A sparse array angle estimation method based on bayesian learning and device thereof

Abstract

The present application belongs to the technical field of signal processing, and particularly relates to a sparse array angle estimation method based on Bayesian learning and a device thereof, which comprises the following steps: vectorizing the corresponding received signals received by each array element in a sparse array to obtain output signals in vector form, outputting the output signals in vector form by the sparse array to obtain a two-dimensional output signal model, reducing the dimension of the two-dimensional output signal model to obtain a one-dimensional output signal model; extracting a measurement matrix and a two-dimensional spatial spectrum matrix to be recovered from the obtained one-dimensional output signal model; using a Bayesian learning method to construct an optimization function according to the obtained one-dimensional output signal model and the measurement matrix when the two-dimensional spatial spectrum matrix to be recovered satisfies the RIP characteristic; solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a spatial spectrum of a target, and performing constant false alarm detection on the spatial spectrum of the target to obtain an azimuth estimation of the target.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and beam direction estimation technology for radar signals, acoustic signals and electromagnetic signals. Specifically, it relates to a sparse array angle estimation method and apparatus based on Bayesian learning. Background Technology

[0002] Beamforming is a crucial task in array signal processing, widely applied in radar, sonar, and communications. It suppresses spatial interference, estimates signal direction of arrival, and thus enables target detection and localization. Modern array signal processing, operating in multi-target and clustered target environments, demands increasingly higher angular resolution. Increasing array size and the variation in signal orientation information among different elements can lead to higher resolution, but this incurs high hardware manufacturing costs. Therefore, improving spatial gain and angular resolution under sparse array conditions has become a hot topic in array signal processing. When the number of array elements is finite, the sampling of spatial signals by the elements will not satisfy the Nyquist sampling theorem, making it difficult for conventional beamforming algorithms to guarantee angle estimation performance.

[0003] Common beamforming methods include Delay-and-sum (DAS) beamforming and Minimum Variance Distortion-less Response (MVDR) beamforming. DAS obtains the beam output by summing the time delay differences of each channel, exhibiting low computational complexity and high robustness. Capon's MVDR beamforming employs the minimum variance criterion to minimize output power and maximize array gain. Meanwhile, in the past 30 years, several high-resolution subspace orientation estimation algorithms have emerged, the most representative being the Multiple Signal Classification (MUSIC) algorithm. MUSIC first constructs a covariance matrix from the array's received data, then performs eigenvalue decomposition on the covariance matrix to obtain the signal subspace and noise subspace corresponding to the signal and noise components. Finally, utilizing the orthogonality of the signal and noise subspaces, a spatial spectral function is constructed. Through spectral peak search, the angular information of the signal is estimated, theoretically overcoming the Rayleigh criterion and achieving super-resolution estimation of the target angle.

[0004] However, traditional DAS algorithms suffer from low spatial resolution due to aperture size limitations, and increasing the number of array elements to improve resolution increases the hardware cost of the system. Both MVDR and MUSIC algorithms require decomposition of the covariance matrix and spectral peak search, making them highly susceptible to noise and computationally complex. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, this invention proposes a sparse array angle estimation method based on Bayesian learning, which includes:

[0006] The received signal of each element in the sparse array is vectorized to obtain the output signal in vector form. The sparse array outputs the output signal in vector form to obtain a two-dimensional output signal model. This model is then reduced in dimension to obtain a one-dimensional output signal model.

[0007] From the obtained one-dimensional output signal model, the measurement matrix and the two-dimensional spatial spectrum matrix to be recovered are extracted; using the Bayesian learning method, when the two-dimensional spatial spectrum matrix to be recovered satisfies the RIP characteristic, an optimization function is constructed based on the obtained one-dimensional output signal model and the measurement matrix.

[0008] The constructed optimization function is solved to obtain a two-dimensional space-time spectrum. The obtained two-dimensional space-time spectrum is accumulated in time to obtain the spatial spectrum of the target. Then, constant false alarm detection is performed on it to obtain the orientation estimate of the target.

[0009] As an improvement to the above technical solution, the received signal of each element in the sparse array is vectorized to obtain a vector-form output signal. The sparse array outputs this vector-form output signal to obtain a two-dimensional output signal model, which is then reduced in dimension to obtain a one-dimensional output signal model. The specific implementation process is as follows:

[0010] Assume the sparse array is a random array with M elements, represented using rectangular coordinates; assume there are long-range incoming waves from N directions in space, and each element receives the long-range incoming waves from each direction as the received signal.

