Off-grid DOA estimation method based on variational SBL in non-uniform noise environment

Abstract

The present invention provides a method for estimating off-grid DOA based on variational SBL in a non-uniform noise environment. The method first vectorizes the covariance of the data received by the uniform linear array, and models the non-uniform noise covariance into the variational signal vector to construct a new variational data model; secondly, a variational grid sparse data model is constructed based on the variational data model; then, sparse Bayesian learning (SBL) is used to iteratively estimate the hyperparameter vector and off-grid error vector related to the variational sparse signal vector, and iteratively update the spatial discrete grid points; finally, after the SBL iterative convergence or the number of iterations reaches 1000, the hyperparameter vector related to the signal vector is obtained, and the direction of arrival (DOA) estimation is realized by using a one-dimensional spatial spectrum search. Compared with other existing DOA methods, the present invention does not need to estimate the non-uniform noise covariance separately, and can effectively reduce the influence of off-grid error and non-uniform noise on DOA estimation, thereby achieving robust and accurate DOA estimation.

Description

Technical Field

[0001] The present invention relates to the fields of array signal processing and signal parameter estimation, and in particular to an off-grid DOA estimation method based on variational SBL in a non-uniform noise environment. Background Art

[0002] As an important branch of signal parameter estimation, signal direction of arrival (DOA) estimation has always been highly valued and has been widely used in fields such as radar imaging and target detection. In the past few decades, subspace-based DOA estimation methods represented by the MUSIC method and the ESPRIT method have been extensively studied. However, the performance of subspace-based methods is limited by the signal-to-noise ratio and the number of snapshots. In recent years, the development of sparse signal recovery (SSR) technology has provided many new perspectives for DOA estimation. The DOA estimation methods based on SSR technology can be roughly divided into two categories. One is L p The other is the sparse Bayesian learning (SBL) algorithm. Compared with the SBL algorithm, L p Since the norm optimization algorithm uses convex optimization technology, its performance is limited to a certain extent, and its computational complexity is also higher. p Norm optimization algorithms have certain advantages, but their DOA estimation performance is still limited by the degree of spatial discretization. A high degree of discretization increases the algorithm's computational complexity, while a low degree of discretization introduces off-grid errors, which in turn reduces estimation accuracy. To address this shortcoming of SBL algorithms, researchers have proposed an algorithm called OGSBI, which uses linear approximation to construct an off-grid signal model to reduce the impact of off-grid errors on DOA estimation. Furthermore, based on OGSBI, an algorithm called ROGSBL has been proposed. This algorithm treats the discrete grid points as dynamic parameters and iteratively updates them by solving a specific polynomial. However, both OGSBI and ROGSBL algorithms perform DOA estimation in a Gaussian white noise (i.e., uniform) environment, which is not applicable in real-world environments. Since array responses and receiving channels are often non-uniform and non-ideal, real-world noise is often non-uniform. Therefore, for DOA estimation in non-uniform noise environments, an algorithm using sparse representation of array covariance vectors (referred to as CVSR algorithm) was proposed, which uses a specific selection matrix to eliminate non-uniform noise covariance. However, although the CVSR algorithm can effectively eliminate non-uniform noise covariance, it sacrifices the array aperture and does not consider the impact of grid error. Summary of the Invention

[0003] The present invention aims to provide a variational SBL-based off-grid DOA estimation method in a non-uniform noise environment, aiming to address the problem of performance degradation of existing methods for direction of arrival (DOA) estimation under non-uniform noise and off-grid error conditions. This method constructs a novel variational lattice sparse model based on the covariance vector by modeling the non-uniform noise covariance vector into the signal vector. Within the sparse Bayesian learning (SBL) framework, the expectation maximization (EM) method is used to iteratively estimate the hyperparameter vector and off-grid error vector associated with the variational signal vector, and the spatial discrete grid points are iteratively updated to reduce the impact of off-grid error on DOA estimation.

