Figure 2 It is a flowchart of minimizing the objective function by using the particle swarm optimization algorithm provided by an embodiment of the present invention;

[0057] Figure 3 It is a comparison graph of the relationship between different SNR values and RMSE generated by different methods;

[0058] Figure 4 It is a comparison graph of the relationship between the number of snapshots and RMSE generated by different methods;

[0059] Figure 5 It is a comparison graph of the relationship between the number of array elements and RMSE generated by different methods. Detailed implementation manners

[0060] The present invention will be further described in detail below in conjunction with specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0061] Figure 1 It is a flowchart of the high-resolution subspace estimation method for correcting the array covariance matrix provided by an embodiment of the present invention. As Figure 1 shown, an embodiment of the present invention provides a high-resolution subspace estimation method for correcting the array covariance matrix, including:

[0062] S1. Based on the transmitted signals received by M array elements of the array antenna at time t, establish a received signal model, where the transmitted signals are P far-field narrowband signals, and P < M;

[0063] S2. Divide the array antenna into a first sub-array and a second sub-array, respectively obtain the covariance matrices of the first sub-array and the second sub-array and perform eigenvalue decomposition, and divide the signal space U S into two signal sub-spaces;

[0064] S3. Determine the rotation invariant factor matrix Ψ LS according to the two signal sub-spaces, solve the P eigenvalues of the rotation invariant factor matrix ψ LS to obtain P signal arrival angle estimation values;

[0065] S4. Determine the probability density function of L snapshots according to the received signal model, the first moment and the second moment of the received signal, and obtain the maximum likelihood function formula about the signal arrival angle by solving the probability density function as the objective function;

[0066] S5. Reconstruct the signal space U S according to the signal arrival angle estimation values, and the reconstructed signal space Substitute into the objective function and use the particle swarm optimization algorithm to minimize the objective function for high-resolution subspace estimation.

[0067] Specifically, in this embodiment, it is considered that P far-field narrowband signals are incident on a certain array antenna in space. The array antenna consists of M array elements, where P < M. In an ideal case, the received signals of the M array elements at time t are arranged into a column vector, and the received signal model can be expressed as:

[0068] X(t) = A(θ)S(t) + N(t);

[0069] In the formula, X(t) represents the M×1-dimensional received signal vector, A(θ) represents the M×P-dimensional manifold matrix of the array antenna, S(t) represents the P×1-dimensional manifold matrix of the transmitted signal, N(t) represents the M×1-dimensional noise data vector of the received signal, and θ represents the signal arrival angle to be estimated.

[0070] It should be understood that the bandwidth W of the narrowband signal B is negligible compared to its center frequency f 0 Generally speaking, those satisfying are considered narrowband signals, otherwise they are broadband signals.

[0071] Optionally, in step S3, determining the rotation invariant factor matrix ψ LS according to the two signal subspaces, and solving the P eigenvalues of the rotation invariant factor matrix Ψ LS to obtain the P signal arrival angle estimation values includes:

[0072] S301. Determine the rotation invariant factor matrix according to the two signal subspaces:

[0073]

[0074] In the formula, U S1 and U S2 respectively represent the signal subspace of the first subarray and the signal subspace of the second subarray, represents the pseudo-inverse of the matrix;

[0075] S302. Perform eigenvalue decomposition on the rotation invariant factor matrix, and determine the obtained P eigenvalues as the P signal arrival angle estimation values

[0076] Optionally, in step S4, determining the probability density function of L snapshots according to the received signal model, the first moment and the second moment of the received signal, and obtaining the maximum likelihood function formula about the signal arrival angle by solving the probability density function as the objective function includes:

[0077] S401. Determine the probability density function of L snapshots according to the received signal model, the first moment and the second moment of the received signal:

[0078]

[0079] where I represents the identity matrix, and x i represents the received signal vector of the i-th snapshot, and σ 2 represents the noise power, and s i represents the transmitted signal vector of the i-th snapshot;

[0080] S402. Take the negative logarithm of the probability density function to obtain the maximum likelihood function formula for the signal arrival angle, and use it as the objective function.

[0081] The objective function is expressed as:

[0082]

[0083] where tr represents the trace of the matrix, and P A represents the projection matrix of the signal space U S , R X represents the covariance matrix of the received signal vector X, and θ represents the signal arrival angle to be estimated.