[0011] The m-th array element receives the corresponding received signal y. m (t), and output it as: M = 1, 2, 3, ..., m, ..., M;

[0012]

[0013] Where, τ m,n τ is the time delay of a long-range wave arriving at the m-th array element from the n-th direction relative to its arrival at the reference point; m,n =R m,n / c; where c is the propagation speed of the distant incoming wave; R m,n s(t-τ) represents the distance from the target in the nth direction to the mth array element. m,n ) represents the incoming wave from the target located in the nth direction received by the m-th array element; t represents the reception time of the incoming wave from the target.

[0014] ε m (t) represents the noise of the m-th array element;

[0015] For the narrowband case, the time delay is equivalent to the phase shift, denoted as . Among them, f c The carrier frequency for narrowband signals; Then y m (t) can be rewritten as:

[0016]

[0017] The vector form of the output signal of the M array elements is as follows:

[0018]

[0019] Where y(t) is the vector array output of M elements; where y(t) = [y1(t), y2(t), ..., y M (t)] T ; where y M (t) represents the vector output of the Mth array element;

[0020] s(t) is the spatial spectrum of the incoming wave; where s(t) = [s0(t), s1(t), ..., s n (t),…,s (N-1) (t)] T ;s n (t) represents the target wave spatial spectrum in the nth direction;

[0021] ε(t) represents noise; where ε(t) = [ε1(t), ε2(t), ..., ε M (t)] T ;ε M (t) represents the noise received by the Mth array element;

[0022] a(θ n ) is the steering vector for the nth observation angle;

[0023] in

[0024] A is the orientation matrix; where A = [a(θ0), a(θ1), ..., a(θ)] N-1 )];

[0025] Dividing the observation angle range into H observation angle units, the corresponding steering matrix A becomes an M×H matrix:

[0026] A = [a(θ0), a(θ1), ..., a(θ)] h ),…,a(θ H-1 )];

[0027] Where, a(θ) h ) is the steering vector for the h-th observation angle;

[0028] in,

[0029] When the received data y(t) has K snapshots, the output signal of the M array elements is vectorized to obtain the output signal matrix in vector form, denoted as the two-dimensional output signal model y:

[0030] y=As+ε (4)

[0031] Where y = [y(1) y(2) … y(K)] represents a matrix of size M×K; s is the two-dimensional spatial spectrum matrix to be recovered, with the element in the nth row and kth column being s. n (k); ε is the noise vector matrix;

[0032] The two-dimensional output signal model is reduced in dimension to obtain a one-dimensional output signal model Y;

[0033]

[0034] in, It is a measurement matrix of MK×HK dimensions; where,

[0035] Among them, Y=vec(y); S=vec(s); E=vec(ε).

[0036] As an improvement to the above technical solution, the measurement matrix and the two-dimensional spatial spectrum matrix to be recovered are extracted from the obtained one-dimensional output signal model. When the two-dimensional spatial spectrum matrix to be recovered satisfies the RIP characteristic, an optimization function is constructed based on the obtained one-dimensional output signal model and the measurement matrix. The specific process is as follows:

[0037] Extract the measurement matrix from the obtained one-dimensional output signal model Y. and the two-dimensional spatial spectral matrix S that needs to be recovered;

[0038] Determine whether the two-dimensional spatial spectral matrix S to be recovered satisfies the RIP property; where the condition for satisfaction is:

[0039]

[0040] in,

[0041]

[0042] in, For matrix The relevant vector; θ p This is the p-th observation angle; θ q Let q be the q-th observation angle;

[0043] If the above conditions are not met, the two-dimensional spatial spectral matrix S to be recovered does not satisfy the RIP property, and the process ends.

[0044] If the above conditions are met, the two-dimensional spatial spectral matrix S to be recovered satisfies the RIP property, and the optimization function can be further constructed as follows:

[0045] S = arg min{J(S)} (8)

[0046] in,

[0047]

[0048] Among them, ||·|| F denot represents the norm of the F matrix; min(·) is the minimization operation; ρ is the sparse coefficient.

[0049] As an improvement to the above technical solution, the constructed optimization function is solved to obtain a two-dimensional spatiotemporal spectrum, and the obtained two-dimensional spatiotemporal spectrum is accumulated in time to obtain the spatial spectrum of the target. Then, constant false alarm rate (CFAR) detection is performed on it to obtain the target's azimuth estimate. The specific process is as follows:

[0050] The conjugate gradient method is used to calculate the conjugate gradient of the optimization function with respect to the spatial spectral matrix S.

[0051]

[0052] Where H(S) is the Hessian matrix; For the measurement matrix; (·) H The conjugate of the matrix is ​​represented by H(S); H(S) is the coefficient matrix of S, which can be expressed as...