[0004] The technical solution adopted in the present invention is as follows:

[0005] A method for estimating off-grid DOA based on variational SBL in a non-uniform noise environment comprises the following steps:

[0006] (1) A uniform linear array (ULA) consisting of M sensors or antennas receives narrowband signals transmitted from K far-field sources and obtains the uniform linear array received data Y;

[0007] (2) Vectorize the covariance of the array received data Y and the non-uniform noise covariance R n Modeling to variational signal vector Among them, build a variational data model;

[0008] (3) Discretize the spatial domain into L grid points and construct a variational grid sparse data model based on the variational data model using the first-order Taylor expansion;

[0009] (4) In the sparse Bayesian learning (SBL) framework, the variational sparse signal vector Initialize the related hyperparameter vector α;

[0010] (5) Under the SBL framework, calculate the variational sparse signal obtained after Bayesian derivation The mean μ and variance Σ of the posterior distribution;

[0011] (6) Under the SBL framework, the expectation maximization (EM) method is used to iteratively estimate the hyperparameter vector α;

[0012] (7) Under the SBL framework, the EM method is used to iteratively estimate the off-grid error vector β, and β is used to directly iteratively update the spatial discrete grid points;

[0013] (8) Determine whether the iterative convergence condition is met or whether the number of iterations reaches 1000;

[0014] (9) If the iterative convergence condition is met or the number of iterations reaches 1000, the hyperparameter vector α is output; if not, μ, Σ, α, and β are repeatedly iterated and estimated until the iterative convergence condition is met or the number of iterations reaches 1000, and then the hyperparameter vector α is output;

[0015] (10) On the updated spatial discrete grid, a one-dimensional spatial spectrum search is performed on the first L elements of the hyperparameter vector α, and the direction of arrival (DOA) estimation is achieved based on the index of the spectrum peak.

[0016] Furthermore, the array data received by the uniform linear array composed of M sensors or antennas in step (1) is:

[0017] Y=AS+N

[0018] Among them, A is the steering matrix, S is the signal matrix, and N is the noise matrix.

[0019] Furthermore, the variational data model constructed in step (2) is:

[0020]

[0021] Where C is a block diagonal matrix, r s is the signal covariance vector, r n is the noise covariance vector, ω is the error between the actual received data covariance and the ideal received data covariance after vectorization, In this invention, it is called the variational steering matrix, is the corresponding variational signal vector, (·) * represents matrix conjugation, and ⊙ represents Khatri-Rao product.

[0022] Furthermore, in step (3), the spatial domain is discretized to obtain a discrete grid point set containing L angles. Based on a set of discrete grid points, the variational grid sparse data model constructed using first-order Taylor expansion is:

[0023]

[0024] in, is the variational sparse steering matrix after linear approximation using the first-order Taylor expansion, is the variational sparse signal vector, (·) T represents the matrix transpose, for The first-order linear approximation matrix of for about is the first-order partial derivative of , β is the off-grid error vector, and diag{·} denotes the diagonal matrix obtained by diagonalizing the vector.

[0025] Furthermore, the initialization of the hyperparameter vector α in step (4) is specifically to initialize it to an L+M-dimensional column vector with all elements being 1.

[0026] Furthermore, the specific calculation method for the mean μ and variance Σ in step (5) is:

[0027]

[0028]

[0029] in, represents the covariance matrix of the array received data, T represents the number of sampling snapshots of the array received data. Λ = diag{α} is a diagonal matrix composed of the elements of the hyperparameter vector α as diagonal elements, represents the Kronecker product, (·) H represents the conjugate transpose of the matrix, (·) -1 Represents matrix inversion.

[0030] Furthermore, the specific calculation method for iteratively estimating the hyperparameter vector α in step (6) is:

[0031]

[0032] in, represents the hyperparameter vector α after iterative estimation, (·) i represents the i-th element of the vector, (·) i,i represents the (i, i)th element of the matrix, and τ is a positive constant tending to zero, which is usually set to 0.01.

