Asymmetrically active coupled radar array off-grid doa estimation method and system

Abstract

The application discloses an asymmetric active coupling radar array off-grid DOA estimation method and system, and belongs to the technical field of radar array signal processing. The method comprises the following steps: constructing a noise and signal covariance manifold joint tensorization variational signal representation, quantifying non-uniform noise statistical uncertainty through differential entropy, and constructing an entropy-weighted sparse off-grid dictionary; an entropy-guided real variational sparse Bayesian learning algorithm is proposed, sample entropy is used as a quantitative measure of dynamic stability of iterative inference, adaptive hyperparameter modulation and accelerated convergence are realized; the algorithm is expanded into an entropy-guided deep expansion variational sparse Bayesian learning network, and entropy regularization is introduced into an end-to-end loss function to enhance the discriminability of sparse features. The application solves the problems of large off-grid mismatch error, poor non-uniform noise robustness, high computational complexity and lack of strict convergence guarantee in the prior art.

Description

Technical Field

[0001] This invention relates to the field of radar array signal processing technology, specifically to a method and system for estimating the direction of arrival (DOA) of an asymmetric active coupled radar array away from the grid. Background Technology

[0002] Direction of Arrival (DOA) estimation is one of the core technologies in radar array signal processing, with wide applications in far-field target localization, autonomous driving perception, millimeter-wave massive MIMO, and electronic warfare surveillance. Sparse Bayesian Learning (SBL), due to its ability to fully utilize the spatial sparsity of far-field incident signals to achieve high-resolution DOA parameter estimation, has become the mainstream research paradigm.

[0003] However, traditional direction-of-arrival (DOA) estimation methods based on sparse Bayesian learning (SBL) suffer from a fundamental limitation: the off-grid (OG) mismatch effect. When the true ODA of the incident source does not perfectly coincide with the pre-discrete spatial grid points, the estimation performance degrades sharply in high-resolution scenarios. To mitigate this problem, researchers have proposed various off-grid SBL frameworks, such as off-grid sparse Bayesian inference, off-grid block SBL methods, and root-based off-grid SBL. However, these algorithms typically require hundreds of iterations to achieve numerical convergence, resulting in extremely high computational complexity, which severely limits their real-time performance in practical radar systems with stringent time delay requirements.

[0004] In recent years, inspired by the Omia brown fly's coupled auditory perception system, bio-inspired coupling (BIC) array systems have become a breakthrough technology in array antenna design. BIC arrays significantly amplify the phase difference between adjacent receiving elements through passive mechanical coupling, thus breaking through the basic angular resolution limit imposed by the physical aperture of traditional antenna arrays. However, BIC arrays have two inherent key drawbacks: first, the passive coupling structure introduces severe signal power attenuation, significantly reducing the output signal-to-noise ratio; second, the coupling mechanism transforms originally uncorrelated received noise into strongly spatially correlated noise, significantly deteriorating the estimation performance of traditional direction-of-arrival (DOA) algorithms.

[0005] To address the aforementioned issues of BIC arrays, an asymmetric active coupling (AC) radar array design paradigm has been proposed. This method effectively eliminates the inherent signal power loss while retaining the excellent phase difference enhancement capability of BIC arrays, significantly improving the output signal-to-noise ratio. However, the active coupling structure cannot inherently suppress antenna noise accompanying the incident received signal, making AC arrays still highly susceptible to spatially heterogeneous and non-uniform noise in practical deployment scenarios. Although some advanced algorithms attempt to improve parameter estimation performance under these conditions, they still lag significantly behind the theoretical Crammér-Rao bound (CRB) for direction-of-arrival estimation under non-uniform noise.

[0006] With the exponential growth of computing resources and the rapid development of artificial intelligence, data-driven deep learning techniques are widely used in direction-of-arrival (DOA) estimation tasks. Compared with traditional model-driven methods, deep learning methods employ an offline, one-time training and online, single-inference paradigm, resulting in significantly higher inference efficiency. However, purely data-driven methods generally suffer from inherent "black box" limitations, lacking rigorous theoretical interpretability and convergence guarantees, which severely restricts their practical application in safety-critical radar systems.