[0053] H(S)=2Y H Y+ρΛ(S) (15)

[0054] Where ρ is the sparsity coefficient;

[0055]

[0056] Where S(hk) is the element value in the h-th row and k-th column of matrix S; diag[] is a diagonal matrix; τ is a minimum positive value, which is 0.01;

[0057] Using Newton's iterative algorithm, we know that the (l+1)th iteration of S is the Newton iterative formula:

[0058]

[0059] Where β is the iteration step size, [·] -1 Represents the inverse of a matrix;

[0060] Conjugate gradient Substituting the expression into the iterative formula (16) above, we obtain:

[0061]

[0062] Assuming the iteration step size β = 1, the iterative equation (16) can be transformed into

[0063]

[0064] To optimize equation (18), the Hessian matrix H(S) needs to be updated in each iteration. l ) = 2Y H Y+ρΛ(S l );

[0065] The algorithm terminates when the following condition is met, yielding the two-dimensional spacetime spectrum s. h (k) represents the spatiotemporal spectrum of the kth snapshot in the h-th orientation;

[0066]

[0067] The obtained two-dimensional space-time spectrum is accumulated over time to obtain the target angle space spectrum.

[0068]

[0069] right Perform routine constant false alarm rate (CFAR) detection to obtain the target's location estimate.

[0070] The present invention also provides a sparse array angle estimation device based on Bayesian learning, the device comprising:

[0071] The model acquisition module is used to vectorize the received signal of each array element in the sparse array to obtain the output signal in vector form. The sparse array outputs the output signal in vector form to obtain a two-dimensional output signal model. It then reduces the dimensionality of the output signal to obtain a one-dimensional output signal model.

[0072] An optimization function construction module is used to extract the measurement matrix and the two-dimensional spatial spectrum matrix to be recovered from the obtained one-dimensional output signal model. Using a Bayesian learning method, when the two-dimensional spatial spectrum matrix to be recovered satisfies the RIP characteristic, an optimization function is constructed based on the obtained one-dimensional output signal model and the measurement matrix.

[0073] The orientation estimation module is used to solve the constructed optimization function to obtain a two-dimensional space-time spectrum. The obtained two-dimensional space-time spectrum is accumulated in time to obtain the spatial spectrum of the target. Then, constant false alarm detection is performed on it to obtain the orientation estimate of the target.

[0074] The present invention also provides a computer device for target orientation estimation, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor implements the method when executing the computer program.

[0075] The present invention also provides a computer-readable storage medium comprising a stored computer program; wherein, when the computer program is executed, it controls the device in which the computer-readable storage medium is located to perform the method described thereon.

[0076] The present invention also provides an information data processing terminal, which is used to implement the method described herein.

[0077] The advantages of this invention compared to the prior art are:

[0078] 1. The method of the present invention is a sparse array azimuth estimation method based on compressed sensing, which can effectively improve the target angular resolution and has the advantages of low sidelobe and strong noise robustness. Using the sparse array azimuth estimation method based on compressed sensing, the performance is usually no less than that of traditional algorithms, and it is superior to MVDR and MUSIC algorithms under low signal-to-noise ratio and finite array element conditions, with a sharper beam response.

[0079] 2. In the method of this invention, the sparsity coefficients are derived through Bayesian compressed sensing theory, which ensures the noise robustness of the algorithm.

[0080] 3. The method of the present invention improves the efficiency of the algorithm by adopting the conjugate gradient algorithm. The algorithm can achieve super-resolution angle estimation with fewer snapshots in the case of sparse array. Attached Figure Description

[0081] Figure 1 This is a flowchart of a sparse array angle estimation method based on Bayesian learning according to the present invention;

[0082] Figure 2 This is a schematic diagram showing the angle estimation results of the method of the present invention and the traditional DAS, MVDR and MUSIC methods in a single-target scenario;

[0083] Figure 3 This is a schematic diagram comparing the relationship between the angle estimation error and signal-to-noise ratio of the method of this invention and the traditional DAS, MVDR, and MUSIC methods;

[0084] Figure 4 This is a schematic diagram comparing the relationship between the angle estimation error and the number of array elements of the method of this invention and the traditional DAS, MVDR, and MUSIC methods;

[0085] Figure 5(a) is a schematic diagram comparing the results of the method of the present invention with those of the traditional DAS, MVDR and MUSIC methods with target azimuth of -5° and 5°.

[0086] Figure 5(b) is a schematic diagram comparing the results of the method of the present invention with those of the traditional DAS, MVDR, and MUSIC methods with target azimuths of -3° and 3°. Detailed Implementation

[0087] The present invention will now be further described with reference to the accompanying drawings.