[0033] Furthermore, the process of iteratively estimating the off-grid error vector β in step (7) is re-derived based on the constructed variational off-grid sparse data model, and the specific calculation method is:

[0034]

[0035] in, represents the off-grid error vector after iterative estimation, is a column vector consisting of the first L elements of μ, μ is a column vector consisting of the last M elements of μ, C Ω =Ω -1 / 2 C, Contains the first L rows and L columns of Σ, and γ contains the first L rows and last M columns of Σ. Represents the realistic part, Represents the Hadamard product. After estimating β, the specific process of iteratively updating the discrete grid points is as follows:

[0036]

[0037] Furthermore, the iterative convergence condition in step (9) is:

[0038]

[0039] Among them, α 1:L represents the vector consisting of the first L elements of the hyperparameter vector α estimated in the previous iteration, and ||·||2 represents the 2-norm.

[0040] The beneficial effects achieved by the present invention are as follows: the off-grid DOA estimation method based on variational SBL in a non-uniform noise environment provided by the present invention constructs a new variational data model by modeling the non-uniform noise covariance into the variational signal vector, and further constructs a variational grid sparse data model. Under the SBL framework, the EM method is used to iteratively estimate the hyperparameter vector related to the variational sparse signal vector; at the same time, based on the EM method, the off-grid error estimation process is re-derived, the off-grid error vector is iteratively estimated, and the discrete grid is directly updated using the off-grid error vector. Compared with some existing methods, the present invention does not need to estimate the non-uniform noise covariance separately, and can effectively reduce the impact of the off-grid error and non-uniform noise on DOA estimation at the same time, thereby achieving robust and accurate DOA estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments.

[0042] Figure 1 Flowchart for the implementation of the off-grid DOA estimation method based on variational SBL in a non-uniform noise environment provided by the present invention;

[0043] Figure 2 This is a comparison diagram of the root mean square error of DOA estimation between the present invention and other methods under different signal-to-noise ratios;

[0044] Figure 3 This is a comparison chart of the DOA estimation success rate of the present invention and other methods under different signal-to-noise ratio conditions;

[0045] Figure 4This is a comparison diagram of the root mean square error of DOA estimation between the present invention and other methods under different snapshot numbers;

[0046] Figure 5 A comparison diagram of the root mean square error of DOA estimation between the present invention and other methods under different worst-case noise power ratios;

[0047] Figure 6 This is a comparison chart of the root mean square error of DOA estimation between the present invention and other methods under different grid spacing conditions. DETAILED DESCRIPTION

[0048] In order to better understand the technical content of the present invention, specific embodiments are provided below, and the specific implementation methods of the present invention are described in more detail with reference to the accompanying drawings.

[0049] Example 1

[0050] Combine Figure 1 The present invention provides a method for estimating off-grid DOA based on variational SBL in a non-uniform noise environment, the method comprising the following steps:

[0051] (1) A uniform linear array (ULA) consisting of M sensors or antennas receives narrowband signals transmitted from K far-field sources and obtains the uniform linear array received data Y;

[0052] The array data received by the uniform linear array composed of M sensors or antennas in step (1) is:

[0053] Y=AS+N

[0054] Among them, A is the steering matrix, S is the signal matrix, and N is the noise matrix.

[0055] Specifically, consider a uniform linear array consisting of M sensors or antennas receiving signals from DOAs θ1, θ2, …, θ K The source signal emitted by K far-field targets is given by the sensor or antenna, and the spacing between adjacent sensors or antennas is 1 / 2 of the signal wavelength. The data received by the uniform linear array at the tth snapshot time is:

[0056] y(t)=As(t)+n(t)

[0057] Where s(t)=[s1(t),s2(t),…,s K (t)] T is the signal data vector, n(t)=[n1(t),n2(t),…,n M (t)] T is the noise data vector. A=[a(θ1),a(θ2),…,a(θ K )] represents the steering matrix containing K DOA information, is the orientation vector, (·) T Represents matrix transpose. After receiving T snapshots, the array receives data as follows:

[0058] Y=AS+N

[0059] Where Y = [y(1), y(2), …, y(T)] is the array received data matrix, S = [s(1), s(2), …, s(T)] is the signal matrix, and N = [n(1), n(2), …, n(T)] is the noise matrix.