[0007] Deep Unfolding Networks (DUNs) offer a promising approach to mitigating the limitations of purely data-driven neural networks. The core idea is to algorithmically map each iteration of a model-driven optimization algorithm to a corresponding layer in a deep neural network, optimizing learnable parameters through data-driven offline training. This design paradigm seamlessly integrates the rigorous theoretical interpretability of model-driven methods with the superior computational efficiency and adaptive learning capabilities of data-driven methods. However, existing deep unfolding-based direction-of-arrival (DOA) estimation methods suffer significant performance degradation in the presence of spatially heterogeneous and non-uniform noise, which is prevalent and unavoidable in practical AC radar array systems.

[0008] Furthermore, existing SBL-based direction-of-arrival (DOA) estimation methods lack quantitative metrics for the dynamic stability of the iterative inference process. Convergence analysis of the corresponding deep expansion variational sparse Bayesian learning networks is often insufficient or even omitted, compromising their theoretical rigor. Information entropy, as a powerful mathematical tool for evaluating the stability of nonlinear dynamical systems and quantifying the statistical uncertainty of system states, has been widely used in modern control theory, but it has not yet been systematically introduced into the off-grid SBL DOA estimation framework for AC radar arrays. Summary of the Invention

[0009] To address the aforementioned problems, this invention provides a method and system for estimating the direction of arrival (DOA) of an asymmetric actively coupled radar array away from the grid. The technical problems to be solved include: This invention addresses the following shortcomings in the prior art: 1. Traditional Sparse Bayesian Learning (SBL)-like Direction of Arrival (DOA) estimation methods suffer from off-grid (OG) mismatch effects. When the actual DOA does not coincide with the pre-discrete grid points, the performance drops sharply and requires hundreds of iterations to converge, resulting in extremely high computational complexity. 2. Asymmetric active coupling (AC) radar arrays are susceptible to spatial heterogeneous and non-uniform noise in actual deployment. Existing noise suppression methods require explicit estimation of noise power or sacrifice of array aperture, resulting in poor robustness and a significant gap between their performance and the theoretical Cramer-Rao Bound (CRB). 3. Purely data-driven deep learning DOA estimation methods have a "black box" problem, lacking rigorous theoretical interpretability and convergence guarantees, and cannot be applied to safety-critical radar systems; 4. Existing depth unfolding DOA estimation methods suffer severe performance degradation in non-uniform noise scenarios and lack quantitative indicators to evaluate the dynamic stability of the iterative process, resulting in insufficient convergence analysis.

[0010] This invention provides a method for estimating the off-grid DOA of an asymmetric actively coupled radar array, comprising the following steps: S1. Signal preprocessing: Perform coupling and decoupling transformation on the signal received by the asymmetric active coupled radar array, calculate the sample covariance matrix and quantize it to obtain the vectorized sample covariance vector. S2. Construction of Entropy-Weighted Real-Valued Off-Grid Sparse Model: By jointly fusing noise and vectorized sample covariance vectors, a variational signal representation is constructed. The statistical uncertainty of non-uniform noise is quantified using differential entropy. An entropy weighting matrix is ​​designed to weight the variational signal representation, which is then converted into a real-valued Hilbert space representation. S3. Entropy-guided real-valued variational SBL iterative inference: A Bayesian inference framework is constructed based on an entropy-weighted real-valued off-grid sparse model. Sample entropy is used to quantitatively evaluate the dynamic stability of the iterative process. An adaptive learning rate based on sample entropy is designed to realize the dynamic update of hyperparameters and off-grid errors. The asymptotic convergence of the iterative process is proved based on the state entropy evolution theory. S4. Construction and Training of Deep Unfolded Variational Sparse Bayesian Learning Network: Based on the inference results, each iteration of the entropy-guided real-valued variational sparse Bayesian learning algorithm is mapped to a layer of a deep neural network to construct an entropy-guided deep unfolded variational sparse Bayesian learning network. An entropy regularization term is introduced into the end-to-end loss function to enhance the sparse feature learning ability. A hierarchical end-to-end training strategy is adopted to optimize the parameters of the entropy-guided deep unfolded variational sparse Bayesian learning network. S5, DOA estimation output: Input the radar received signal to be processed into the trained deep unfolded variational sparse Bayesian learning network to obtain the estimation results of sparse vector and off-grid error vector. The final DOA estimate is obtained through peak detection and off-grid error correction.