[0084] Optionally, in step S5, according to the estimated value of the signal arrival angle, reconstruct the signal space U S , and substitute the reconstructed signal space into the objective function, and use the particle swarm optimization algorithm to minimize the objective function to perform high-resolution subspace estimation, including:

[0085] S501. Based on P estimated values of the signal arrival angle, reconstruct the steering matrix of the array antenna:

[0086]

[0087] where respectively represent the estimated values of the 1st, 2nd,..., P-th signal arrival angles, represents the steering vector;

[0088] S502. According to the reconstructed steering matrix of the array antenna reconstruct the signal space

[0089]

[0090] where H represents the conjugate transpose;

[0091] S503. Substitute the reconstructed signal space into the objective function:

[0092]

[0093] S504. Determine the optimal diagonal complex matrix by using the particle swarm algorithm to perform complex weighting processing on the covariance matrix R of the received signal vector X X to obtain a high-resolution subspace estimation result.

[0094] Since the objective function obtained from the maximum likelihood estimation is a positive value and its maximum value is required, a negative sign is added before the objective function as the fitness function in the particle swarm, converting it into a minimization problem. To minimize the mean square error and make the angle estimation more accurate, by performing complex weighting processing on the sample covariance matrix, the particle swarm is used to determine the optimal diagonal complex matrices L′ and G′, thereby obtaining a high-resolution subspace estimation result.

[0095] Figure 2 is the flowchart of using the particle swarm optimization algorithm to minimize the objective function provided by the embodiment of the present invention. As Figure 2 shown, specifically, step S504 includes:

[0096] Initialize and generate two diagonal complex matrices L and G with dimensions M×M. The diagonal complex matrices L and G are identity matrices;

[0097] Take each element on the diagonal of the diagonal complex matrices L and G as a particle, and use the particle swarm optimization algorithm to sequentially determine the 2M diagonal elements in the diagonal complex matrices L and G to generate the optimal diagonal complex matrices L′ and G′;

[0098] Use the optimal diagonal complex matrices L′ and G′ to correct the covariance matrix R X to obtain the corrected covariance matrix

[0099] Perform eigenvalue decomposition on the corrected covariance matrix to obtain the corrected signal space

[0100] According to the ESPRIT algorithm and the corrected signal space re-estimate to obtain P signal arrival angle estimation values

[0101] Optionally, determine each diagonal element in sequence according to the following steps:

[0102] Define the number of iterations iter = 1, the population size as N, and randomly initialize the velocity and position of each particle in the population, the individual best position of each particle, and the global best position of each particle;

[0103] Calculate the fitness function value corresponding to the position of each particle at the iter-th iteration;

[0104] If the fitness function value corresponding to the position of the k-th particle at the iter-th iteration is less than the fitness function value corresponding to its personal best position at the (iter - 1)-th iteration, then update the fitness function value corresponding to the personal best position of the k-th particle;

[0105] If the fitness function value corresponding to the personal best position of the current k-th particle is less than the fitness function value corresponding to the global best position of each particle, then take the personal best position of the current k-th particle as the current global best position;

[0106] Update the velocity and position of the k-th particle;

[0107] Judge whether the iteration number iter is greater than or equal to the preset iteration number T maz ; If not, let iter = iter + 1, and return to the above step of calculating the fitness function value corresponding to the position of each particle at the iter-th iteration; otherwise, output the current global best position as the diagonal element.

[0108] In addition, the Root Mean Square Error (RMSE) can be used to evaluate the effectiveness of the above high-resolution subspace evaluation method for array covariance matrix correction. The calculation formula is as follows:

[0109]

[0110] In the formula, N e represents the number of independent experiments, θ p is the actual signal arrival angle, represents the signal arrival angle estimated in the n-th independent experiment.

[0111] Next, the high-resolution subspace estimation method for array covariance matrix correction provided by the present invention will be further described through simulation experiments.

[0112] Under different SNR (signal-to-noise ratio) values, different snapshot numbers, and different array element numbers, the RMSE values of the high-resolution subspace method for array covariance matrix correction provided by the present invention and the existing ESPRIT algorithm are compared to evaluate the effectiveness of the present invention. Among them, the specific values of multiple parameters involved in the present invention are shown in Table 1 as follows:

[0113] Table 1

[0114] Parameter Value Number of array elements in a uniform linear array 8 to 12 DOA 5°,15°,30° SNR -25 to -10 Element spacing Half wavelength Number of snapshots 10 to 60 Number of iterations 100 Number of independent experiments 200

[0115] Figure 3It is a comparison graph of the relationship between different SNR values and the RMSE generated by different methods. Among them, the SNR ranges from -25 to -10 dB, and the experimental parameters are set as follows: an 8-element uniform linear array and 3 uncorrelated narrowband source signals are used, and the DOA (5°, 15°, 30°) is incident on the ULA (uniform linear array). The number of snapshots is fixed at 30 times, and a total of 200 independent experiments are simulated.