[0088] This invention provides a sparse array angle estimation method based on Bayesian learning. This method employs a sparse array azimuth estimation algorithm based on compressed sensing. This algorithm is a novel target angle estimation method utilizing sparse prior information in the target spatial domain, and it is also a super-resolution angle estimation algorithm under finite element conditions. By analyzing scene sparsity, this method constructs a mathematical model of a beamforming algorithm based on compressed sensing, constructs a measurement matrix and an optimization function with respect to the matrix norm, and uses an optimization algorithm based on conjugate gradients to recover the angle in the entire spatial domain, obtaining super-resolution angle estimates under finite element conditions. Since scene background noise is considered when constructing the constraints of the optimization problem, the optimization algorithm can effectively suppress noise, further improving the estimation quality. The sparse coefficients are derived through Bayesian compressed sensing, enabling the method to adaptively recover the target azimuth, making the algorithm robust. A modified Newton's method is designed to solve the optimization problem, which is independent of the solution software and facilitates hardware deployment.

[0089] like Figure 1 As shown, the method includes:

[0090] The received signal of each element in the sparse array is vectorized to obtain the output signal in vector form. The sparse array outputs the output signal in vector form to obtain a two-dimensional output signal model. This model is then reduced in dimension to obtain a one-dimensional output signal model.

[0091] Specifically, sparse arrays can be classified into linear arrays, area arrays, and volume arrays, depending on the placement of the array elements.

[0092] Assume the sparse array is a random array with M elements, represented in rectangular coordinates; assume there are N long-range incoming waves in space, each element is a sensor with receiving and transmitting functions, receiving the long-range incoming waves from each direction as received signals; all sensors are isotropic.

[0093] The m-th array element receives the corresponding received signal y. m (t), and output it as: M = 1, 2, 3, ..., m, ..., M;

[0094]

[0095] Where, τ m,n τ is the time delay of a long-range wave arriving at the m-th array element from the n-th direction relative to its arrival at the reference point; m,n =R m,n / c; where c is the propagation speed of the distant incoming wave; R m,n s(t-τ) represents the distance from the target in the nth direction to the mth array element. m,n ) represents the incoming wave from the target located in the nth direction received by the m-th array element; t represents the reception time of the incoming wave from the target.

[0096] ε m (t) represents the noise of the m-th array element, where it is assumed that the noise and the incoming wave are statistically independent;

[0097] For the narrowband case, the time delay is equivalent to the phase shift, denoted as . Among them, f c The carrier frequency for narrowband signals; Then y m (t) can be rewritten as:

[0098]

[0099] The vector form of the output signal of the M array elements is as follows:

[0100]

[0101] Where y(t) is the vector array output of M elements; where y(t) = [y1(t), y2(t), ..., y M (t)] T ; where y M (t) represents the vector output of the Mth array element;

[0102] s(t) is the spatial spectrum of the incoming wave; where s(t) = [s0(t), s1(t), ..., s n (t),…,s (N-1) (t)] T ;s n (t) represents the target wave spatial spectrum in the nth direction;

[0103] ε(t) represents noise; where ε(t) = [ε1(t), ε2(t), ..., ε M (t)] T ;ε M(t) represents the noise received by the Mth array element;

[0104] a(θ n ) is the steering vector for the nth observation angle, representing the phase difference between the target direction and the positions of each array element; where

[0105] A is the orientation matrix; where A = [a(θ0), a(θ1), ..., a(θ)] N-1 )];

[0106] Dividing the observation angle range into H observation angle units, the corresponding steering matrix A becomes an M×H matrix:

[0107] A = [a(θ0), a(θ1), ..., a(θ)] h ),…,a(θ H-1 )];

[0108] Where, a(θ) h ) is the steering vector for the h-th observation angle;

[0109] in,

[0110] When the received data has K snapshots, the output signal of the M array elements is vectorized to obtain the output signal matrix in vector form, denoted as the two-dimensional output signal model y:

[0111] y=As+ε (4)

[0112] Where y = [y(1) y(2) … y(K)] represents a matrix of size M×K; s is the two-dimensional spatial spectrum matrix to be recovered, with the element in the nth row and kth column being s. n (k); ε is the noise vector matrix;

[0113] The two-dimensional output signal model is reduced in dimension to obtain a one-dimensional output signal model Y;

[0114]

[0115] in, It is a measurement matrix of MK×HK dimensions; where,

[0116] Where Y = vec(y); vec(y) is the operation of stacking the column vectors of the two-dimensional output signal model y into a single vector;

[0117] S = vec(s) is the operation of stacking the column vectors of the two-dimensional spatial spectrum matrix s to be recovered into a single vector;

[0118] E = vec(ε) is the operation of stacking the column vectors of the noise vector matrix ε into a single vector;

[0119] Here, `vec(·)` represents the operation of stacking the column vectors of the matrix sequentially to form a single vector. Assuming that the target angle remains unchanged during multiple snapshots, i.e., there is no spatiotemporal coupling, the temporal summation of the spatiotemporal spectrum can be used as a spatial spectrum estimate.