[0011] This invention also provides an off-grid DOA estimation system for asymmetric active-coupled radar arrays, comprising: The signal preprocessing module is used to perform coupling and decoupling transformation on the signals received by the asymmetric active coupling radar array, calculate the sample covariance matrix and quantize it to obtain the vectorized sample covariance vector. The sparse model building module is used to construct a variational signal representation by jointly fusing noise and vectorized sample covariance vectors. It uses differential entropy to quantify the statistical uncertainty of non-uniform noise, designs an entropy weighting matrix to weight the variational signal representation, and converts it into a real-valued Hilbert space representation. The iterative inference module is used to construct a Bayesian inference framework based on an entropy-weighted real-valued off-grid sparse model. It uses sample entropy to quantitatively evaluate the dynamic stability of the iterative process and designs an adaptive learning rate based on sample entropy to achieve dynamic updates of hyperparameters and off-grid errors. It also proves the asymptotic convergence of the iterative process based on the state entropy evolution theory. The Deep Unfolded Variational Sparse Bayesian Learning Network module is used to map each iteration of the entropy-guided real-valued variational sparse Bayesian learning algorithm to a layer of a deep neural network based on the inference results, constructing an entropy-guided deep unfolded variational sparse Bayesian learning network. An entropy regularization term is introduced into the end-to-end loss function to enhance the sparse feature learning ability. A hierarchical end-to-end training strategy is adopted to optimize the parameters of the entropy-guided deep unfolded variational sparse Bayesian learning network. The output module is used to input the radar received signal to be processed into the trained deep unfolded variational sparse Bayesian learning network to obtain the estimation results of sparse vector and off-grid error vector. The final DOA estimate is obtained through peak detection and off-grid error correction.

[0012] Compared with the prior art, the present invention has the following beneficial effects: 1. Strong robustness to non-uniform noise: By constructing a variational signal representation with joint tensor quantization of noise and signal covariance manifolds, there is no need to explicitly estimate noise power or sacrifice array aperture. Combined with the entropy weighting mechanism, the robustness to spatially heterogeneous non-stationary noise is significantly enhanced.

[0013] 2. Fast convergence speed: The learning rate is adaptively adjusted by sample entropy, which effectively prevents iterative divergence and reduces the number of convergence iterations of the traditional SBL algorithm from hundreds to tens of times; the deep unfolded variational sparse Bayesian learning network further shortens the inference time to the millisecond level, meeting the real-time requirements.

[0014] 3. High theoretical rigor: Based on the state entropy evolution theory, a rigorous convergence analysis was conducted on the iterative algorithm and the deep unfolded variational sparse Bayesian learning network, which solved the problem that pure data-driven methods lack interpretability and convergence guarantee.

[0015] 4. High estimation accuracy: The entropy regularization loss function enhances the discriminative power of sparse features, and the off-grid error correction effectively alleviates the basis mismatch problem. Under different signal-to-noise ratios, snapshot numbers, and non-uniform noise levels, the estimation performance is close to the theoretical CRB.

[0016] 5. Strong generalization ability: The design paradigm that combines model-driven and data-driven approaches enables the network to maintain good performance even outside the scenarios covered by the training data, making it suitable for complex and ever-changing real-world radar environments. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention.