[0060] Step 02: Vectorize the covariance of the array received data Y and the non-uniform noise covariance R n Modeling to variational signal vector Among them, build a variational data model.

[0061] The variational data model constructed in step (2) is:

[0062]

[0063] Where C is a block diagonal matrix, r s is the signal covariance vector, r n is the noise covariance vector, ω is the error between the actual received data covariance and the ideal received data covariance after vectorization, In this invention, it is called the variational steering matrix, is the corresponding variational signal vector, (·) * represents matrix conjugation, and ⊙ represents Khatri-Rao product.

[0064] Specifically, calculate the actual array data covariance Its mathematical formula can be expressed as:

[0065]

[0066] in, is the source signal covariance, is the noise covariance, and Denote the variance of the kth source signal and the noise variance received by the mth sensor, respectively. W denotes the error matrix between the actual array data covariance and the ideal array data covariance. (·) * represents the matrix conjugate, (·) H represents the matrix conjugate transpose, and diag{·} represents the diagonal matrix obtained by diagonalizing the vector. Column vectorization gives:

[0067]

[0068] in, is the signal covariance column vector, ω is the error vector between the actual data covariance vector and the ideal data covariance vector, which obeys the complex Gaussian distribution in where ε m Represents a column vector whose mth element is 1 and other elements are all 0. n Modeling to variational signal vector Among them, the variational data model can be obtained:

[0069]

[0070] in, C=blkdiag{ε1,ε2,…,ε M} represents a system consisting of ε1,ε2,…,ε M As a block diagonal matrix consisting of vectors on the block diagonal, is the noise covariance column vector. In this invention, it is called the variational steering matrix, is the corresponding variational signal vector. ⊙ denotes the Khatri-Rao product.

[0071] (3) Discretize the spatial domain into L grid points and construct a variational grid sparse data model based on the variational data model using the first-order Taylor expansion;

[0072] In step (3), the spatial domain is discretized to obtain a discrete grid point set containing L angles. Based on the discrete grid point set, the variational grid sparse data model constructed using the first-order Taylor expansion is:

[0073]

[0074] in, To obtain the sparse steering matrix after linear approximation using the first-order Taylor expansion, is the variational sparse signal vector, (·) T represents the matrix transpose, for The first-order linear approximation matrix of for about is the first-order partial derivative of , β is the off-grid error vector, and diag{·} denotes the diagonal matrix obtained by diagonalizing the vector.

[0075] Specifically, the range from -90° to 90° in the spatial domain is uniformly discretized into L grid points to obtain an angle set containing the true DOA of the source signal. When the true DOA of the source signal is located on the grid point, the variational sparse data model is:

[0076]

[0077] in, is the variational sparse steering matrix, (·) T Represents matrix transpose. is the variational sparse signal vector, is an L-dimensional K-order sparse vector whose non-zero elements are related to the signal covariance vector r s In order to reduce the grid error caused by the mismatch between the discrete grid points and the true DOA, the first-order Taylor expansion is introduced to Make a linear approximation:

[0078]

[0079] Among them, l k ∈{1,2,…L}, Indicates the closest to θ k grid points, and (·)′ means to find the first-order partial derivative. Accordingly, using To approximate expression and β=[β1,β2,…,β L ] T Represents the grid error vector. When k=1,2,…K, the lth k The elements are All other elements are 0. Therefore, the variational lattice sparse data model is:

[0080]

[0081] in,

[0082] (4) In the sparse Bayesian learning (SBL) framework, the variational sparse signal vector Initialize the related hyperparameter vector α;

[0083] The initialization of the hyperparameter vector α in step (4) is specifically to initialize it to an L+M-dimensional column vector with all elements being 1.