[0116] From Figure 3 It can be seen that as the signal-to-noise ratio increases, the RMSE decreases. When the signal-to-noise ratio is very low, the signal strength is weaker than the noise strength, resulting in a greater impact of the noise. Therefore, the existing ESPRIT algorithm will produce a large DOA estimation error. In contrast, the present invention effectively reduces the DOA estimation error under the same conditions by refining the covariance matrix of the array data.

[0117] Figure 4 It is a comparison graph of the relationship between the number of snapshots and the RMSE generated by different methods. Further, please refer to Figure 4 , the SNR is fixed at -15 dB, the number of snapshots is from 10 to 60, and the other simulation conditions are the same as those in the first simulation. As Figure 4 shown, as the number of snapshots increases, the RMSE decreases. When estimating the DOA using the existing ESPRIT algorithm, the error generated is very large. In contrast, the present invention optimizes the DOA estimation, thereby reducing the error.

[0118] Figure 5 It is a comparison graph of the relationship between the number of array elements and the RMSE generated by different methods. As Figure 5 shown, the SNR is fixed at -15 dB, the number of snapshots is 30, and the number of array elements is from 6 to 16. The other simulation conditions are the same as those in the first simulation. As Figure 5 shown, as the number of array elements increases, the RMSE generally shows a downward trend. In addition, compared with the existing ESPRIT algorithm, the DOA estimation accuracy of the present invention is higher.

[0119] From the above embodiments, it can be seen that the beneficial effects of the present invention are as follows:

[0120] The present invention provides a high-resolution subspace estimation method for correcting the array covariance matrix, uses the maximum likelihood algorithm to obtain the maximum likelihood function formula related to the signal arrival angle, and takes it as the objective function. Then, two diagonal complex matrices are defined as the weighted matrices of the covariance matrix R Z of the received signal vector X, and further uses the particle swarm optimization algorithm to make the objective function converge to the minimum value while minimizing the RMSE value, so as to update the values of each element on the diagonal complex matrix, thereby correcting the covariance matrix R X and re-estimating P signal arrival angle estimation values Therefore, the accuracy of the signal subspace is improved, thereby improving the quality of subsequent high-resolution subspace estimation.

[0121] In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality of" means two or more unless otherwise specifically defined.

[0122] The description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials, or characteristics described in connection 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 can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0123] Although the present application has been described in conjunction with various embodiments herein, however, in the process of implementing the claimed present application, those skilled in the art can understand and realize other variations of the disclosed embodiments by viewing the accompanying drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "one" does not exclude a plurality. Certain measures are recited in mutually different dependent claims, but this does not mean that these measures cannot be combined to produce good results.

[0124] The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A high-resolution subspace estimation method for array covariance matrix correction, characterized in that: include: Based on the transmitted signals received by the M array elements of the array antenna at time t, a received signal model is established, wherein the transmitted signals are P far-field narrowband signals, P <M; The array antenna is divided into a first subarray and a second subarray, and the covariance matrices of the first subarray and the second subarray are obtained and eigendecomposed respectively, and the signal space U S Divided into two signal subspaces; Determine the rotation invariant factor matrix Ψ based on the two signal subspaces LS , solve the rotation invariant factor matrix Ψ LS P eigenvalues ​​of the signal are obtained to obtain P signal arrival angle estimation values; Determine the probability density function of L snapshots according to the received signal model, the first-order moment and the second-order moment of the received signal, and obtain the maximum likelihood function of the signal arrival angle by solving the probability density function as the objective function; According to the signal arrival angle estimation value, the signal space U S Reconstruct and reconstruct the signal space Substitute the objective function into the target function, use the particle swarm optimization algorithm to minimize the target function, and perform high-resolution subspace estimation.

2. The high-resolution subspace estimation method for array covariance matrix correction according to claim 1, characterized in that: The received signal model is expressed as: X(t) = A(θ)S(t) + N(t); Wherein, X(t) represents the M×1 dimensional received signal vector, A(θ) represents the M×P dimensional flow matrix of the array antenna, S(t) represents the P×1 dimensional flow matrix of the transmitted signal, N(t) represents the M×1 dimensional noise data vector of the received signal, and θ represents the signal arrival angle to be estimated.