[0018] Figure 2 This is a schematic diagram of the system structure of the present invention. Detailed Implementation

[0019] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0020] Example 1

[0021] This embodiment provides a method for estimating the off-grid DOA of an asymmetric actively coupled radar array. The specific steps are as follows: S1. Signal preprocessing: The signal received by the asymmetric active-coupled radar array is subjected to coupling and decoupling transformation, the sample covariance matrix is ​​calculated and quantized to obtain the vectorized sample covariance vector.

[0022] In this embodiment, consider a containing A uniform linear asymmetric active-coupled radar array with [number] antenna elements, wherein... Even number (in this embodiment) ). No. The array received signal model at each sampling time is as follows:

[0023] in, For complex array observation vectors, The statement belongs to, express OK A complex matrix of columns, This refers to the Active Coupling Matrix (ACM). For block diagonal composite operators, defined as , The mutual coupling matrix for each block ( and These are the front-phase and feedback coupling coefficients of the asymmetric coupling structure, respectively, in this embodiment... , dB represents decibels. For the first A decoupling matrix, , Represents the block diagonalization operator. For the first A decoupling matrix, For array manifold tensors, The number of far-field incident sources, its i.e. Column corresponding array steering vector , For the first The azimuth angle of each source, For the transpose operator, The imaginary unit, Pi For the sine operator, For natural index, The far-field source waveform vector, This is for spatial heterogeneous external antenna noise. This represents the spatially uniform internal thermal noise.

[0024] polymerization A series of rapid snapshots (in this embodiment) ), to obtain the multi-shot received signal matrix:

[0025] in, For receiving signal tensors, The source waveform matrix, and These are the external antenna noise matrix and the internal thermal noise matrix, respectively.

[0026] Due to the active coupling matrix Precise calibration can be achieved through array design parameters, thus allowing the use of inverse linear transformations to decouple coupling effects.

[0027] in, Find the inverse operator for a matrix.

[0028] Calculate the sample covariance matrix of the decoupled signal. :

[0029] in, This is the Hermitian transpose operator. For the sample covariance matrix... Perform column-major vectorization to obtain the vectorized sample covariance vector. :

[0030] S2. Entropy-weighted real-valued sparse model construction: By jointly fusing noise and vectorized sample covariance vectors, a variational signal representation is constructed. The statistical uncertainty of non-uniform noise is quantified by differential entropy. An entropy weighting matrix is ​​designed to weight the variational signal representation, which is then converted into a real-valued Hilbert space representation.

[0031] Through noise and vectorized sample covariance vector Perform variational representation and construct variational signal representation. :

[0032] in, To augment the guiding matrix, The tensor product of column vectors is the guiding matrix. For complex conjugate operators, For column vector tensor products, The noise basis matrix, for The first dimension of the identity matrix List, For block diagonalization operators, To augment sparse vectors, For signal power vector ( For the first (average power of each source) For noise power vector ( For the first (noise power of each antenna element) To estimate the error vector, For Kronecker product, The theoretical covariance matrix, The number of antenna elements. The number of far-field incident sources, It follows a complex normal distribution.

[0033] To quantify the statistical uncertainty of non-uniform noise, the estimation error vector is calculated. Differential entropy :

[0034] in, To estimate the error vector The covariance matrix, It is the determinant of a matrix. It is a natural constant. It represents a logarithmic operation with base 10.

[0035] Design an entropy weighted matrix :

[0036] in, Estimate the error vector within the current noise power range. The maximum possible entropy, It is an exponential function. For matrix This operation involves an entropy-weighted matrix. Based on the estimated error vector The model adaptively adjusts the weights of each data dimension to address uncertainties, thereby enhancing its robustness to non-uniform noise.

[0037] Entropy weighting is applied to the variational signal representation:

[0038] in, This is the weighted variational signal. To augment the guiding matrix, It is a widely sparse vector. To guide an appropriate matrix for the weighted variational signal, , To normalize the error, for 3D identity matrix It follows a complex normal distribution.