[0084] (5) Under the SBL framework, calculate the variational sparse signal obtained after Bayesian derivation The mean μ and variance Σ of the posterior distribution;

[0085] The specific calculation method for the mean μ and variance Σ in step (5) is:

[0086]

[0087]

[0088] in, represents the covariance matrix of the array received data, T represents the number of sampling snapshots of the array received data. Λ = diag{α} is a diagonal matrix composed of the elements of the hyperparameter vector α as diagonal elements, represents the Kronecker product, (·) H represents the conjugate transpose of the matrix, (·) -1 Represents matrix inversion.

[0089] Specifically, due to Available The probability density of Assumptions The probability density is Gaussian prior distribution of , where Λ = diag{α} is a diagonal matrix consisting of the elements of the hyperparameter vector α as diagonal elements, α = [α1, α2, …, α L+M ] T With variational sparse signal vector Related, its sparsity Furthermore, we assume that the elements of the hyperparameter vector α obey independent Gamma distributions, that is, τ is a normal constant that tends to zero and is usually set to 0.01. Based on the above prior distribution, we can deduce The posterior distribution of is:

[0090]

[0091] Among them, the specific calculation methods of mean μ and variance Σ are:

[0092]

[0093]

[0094] (6) Under the SBL framework, the expectation maximization (EM) method is used to iteratively estimate the hyperparameter vector α;

[0095] The specific calculation method for iteratively estimating the hyperparameter vector α in step (6) is:

[0096]

[0097] in, represents the hyperparameter vector α after iterative estimation, (·)i represents the i-th element of the vector, (·) i,i represents the (i, i)th element of the matrix, and τ is a positive constant tending to zero, which is usually set to 0.01.

[0098] Specifically, first construct the objective function in step E:

[0099]

[0100] in, Express about The mathematical expectation of α. In the Mth step, the objective function is maximized. Let the partial derivative of the objective function with respect to α be equal to 0 and solve it, and the iterative estimate of α is obtained as:

[0101]

[0102] in, represents the hyperparameter vector α after iterative estimation, (·) i represents the i-th element of the vector, (·) i,i Represents the (i,i)th element of the matrix.

[0103] (7) Under the SBL framework, the EM method is used to iteratively estimate the off-grid error vector β, and β is used to directly iteratively update the spatial discrete grid points;

[0104] The process of iteratively estimating the off-grid error vector β in step (7) is re-derived based on the constructed variational off-grid sparse data model, and its specific calculation method is:

[0105]

[0106] in, represents the off-grid error vector after iterative estimation, is a column vector consisting of the first L elements of μ, μ is a column vector consisting of the last M elements of μ, C Ω =Ω -1 / 2 C, Contains the first L rows and L columns of Σ, and γ contains the first L rows and last M columns of Σ. Represents the realistic part, Represents the Hadamard product. After estimating β, the specific process of iteratively updating the discrete grid points is as follows:

[0107]

[0108] Specifically, ignoring the terms unrelated to β, the objective function for estimating β constructed in the E step is:

[0109]

[0110] in, c represents an independent constant, and ||·||2 represents the 2-norm. The first term on the right side of the above objective function can be expanded as follows:

[0111]

[0112] in, is a column vector consisting of the first L elements of μ, μ is a column vector consisting of the last M elements of μ, Represents the realistic department, Represents the Hadamard product. Similarly, the second term on the right side of the above objective function can be expanded as follows:

[0113]

[0114] in, is a matrix consisting of the first L rows and L columns of Σ, γ is a matrix consisting of the first L rows and last M columns of Σ, and Tr{·} represents the trace of the matrix. Based on the above derivation, the objective function for estimating β can be reformulated as:

[0115]

[0116] in, Let the partial derivative of the above objective function with respect to β be equal to 0 and solve it, and the iterative estimate of β can be obtained as:

[0117]

[0118] in, Represents the off-grid error vector after iterative estimation. After estimating β, the discrete grid points are directly iteratively updated:

[0119]

[0120] Step 08: Determine whether the iterative convergence condition is met or whether the number of iterations reaches 1000. The iterative convergence condition is:

[0121]

[0122] Among them, α 1:L represents the vector consisting of the first L elements of the hyperparameter vector α estimated in the previous iteration.

[0123] Step 09: If the iterative convergence condition is met or the number of iterations reaches 1000, the hyperparameter vector α is output; if not, μ, Σ, α and β are repeatedly iteratively calculated and estimated until the iterative convergence condition is met or the number of iterations reaches 1000, and then the hyperparameter vector α is output.

[0124] The iterative convergence condition in step (9) is:

[0125]

[0126] Among them, α 1:L represents the vector consisting of the first L elements of the hyperparameter vector α estimated in the previous iteration, and ||·||2 represents the 2-norm.

[0127] Step 10: At the updated discrete grid points, perform a one-dimensional spatial spectrum search on the first L elements of the hyperparameter vector α, and estimate the direction of arrival (DOA) based on the index of the spectrum peak.

[0128] The present invention will be further described below in conjunction with the MALTAB simulation experiment results:

[0129] The present invention uses MATLAB software to conduct simulation experiments. During the simulation experiments, the uniform linear array consists of M = 8 sensors or antennas, and the number of source signals is set to K = 2. Unless otherwise specified, the airspace range from -90° to 90° is evenly divided with a grid spacing of 2°. The non-uniform noise covariance is modeled as R s =diag{[10,6,1.5,7,0.5,0.7,3,5]}. The worst noise power ratio is defined as WNPR = δ 2 max / δ 2 min , where δ 2 max and δ 2 min Respectively represent the maximum and minimum noise variance in the non-uniform noise covariance. In the simulation experiment, multiple DOA estimation methods are introduced to compare with the present invention, including the MUSIC method, the ESPRTI method, the OGSBI method and the CVSR method. In addition, the Cramer-Rao bound (CRB) is introduced to compare and evaluate the performance of these algorithms. At the same time, the root mean square error (RMSE) is introduced to intuitively evaluate the DOA estimation performance, which is specifically defined as Where 500 represents the total number of Monte Carlo simulations during the simulation experiment, K is the number of source signals, and θ k represents the true DOA of the source signal, represents the DOA estimate of the k-th source signal in the i-th Monte Carlo simulation experiment.

[0130] Figure 2 and Figure 3 The comparison of the root mean square error and success rate of DOA estimation between the present invention and other methods under different signal-to-noise ratios (SNR) is shown respectively. The number of snapshots in the simulation experiment is T=200. Figure 2 It can be clearly seen that the present invention has a lower root mean square error than other methods, especially in the case of low signal-to-noise ratio. At the same time, the root mean square error of the DOA estimation of the present invention is closer to the Cramer-Rao bound than other methods. On the other hand, Figure 3 The present invention shows a higher DOA estimation success rate; and compared with other methods, the DOA estimation success rate of the present invention reaches 100% faster as the signal-to-noise ratio increases. It can be noted that although the root mean square error of the CVSR method is lower than that of the present invention when the signal-to-noise ratio is -6dB, the DOA estimation success rate of the CVSR method is much lower than that of the present invention, and is basically 0. Figure 2 and Figure 3 The reason for the results in is that the MUSIC method, ESPRTI method and OGSBI method do not consider non-uniform noise, and the CVSR method does not consider the grid error, while the present invention considers both grid error and non-uniform noise at the same time and can effectively reduce their impact on DOA estimation. Figure 2 and Figure 3 The simulation results in fully demonstrate the superiority of the DOA estimation of the present invention under different signal-to-noise ratios.