[0120] The non-zero positions and number represent the estimated azimuth of the target and the number of targets. In the target scene, there are targets in only a few azimuths, i.e., N << H. The spatial spectrum has strong sparsity. This property can be used to transform the azimuth spectrum estimation process into solving an optimization function.

[0121] In practical applications, the number of targets is less than the number of array elements. Given a measurement matrix S that is transitioned from a high-dimensional to a low-dimensional matrix, recovering the two-dimensional spatial spectrum from finite data is an ill-conditioned process. CS theory indicates that, given a priori information that S is a sparse matrix, if the measurement matrix... If the RIP property is satisfied, the unknown spectral matrix S can be recovered from the received signal Y. Here, satisfying the RIP property means that there exists a restrictive isometry constant δ∈(0,1) such that... This is true. The RIP property is related to the correlation of the basis vectors that make up the measurement matrix; the smaller the correlation coefficient, the better the orthogonality of the basis. Let be a normalized set of basis vectors, and the correlation coefficient between them is...

[0122]

[0123] When the spatial spectral matrix satisfies the following conditions

[0124]

[0125] When, it satisfies the Restricted Isometry Property (RIP property).

[0126] Under sparse signal conditions, the above ill-conditioned problem is transformed into The optimization problem of the norm is used to obtain target angle information.

[0127] From the obtained one-dimensional output signal model, the measurement matrix and the two-dimensional spatial spectrum matrix to be recovered are extracted; using the Bayesian learning method, when the two-dimensional spatial spectrum matrix to be recovered satisfies the RIP characteristic, an optimization function is constructed based on the obtained one-dimensional output signal model and the measurement matrix.

[0128] Specifically, the measurement matrix is ​​extracted from the obtained one-dimensional output signal model Y. and the two-dimensional spatial spectral matrix S that needs to be recovered;

[0129] Determine whether the two-dimensional spatial spectral matrix S to be recovered satisfies the RIP property; where the condition for satisfaction is:

[0130]

[0131] in,

[0132]

[0133] in, For matrix The relevant vector; θ p This is the p-th observation angle; θ q Let q be the q-th observation angle;

[0134] If the above conditions are not met, the two-dimensional spatial spectral matrix S to be recovered does not satisfy the RIP property, and the process ends.

[0135] If the above conditions are met, the two-dimensional spatial spectral matrix S to be recovered satisfies the RIP property, and the optimization function can be further constructed as follows:

[0136] S = arg min{J(S)} (8)

[0137] in,

[0138]

[0139] Among them, ||·|| F denot represents the norm of the F matrix; min(·) is the minimization operation; ρ is the sparse coefficient.

[0140] The constructed optimization function is solved to obtain a two-dimensional space-time spectrum. The obtained two-dimensional space-time spectrum is accumulated in time to obtain the spatial spectrum of the target. Then, constant false alarm detection is performed on it to obtain the orientation estimate of the target.

[0141] Specifically, the conjugate gradient method is used to calculate the conjugate gradient of the optimization function with respect to the spatial spectral matrix S.

[0142]

[0143] Where H(S) is the Hessian matrix; For the measurement matrix; (·) H The conjugate of the matrix is ​​represented by H(S); H(S) is the coefficient matrix of S, which can be expressed as...

[0144] H(S)=2Y HY+ρΛ(S) (15)

[0145] Where ρ is the sparsity coefficient;

[0146]

[0147] Where S(hk) is the element value in the h-th row and k-th column of matrix S; diag[] is a diagonal matrix; τ is a minimum positive value, which is 0.01;

[0148] Using Newton's iterative algorithm, we know that the (l+1)th iteration of S is the Newton iterative formula:

[0149]

[0150] Where β is the iteration step size, [·] -1 Represents the inverse of a matrix;

[0151] Conjugate gradient Substituting the expression into the iterative formula (16) above, we obtain:

[0152]

[0153] Assuming the iteration step size β = 1, the iterative equation (16) can be transformed into

[0154]

[0155] To optimize equation (18), the Hessian matrix H(S) needs to be updated in each iteration. l ) = 2Y H Y+ρΛ(S l );

[0156] The algorithm terminates when the following condition is met, yielding the two-dimensional spacetime spectrum s. h (k) represents the spatiotemporal spectrum of the kth snapshot in the h-th orientation;

[0157]

[0158] The obtained two-dimensional space-time spectrum is accumulated over time to obtain the target angle space spectrum.