[0039] spatial domain (In this embodiment) Uniform discretization grid points (In this embodiment) Grid spacing Construct a sparse model:

[0040] in, The variational signal is weighted by entropy. It is a sparse guided matrix. , For grid-guided vector matrix, It is a sparse vector. for The non-zero vector at each grid point that is closest to the true DOA. The weighted grid guiding vector matrix, For conjugate operators, Indicates the angle as The guide vector, For the transpose operator, For noise power vector, To normalize the error, For column vector tensor product operations, For grid-guided vector matrix, Mesh-oriented vector matrix The complex conjugate matrix.

[0041] When the azimuth angle corresponding to the actual DOA When not located at a grid point, an off-grid model is approximated using a first-order Taylor series:

[0042] in, The closest azimuth angle Grid point index, for right The first-order partial derivative at time , True azimuth The corresponding first-order Taylor approximation entropy-weighted steering vector, Indicates the angle as The guiding vector at that time, The closest azimuth angle on the grid Angle, For any spatial azimuth angle The corresponding entropy-weighted array steering vector, This is a spatial azimuth variable.

[0043] The entropy-weighted off-grid sparse model can be expressed as:

[0044] in, The weighted variational signal, , , , This is the distance from the grid error vector. This is the weighted, off-grid dictionary. It is a sparse vector. It is a matrix composed of first-order Taylor delattice approximation guiding vectors. This is the deviation error vector. The noise basis matrix, For angles in the grid set The matrix composed of the guiding vectors in the matrix, For matrix For grid sets The matrix composed of the first-order partial derivatives at each angle. For diagonalization operators, for right The first-order partial derivative at time , For the first One off-standard error, For any spatial azimuth angle The corresponding entropy-weighted array steering vector, This is a spatial azimuth variable.

[0045] To facilitate neural network processing, the entropy-weighted off-grid sparse model is converted into a real-valued Hilbert space representation. :

[0046] in, and These are operators for taking the real part and the imaginary part, respectively. For the real-valued estimation error vector, , For real-valued mesh orientation matrices, Let Variance be the variance of the error vector. For quantization of differential entropy, Estimate the error vector within the current noise power range. The maximum possible entropy, For the real-valued estimation error vector, This is the weighted, undefined dictionary.

[0047] In this embodiment, the sample entropy adaptive learning rate The sample entropy decreases monotonically as it increases, and the update step size is automatically reduced when the iteration process becomes unstable to prevent divergence.

[0048] S3. Entropy-guided real-valued variational SBL iterative inference: A Bayesian inference framework is constructed based on an entropy-weighted real-valued off-grid sparse model. Sample entropy is used to quantitatively evaluate the dynamic stability of the iterative process, and an adaptive learning rate based on sample entropy is designed to achieve dynamic updates of hyperparameters and off-grid errors. The asymptotic convergence of the iterative process is proved based on the state entropy evolution theory.

[0049] In this embodiment, the design method for the sample entropy adaptive learning rate is as follows: During iterative inference, a time series consisting of the Euclidean norm of the posterior mean vector is constructed. ,in, For the number of iterations, Denotes the Euclidean norm; Calculate time series Sample entropy ,in, For embedded dimensions, For the natural index Logarithmic operations with base 0. For similarity threshold, for The average probability of vector similarity in a dimensional embedding space. for The average probability of vector similarity in a dimensional embedding space; Design a sample entropy adaptive learning rate. ,in, This refers to the sensitivity parameter.

[0050] In this embodiment, the convergence proof based on the state entropy evolution theory is as follows: The iterative process of the entropy-guided real-valued variational sparse Bayesian learning algorithm is modeled as a discrete-time nonlinear dynamical system. Among them, state variables , For hyperparameter vectors, This is the distance from the grid error vector. It is a nonlinear mapping. This is the weighted variational signal in Hilbert space. For the first The system state variables of the nth iteration are derived from the nth iteration. The state variables of the next iteration After nonlinear mapping Evolutionary, including the first The hyperparameter vector updated in the next iteration and mesh error vector .