[0131] Figure 4 The comparison of the root mean square error of DOA estimation between the present invention and other methods under different snapshot numbers is shown. The signal-to-noise ratio in the simulation experiment is SNR=0dB. Figure 4 As shown in , under all snapshot number conditions, the present invention achieves the lowest RMS error among all compared methods, and the RMS error decreases with increasing snapshot number. Furthermore, the RMS error of the present invention is closest to the Cramer-Rao bound among all compared methods. This is attributed to the present invention's effective handling of off-grid errors and non-uniform noise. Figure 4 The simulation results in effectively demonstrate the superiority of the DOA estimation performance of the present invention under different snapshot numbers.

[0132] Figure 5 The comparison of the root mean square error of DOA estimation between the present invention and other methods under different worst noise power ratios is shown. The signal-to-noise ratio and the number of snapshots in the simulation are SNR=0dB and T=200 respectively. Figure 5It can be found that the RMS errors of the MUSIC, ESPRTI, and OGSBI methods are significantly higher than those of the present invention, and their RMS errors also increase with the increase of the worst-noise power ratio. Even though the RMS error of the CVSR method does not increase with the increase of the worst-noise power ratio, its RMS error is still larger than that of the present invention. This is because the CVSR method, while taking into account non-uniform noise, ignores the grid error. On the other hand, the RMS error of the DOA estimation of the present invention is closest to the Cramer-Rao bound under all worst-noise power ratio conditions and can remain relatively stable as the worst-noise power ratio increases. Figure 5 The simulation results show that the present invention has better DOA estimation performance than other methods under different worst-case noise power ratios.

[0133] Figure 6 A comparison of the root mean square error of DOA estimation between the present invention and other methods at different grid spacings is shown. During simulation, the signal-to-noise ratio and the number of snapshots are SNR=0dB and T=200, respectively. Figure 6 It is clearly shown that under different grid spacing conditions, the present invention has a lower root mean square error than the OGSBI method and the CVSR method. The root mean square error of the OGSBI method remains stable as the grid spacing increases, while the root mean square error of the CVSR method increases significantly with increasing grid spacing, but both are lower than that of the present invention. This is because the OGSBI and CVSR methods only consider either grid error or non-uniform noise, while the present invention considers both non-uniform noise and grid error simultaneously.

[0134] Figure 6 The simulation results in fully demonstrate the superiority of the DOA estimation performance of the present invention under different grid spacing conditions.

Claims

1. The off-grid DOA estimation method based on variational SBL in non-uniform noise environment is characterized by: The method comprises the following steps: (1) A uniform linear array (ULA) consisting of M sensors or antennas receives narrowband signals emitted from K far-field sources and obtains uniform linear array received data Y; (2) Vectorize the covariance of the array received data Y and the noise covariance r n Modeling to variational signal vector Among them, a variational data model is constructed, and the constructed variational data model is: Where C is a block diagonal matrix, r s is the signal covariance vector, r n is the noise covariance vector, ω is the error between the actual received data covariance and the ideal received data covariance after vectorization, is called the variational steering matrix, is the corresponding variational signal vector, (·) * represents matrix conjugation, It means Khatri-Rao product; (3) Discretize the spatial domain into L grid points and construct a variational grid sparse data model based on the variational data model using the first-order Taylor expansion; (4) Under the sparse Bayesian learning (SBL) framework, the variational sparse signal vector Initialize the related hyperparameter vector α; (5) Under the SBL framework, calculate the variational sparse signal obtained after Bayesian derivation The mean μ and variance Σ of the posterior distribution; (6) Under the SBL framework, the expectation maximization (EM) method is used to iteratively estimate the hyperparameter vector α; (7) Under the SBL framework, the EM method is used to iteratively estimate the off-grid error vector β, and β is used to directly iteratively update the spatial discrete grid points; (8) Determine whether the iterative convergence condition is met or whether the number of iterations reaches 1000; (9) If the iterative convergence condition is met or the number of iterations reaches 1000, the hyperparameter vector α is output; if not, μ, Σ, α, and β are repeatedly iterated and estimated until the iterative convergence condition is met or the number of iterations reaches 1000, and then the hyperparameter vector α is output; (10) On the updated spatial discrete grid, a one-dimensional spatial spectrum search is performed on the first L elements of the hyperparameter vector α, and the direction of arrival (DOA) is estimated based on the index of the spectrum peak.