[0159]

[0160] right Perform routine constant false alarm rate (CFAR) testing to obtain the target's azimuth estimate. The non-zero positions and number of non-zero values ​​after CFAR testing represent the target's azimuth estimate and the number of targets, respectively.

[0161] The present invention also provides a sparse array angle estimation device based on Bayesian learning, the device comprising:

[0162] The model acquisition module is used to vectorize the received signal of each array element in the sparse array to obtain the output signal in vector form. The sparse array outputs the output signal in vector form to obtain a two-dimensional output signal model. It then reduces the dimensionality of the output signal to obtain a one-dimensional output signal model.

[0163] An optimization function construction module is used to extract the measurement matrix and the two-dimensional spatial spectrum matrix to be recovered from the obtained one-dimensional output signal model. Using a Bayesian learning method, when the two-dimensional spatial spectrum matrix to be recovered satisfies the RIP characteristic, an optimization function is constructed based on the obtained one-dimensional output signal model and the measurement matrix.

[0164] The orientation estimation module is used to solve the constructed optimization function to obtain a two-dimensional space-time spectrum. The obtained two-dimensional space-time spectrum is accumulated in time to obtain the spatial spectrum of the target. Then, constant false alarm detection is performed on it to obtain the orientation estimate of the target.

[0165] The present invention also provides a computer device for target orientation estimation, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor implements the method when executing the computer program.

[0166] The present invention also provides a computer-readable storage medium comprising a stored computer program; wherein, when the computer program is executed, it controls the device in which the computer-readable storage medium is located to perform the method described thereon.

[0167] The present invention also provides an information data processing terminal, which is used to implement the method described herein.

[0168] The conventional algorithm for beamforming optimization is generally a convex optimization method. Existing convex optimization algorithms use interior-point solvers such as CVX and SEDUMI, which have the problem of excessive computation. The following uses a quasi-Newton algorithm to solve the optimization problem (8). To ensure the noise robustness of the algorithm, the sparse coefficients in the optimization problem are first derived. It is assumed that the noise matrix E follows a complex Gaussian distribution with a mean of zero and a variance of σ. 2 The probability density function of E is

[0169]

[0170] Therefore, when S is known, the probability density function of Y can be expressed as:

[0171]

[0172] Based on the Bayesian compressed sensing principle, given the strong sparsity of the spatial spectrum, the sparse signal follows a Laplace distribution, and the probability density function of S can be expressed as:

[0173]

[0174] in, These are the Laplace function scaling coefficients. Given the sparse array receiver matrix Y, the super-resolution spatial spectrum can be estimated using the maximum a posteriori probability criterion. The maximum a posteriori probability estimate of S is...

[0175]

[0176] Substituting (10) and (11) into (12) and solving, we get

[0177]

[0178] Therefore, the sparsity coefficient can be obtained through Determine, where σ 2 and The target distribution can be determined by analyzing its spatial characteristics using statistical methods and the maximum likelihood method, respectively.

[0179] To solve for the spatial spectral matrix S, the conjugate gradient of the cost function in equation (8) with respect to S is calculated.

[0180]

[0181] Where the Hessian matrix is ​​the coefficient matrix of S, it can be represented as:

[0182] H(S)=2Y H Y+ρΛ(S) (15)

[0183] in, Traditional Newton's method and quasi-Newton methods are unsuitable for handling optimization problems involving non-quadratic forms, especially when the cost function contains the modulus of S, which significantly increases the complexity of the solution. This invention uses a modified Newton iteration algorithm to solve this optimization problem. According to Newton's method, the (l+1)th iteration of S is...

[0184]

[0185] In the formula, β is the iteration step size, [·] -1 This represents the inverse of the matrix. Substituting the conjugate gradient equation (14) into the above iterative derivation, we get...

[0186]

[0187] If the iteration step size is set to β = 1, the iteration formula can be transformed into

[0188]

[0189] In the optimization solution, the Hessian matrix H(S) needs to be updated in each iteration. l ) = 2Y H Y+ρΛ(S l Therefore, the computational complexity of the algorithm mainly lies in the Hessian matrix H(S). w The inverse of H(S) can be found from the above derivation. w Let be a matrix of size HK × HK. Using the common Cholesky decomposition, each iteration requires (HK). 3 / 3+2(HK) 2 The computational complexity of multiplication operations is too high. This invention employs the conjugate gradient method to solve the problem, thus resolving the issue of high computational complexity caused by inverting the Hessian matrix. The algorithm terminates when the following condition is met during iteration.

[0190]

[0191] The target angular spatial spectrum can be obtained by summing the obtained two-dimensional spatiotemporal spectra over time.

[0192]

[0193] right Performing a routine constant false alarm rate (CFAR) test can obtain the target's azimuth estimate. The non-zero position and number of non-zero values ​​obtained after CFAR test represent the target's azimuth estimate and the number of targets.