[0051] Define the system in the first The state entropy of the next iteration is Its change is ,in, Let be the probability density function of the state variable. The integral symbol is used. For differential elements, Let Jacobian matrix be the result of the iterative mapping. For partial derivative operators, In the first The state entropy of the next iteration; Prove that when the array manifold matrix is ​​full rank, the source signal and noise are statistically independent, and the sample entropy adaptive learning rate satisfies... Under the condition that the spectral radius of the Jacobian matrix is ​​less than 1, the state entropy Strictly decreasing and bounded, the iterative process converges to a unique fixed point, where, The adaptive learning rate is set to minimize sample entropy. The learning rate is adapted to the sample entropy. The adaptive learning rate is the maximum sample entropy.

[0052] A Bayesian inference framework is constructed based on an entropy-weighted real-valued sparse grid model, with the likelihood function being:

[0053] in, Let be the likelihood function, representing the likelihood of a given sparse vector. Under these conditions, variational signal The conditional probability density of occurrence It follows a normal distribution. Let Variance be the variance of the error vector. for An identity matrix of dimension 1 It is a real-valued mesh orientation matrix.

[0054] For sparse vectors Apply a Gaussian prior to enforce space sparsity:

[0055] in, Let be the prior probability density function, representing the probability density function given hyperparameters. Under the condition of sparse vectors It follows a zero-mean multivariate normal distribution. It is a diagonal covariance matrix, whose diagonal elements are determined by the hyperparameters. The elements are arranged sequentially. For the first One hyperparameter controls the sparse vector. The sparsity of the Gaussian hyperparameters corresponding to the true DOA and noise components. It converges to a larger value, and the rest converge to zero. Let be the Gaussian hyperparameter corresponding to the noise component.

[0056] According to Bayes' theorem, sparse vectors The posterior distribution is:

[0057] in, sparse vector The posterior distribution, The posterior mean is... Let covariance matrix be the variance matrix. This is a hyperparameter.

[0058] The Expectation Maximization (EM) algorithm is used for iterative solution: Expected step: Calculate the posterior mean Covariance Matrix :

[0059] Maximization steps: (updating hyperparameters) and grid error )

[0060]

[0061] in, For the number of iterations, for The One element, for The diagonal elements, For the first The hyperparameter at the th ... Updated value after the next iteration For the first The posterior mean of the sparse signal vector obtained in the next iteration. For the first The posterior covariance matrix of the sparse signal vector obtained in the next iteration. For the first The off-grid error vector obtained in the next iteration For the first The coefficient matrix used in the next iteration to update the off-grid error For the first The right-hand side vector used in the next iteration to update the off-grid error The distance from the grid error vector is the first The element in the first... Updated value after the next iteration The right-hand term vector The One element, Coefficient matrix The diagonal elements, and These are the coefficient matrix and the right-hand side vector in the grid error update formula, respectively.

[0062] and The specific expression is:

[0063] in, The derivative matrix of the entropy-weighted real-valued guiding vector. The entropy-weighted real-valued off-grid dictionary matrix. This is the entropy-weighted real-valued noise basis matrix. and These are the posterior means. The former One and after A vector consisting of n elements Covariance matrix The former OK Submatrix, Covariance matrix The former After the trip Submatrix, , , , It represents the Hadamah accumulation. The column vector tensor product steering matrix is ​​constructed based on spatial grid points. and These are the operators for taking the real part and the imaginary part, respectively.

[0064] In this embodiment, to address the slow convergence or divergence issues caused by the fixed learning rate in the traditional Sparse Bayesian Learning (SBL) algorithm, sample entropy is introduced to quantitatively evaluate the dynamic stability of the iterative process. A time series is constructed based on the Euclidean norm of the posterior mean vector. :

[0065] in, For the number of iterations, This represents the Euclidean norm.

[0066] Calculate this time series Sample entropy :

[0067] in, For the natural index Logarithmic operations with base 0. For the embedded dimension (in this embodiment) ), The similarity threshold (in this embodiment) ), for The average probability of vector similarity in a dimensional embedding space. for The average probability of similar vectors in a dimensional embedding space.