2. The off-grid DOA estimation method based on variational SBL in a non-uniform noise environment according to claim 1 is characterized in that: The array data received by the uniform linear array composed of M sensors or antennas in step (1) is: Y=AS+N Among them, A is the steering matrix, S is the signal matrix, and N is the noise matrix.

3. The off-grid DOA estimation method based on variational SBL in a non-uniform noise environment according to claim 1, characterized in that: In step (3), the spatial domain is discretized to obtain a discrete grid point set θ={θ1,θ2,…,θ L }, based on the discrete grid point set, the variational grid sparse data model constructed using the first-order Taylor expansion is: in, is the variational sparse steering matrix after linear approximation using the first-order Taylor expansion, is the variational sparse signal vector, (·) T represents the matrix transpose, Φ θ (β)=Β θ +D θ diag{β} is β θ The first-order linear approximation matrix, D θ For Β θ The first-order partial derivative with respect to θ, β is the off-grid error vector, and diag{·} denotes the diagonal matrix obtained by diagonalizing the vector.

4. The off-grid DOA estimation method based on variational SBL in a non-uniform noise environment according to claim 1, characterized in that: The initialization of the hyperparameter vector α in step (4) is specifically to initialize it to an L+M-dimensional column vector with all elements being 1.

5. The off-grid DOA estimation method based on variational SBL in a non-uniform noise environment according to claim 3, characterized in that: The specific calculation method for the mean μ and variance Σ in step (5) is: in, represents the covariance matrix of the array received data, T represents the number of sampling snapshots of the array received data, Λ = diag{α} is a diagonal matrix composed of the elements of the hyperparameter vector α as diagonal elements, represents the Kronecker product, (·) H represents the conjugate transpose of the matrix, (·) -1 Represents matrix inversion.

6. The off-grid DOA estimation method based on variational SBL in a non-uniform noise environment according to claim 5, characterized in that: The specific calculation method for iteratively estimating the hyperparameter vector α in step (6) is: in, represents the hyperparameter vector α after iterative estimation, (·) i represents the i-th element of the vector, (·) i,i represents the (i, i)th element of the matrix, and τ is a positive constant tending to zero, which is set to 0.

01.

7. The off-grid DOA estimation method based on variational SBL in a non-uniform noise environment according to claim 6, characterized in that: The process of iteratively estimating the off-grid error vector β in step (7) is re-derived based on the constructed variational off-grid sparse data model, and its specific calculation method is: in, represents the off-grid error vector after iterative estimation, is a column vector consisting of the first L elements of μ, μ is a column vector consisting of the last M elements of μ, B Ω =Ω -1 / 2 Β θ , C Ω =Ω -1 / 2 C, D Ω =Ω -1 / 2 D θ , Contains the first L rows and L columns of Σ, γ contains the first L rows and last M columns of Σ, Represents the realistic department, Denotes the Hadamard product. After estimating β, the specific process of iteratively updating the discrete grid points is as follows:

8. The off-grid DOA estimation method based on variational SBL in a non-uniform noise environment according to claim 1, characterized in that: The iterative convergence condition in step (9) is: Among them, α 1:L represents the vector consisting of the first L elements of the hyperparameter vector α estimated in the previous iteration, and ||·||2 represents the 2-norm.

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