[0194] Performance Analysis

[0195] like Figure 2 As shown, the speed of sound in the simulation experiment is 1500 m / s, the signal carrier frequency is 1 kHz, and the half-wavelength is 0.75 m. It is assumed that the sparse array is a randomly placed linear array with a length of 12 m and the number of array elements M = 10. Gaussian white noise with a mean of 0 is added to the received data of each array element, and the signal-to-noise ratio (SNR) is 0–10 dB.

[0196] First, a single-target simulation was performed. The true azimuth of the underwater acoustic target was 0°, the number of snapshots K = 20, and the signal-to-noise ratio (SNR) SNR = 10dB. From... Figure 2 It can be seen that for sparsely deployed arrays, the azimuth estimation algorithm based on compressed sensing can accurately estimate the target azimuth with a sidelobe of -70dB, which is much lower than that of DAS, MVDR and MUSIC algorithms. Figure 3The mean square error (MSE) of azimuth estimation as a function of signal-to-noise ratio (SNR) is presented. The experiment involved 50 runs with SNRs ranging from 0 dB to 10 dB in 2 dB increments. Due to the sparse array, the DAS algorithm fails at low SNRs and cannot accurately estimate the target azimuth. The MUSIC algorithm cannot recover the target angle due to missing received data. The MVDR and CS algorithms maintain consistent MSE estimates with low MSE values.

[0197] Next, to verify the sparse recovery performance of the algorithms, experiments were conducted on each algorithm with different numbers of array elements. Figure 4 The relationship between angle estimation error and the number of array elements is presented. Experiments were conducted with array element numbers ranging from 6 to 16, with random element placement, an SNR of 10 dB, and 20 snapshots. The results show that when the number of array elements is greater than 10, the DAS, MVDR, and CS algorithms have small mean square errors. MUSIC is not robust under sparse array element conditions, while the CS algorithm proposed in this invention can still recover the target angle with high accuracy even with only 6 array elements. This will significantly reduce the hardware cost for practical applications.

[0198] Finally, the super-resolution performance of the algorithm was verified through multi-target angle estimation. Figure 5(a) and 5(b) The results show the angle estimation results for azimuth angles of [-5°, 5°] and [-3°, 3°], respectively. The results show that the CS algorithm produces the sharpest main lobe and the highest angular resolution. When the two targets move closer, traditional DAS, MVDR, and MUSIC algorithms can no longer distinguish between them, while the method proposed in this invention still achieves good super-resolution results.

[0199] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A sparse array angle estimation method based on Bayesian learning, the method comprising: The received signal of each element in the sparse array is vectorized to obtain the output signal in vector form. The sparse array outputs the output signal in vector form to obtain a two-dimensional output signal model. This model is then reduced in dimension to obtain a one-dimensional output signal model. From the obtained one-dimensional output signal model, extract the measurement matrix and the two-dimensional spatial spectrum matrix to be recovered; Using the Bayesian learning method, when the two-dimensional spatial spectrum matrix to be recovered satisfies the RIP characteristic, an optimization function is constructed based on the obtained one-dimensional output signal model and measurement matrix; Its specific process includes: From the obtained one-dimensional output signal model Extract the measurement matrix and the two-dimensional spatial spectral matrix to be recovered ; Determine the two-dimensional spatial spectral matrix to be recovered. Does it meet the RIP characteristics? The conditions for meeting the requirements are: (6) in, (7) in, For matrix The relevant vector; ; This is the p-th observation angle; ; Let q be the q-th observation angle; For the first n Long-range waves from one direction arrive at the first m The time delay of each array element compared to the time it takes to reach the reference point; The carrier frequency for narrowband signals; = ; If the above conditions are not met, then the two-dimensional spatial spectral matrix needs to be recovered. RIP characteristics not met, end; If the above conditions are met, then the two-dimensional spatial spectral matrix to be recovered is... To satisfy RIP characteristics, further construct the optimization function: (8) in, in, express Matrix norm; It is a minimization operation; The sparsity coefficient; The constructed optimization function is solved to obtain a two-dimensional space-time spectrum. The obtained two-dimensional space-time spectrum is accumulated in time to obtain the spatial spectrum of the target. Then, constant false alarm detection is performed on it to obtain the orientation estimate of the target.