3. The high-resolution subspace estimation method for array covariance matrix correction according to claim 1, characterized in that: Determine the rotation invariant factor matrix Ψ based on the two signal subspaces LS , solve the rotation invariant factor matrix Ψ LS The step of obtaining P signal arrival angle estimation values ​​from P eigenvalues ​​of , comprises: According to the two signal subspaces, the rotation invariant factor matrix Ψ is determined LS : Where U S1 and U S2 represent the signal subspace of the first subarray and the signal subspace of the second subarray respectively, represents the pseudo-inverse of a matrix; The rotation invariant factor matrix Ψ LS Perform eigendecomposition and determine the obtained P eigenvalues ​​as P signal arrival angle estimates 4. The high-resolution subspace estimation method for array covariance matrix correction according to claim 2, characterized in that: The steps of determining the probability density function of L snapshots according to the received signal model, the first-order moment and the second-order moment of the received signal, and obtaining the maximum likelihood function formula about the signal arrival angle as the objective function by solving the probability density function include: According to the received signal model, the first-order moment and the second-order moment of the received signal, the probability density function of L snapshots is determined: In the formula, I represents the unit matrix, x i represents the received signal vector of the i-th snapshot, σ 2 represents the noise power, s i represents the transmitted signal vector of the i-th snapshot; The negative logarithm of the probability density function is taken to obtain the maximum likelihood function formula about the signal arrival angle, and the maximum likelihood function formula is used as the objective function.

5. The high-resolution subspace estimation method for array covariance matrix correction according to claim 4, characterized in that, The objective function is expressed as: In the formula, tr represents the trace of the matrix, P A Denotes the signal space U S The projection matrix, R X represents the covariance matrix of the received signal vector X.

6. The high-resolution subspace estimation method for array covariance matrix correction according to claim 5, characterized in that: According to the signal arrival angle estimation value, the signal space U S Reconstruct and reconstruct the signal space Substituting the objective function into the target function, minimizing the target function using a particle swarm optimization algorithm, and performing high-resolution subspace estimation steps include: Based on the P signal arrival angle estimation values, the flow matrix of the array antenna is reconstructed: In the formula, Respectively represent the estimated arrival angles of the 1st, 2nd, …, Pth signals, represents the steering vector; According to the reconstructed array antenna flow matrix Reconstructing the signal space In the formula, H represents conjugate transpose; The reconstructed signal space Substituting into the objective function: The optimal diagonal complex matrix is ​​determined by using the particle swarm algorithm to calculate the covariance matrix R of the received signal vector X. X Complex weighted processing is performed to obtain high-resolution subspace estimation results.

7. The high-resolution subspace estimation method for array covariance matrix correction according to claim 6, characterized in that: The optimal diagonal complex matrix is ​​determined by using the particle swarm algorithm to calculate the covariance matrix R of the received signal vector X. X The steps of performing complex weighting processing include: Initialize and generate two diagonal complex matrices L and G with dimensions of M×M, wherein the diagonal complex matrices L and G are unit matrices; Taking each element on the diagonal of the diagonal complex matrices L and G as a particle, using a particle swarm optimization algorithm to sequentially determine 2M diagonal elements in the diagonal complex matrices L and G to generate optimal diagonal complex matrices L′ and G′; Modify the covariance matrix R using the optimal diagonal complex matrix L', G' X , and obtain the corrected covariance matrix The modified covariance matrix Perform feature decomposition to obtain the corrected signal space According to the ESPRIT algorithm and the modified signal space Re-estimate the P signal arrival angle estimates 8. The high-resolution subspace estimation method for array covariance matrix correction according to claim 7, characterized in that: Determine each diagonal element in turn as follows: Define the number of iterations iter = 1, the population size is N, and randomly initialize the speed and position of each particle in the population, the individual best position of each particle, and the global best position of each particle; Calculate the fitness function value corresponding to the position of each particle at the iterth iteration; If the fitness function value of the position of the kth particle at the iter-th iteration is less than the fitness function value corresponding to its individual best position at the iter-1-th iteration, then the fitness function value corresponding to the individual best position of the kth particle is updated; If the fitness function value corresponding to the individual best position of the current k-th particle is less than the fitness function value corresponding to the global best position of each particle, the individual best position of the current k-th particle is used as the current global best position; Update the speed and position of the kth particle; Determine whether the number of iterations iter is greater than or equal to the preset number of iterations T max ; If not, let iter=iter+1, and return to the step of calculating the fitness function value corresponding to the position of each particle at the iter-th iteration; otherwise, output the current global optimal position as a diagonal element.

9. The high-resolution subspace estimation method for array covariance matrix correction according to claim 7, characterized in that: Corrected covariance matrix

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