2. The sparse array angle estimation method based on Bayesian learning according to claim 1, characterized in that, The process involves vectorizing the received signal received by each element in the sparse array to obtain a vector output signal. The sparse array outputs this vector output signal to obtain a two-dimensional output signal model. This model is then reduced in dimensionality to obtain a one-dimensional output signal model. Its specific implementation process includes: Assume that the sparse array has M A random array of elements is represented using rectangular coordinates; it is assumed that there exists in space. Each array element receives remote incoming waves from each direction as a received signal. No. m Each array element receives the corresponding received signal. and output it: M =1, 2, 3, …, m , …, M ; (1) in, For the first n Long-range waves from one direction arrive at the first m The time delay of each array element compared to the time it takes to reach the reference point; ;in, c The propagation speed of incoming waves from a distance; For the position located at the n The goal in the first direction is to reach the... m The distance between each array element; For the first m The element receives the data located at the first array element. n The target wave comes from one direction; The reception time of the incoming wave to the target; For the first m Noise of each array element; For the narrowband case, the time delay is equivalent to the phase shift, denoted as . ;in, The carrier frequency for narrowband signals; = ;but Rewritten as: (2) but M Vector form of the output signal of each array element: (3) in, for M The vector array output of each array element; where... ;in, For the first M Vector output of each array element; It is the incoming wave spatial spectrum; among which, ; For the first n The target comes from the spatial spectrum of the wave; For noise; among which, ; For the first M Noise received by each array element; For the first n The guiding vector of each observation angle; in ; For the guiding matrix; where, ; Divide the observation angle range into Each observation angle unit, and the corresponding steering matrix Become The matrix: ； in, For the first h The guiding vector of each observation angle; in, ; When receiving data have When taking a quick snapshot, for M The output signals of each array element are vectorized to obtain a vector-form output signal matrix, denoted as the two-dimensional output signal model. : (4) in, , indicating size is Matrix; For the two-dimensional spatial spectral matrix that needs to be recovered, the first... Line number Column elements are ; This is the noise vector matrix; The two-dimensional output signal model is reduced in dimension to obtain a one-dimensional output signal model. ; (5) in, yes A dimensional measurement matrix; where, ; in, ; ; .

3. The sparse array angle estimation method based on Bayesian learning according to claim 1, characterized in that, The constructed optimization function is solved to obtain a two-dimensional space-time spectrum. The obtained two-dimensional space-time spectrum is accumulated in time to obtain the spatial spectrum of the target. Then, constant false alarm detection is performed on it to obtain the orientation estimate of the target. Its specific process includes: The conjugate gradient method is used to calculate the optimization function with respect to the spatial spectral matrix. conjugate gradient : (14) in, It is a Hessian matrix; For measurement matrix; Represents the conjugate of a matrix yes The coefficient matrix can be represented as (15) in, The sparsity coefficient; in, For matrix The h Line number k The element values ​​of the column; It is a diagonal matrix; For the smallest positive value, take 0.01; Using Newton's iterative algorithm, we can see that... The The next iteration is the Newton iteration: (16) in, The iteration step size, Represents the inverse of a matrix; Conjugate gradient Substituting the expression into the iterative formula (16) above, we derive: (17) Assuming iteration step size The iterative equation (16) can be transformed into (18) To optimize equation (18), the Hessian matrix needs to be updated in each iteration. ; The algorithm terminates when the following condition is met, yielding the two-dimensional spacetime spectrum. , representing the h The first direction k The temporal spectrum of the next fast shot; (19) The obtained two-dimensional space-time spectrum is accumulated over time to obtain the target angle space spectrum. : (20) right Perform routine constant false alarm rate (CFAR) detection to obtain the target's location estimate.

4. An apparatus based on the Bayesian learning-based sparse array angle estimation method as described in claim 1, characterized in that, The device includes: The model acquisition module is used to vectorize the received signal of each array element in the sparse array to obtain the output signal in vector form. The sparse array outputs the output signal in vector form to obtain a two-dimensional output signal model. It then reduces the dimensionality of the output signal to obtain a one-dimensional output signal model. An optimization function construction module is used to extract the measurement matrix and the two-dimensional spatial spectrum matrix to be recovered from the obtained one-dimensional output signal model. Using a Bayesian learning method, when the two-dimensional spatial spectrum matrix to be recovered satisfies the RIP characteristic, an optimization function is constructed based on the obtained one-dimensional output signal model and the measurement matrix. The orientation estimation module is used to solve the constructed optimization function to obtain a two-dimensional space-time spectrum. The obtained two-dimensional space-time spectrum is accumulated in time to obtain the spatial spectrum of the target. Then, constant false alarm detection is performed on it to obtain the orientation estimate of the target.

5. A computer device for target orientation estimation, characterized in that, The method includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor, when executing the computer program, implements the method as described in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program; wherein, when the computer program is executed, it controls the device on which the computer-readable storage medium is located to perform the method as described in any one of claims 1 to 4.

7. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the method as described in any one of claims 1 to 4.

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