[0068] Sample Entropy A larger value indicates a more unstable iterative process and a higher risk of divergence. An adaptive learning rate based on sample entropy is designed. :

[0069] in, Sensitivity parameters (in this embodiment) Sample entropy adaptive learning rate. It monotonically decreases as the sample entropy increases, and automatically reduces the update step size when the iteration is unstable.

[0070] Adaptive learning rate using sample entropy Update hyperparameters and off-mesh error:

[0071]

[0072] in, For the first The off-grid error vector obtained in the next iteration For the first The hyperparameter vector obtained from the next iteration. For the first The posterior mean of the sparse signal vector obtained in the next iteration. For the first The posterior covariance matrix of the sparse signal vector obtained in the next iteration. For the first The coefficient matrix used in the next iteration to update the off-grid error For the first The right-hand side term vector used in the next iteration is used to update the off-grid error.

[0073] Convergence Analysis: The iterative process of the entropy-guided real-valued variational sparse Bayesian learning algorithm EG-RV-VSBL is modeled as a discrete-time nonlinear dynamical system:

[0074] in, For the first The system state variables of the nth iteration are derived from the nth iteration. The state variables of the next iteration After nonlinear mapping Evolutionary, including the first The hyperparameter vector updated in the next iteration and mesh error vector State variables , It is a nonlinear mapping. This is the weighted variational signal in Hilbert space.

[0075] Define the system in the first The state entropy of the next iteration is its change for:

[0076] in, Let be the probability density function of the state variable. The integral symbol is used. For differential elements, Let Jacobian matrix be the result of the iterative mapping. For partial derivative operators, In the first The state entropy of the next iteration.

[0077] Under the following assumptions: 1. Array manifold tensor Satisfying the full rank condition, i.e. , for rank, For rank operators; 2. The source signal is a zero-mean stationary random process and is statistically independent of noise; 3. The sample entropy adaptive learning rate satisfies .

[0078] It can be proven that the Jacobian matrix of the iterative mapping lies at the fixed point. The spectral radius at point is less than 1, therefore the state entropy is strictly decreasing and has a lower bound, and the iterative process asymptotically converges to the unique fixed point. .

[0079] S4: Construction and Training of Deep Unfolded Variational Sparse Bayesian Learning Network: Based on the inference results, each iteration of the entropy-guided real-valued variational sparse Bayesian learning algorithm is mapped to a layer of a deep neural network to construct an entropy-guided deep unfolded variational sparse Bayesian learning network. An entropy regularization term is introduced into the end-to-end loss function to enhance the sparse feature learning ability. A hierarchical end-to-end training strategy is adopted to optimize the parameters of the entropy-guided deep unfolded variational sparse Bayesian learning network.

[0080] Each iteration of the entropy-guided real-valued variational sparse Bayesian learning algorithm EG-RV-VSBL is mapped to a layer of a deep neural network, constructing a layer containing... Layer entropy-guided depth unrolling variational sparse Bayesian learning network EG-DU-VSBLnet (in this embodiment) The network input is a real-valued covariance vector. Entropy weighted matrix The output is the estimated sparse vector. and mesh error vector .

[0081] Each layer of the entropy-guided deep unrolling variational sparse Bayesian learning network comprises four core modules: Bayesian inference module: corresponds to the expected steps of the algorithm, based on the input hyperparameters. Off-grid error and real-valued Hilbert space representation Calculate the posterior mean Covariance Matrix To enhance numerical stability, a small regularization term is added to the matrix inversion operation. ( ), Regularization coefficients are used to calculate the inversion of a matrix, preventing singular or ill-conditioned matrices, avoiding numerical overflow or computational divergence, and enhancing the numerical stability of the Bayesian inference process. It is an identity matrix.

[0082] Sample entropy adaptive adjustment module: Calculates sample entropy using historical posterior mean norm. And generate an adaptive learning rate. Sensitivity parameters Set as a learnable parameter and optimize during training.

[0083] Learnable Convolutional Neural Network (CNN) Hyperparameter Update Module: This module replaces the fixed maximization step update rule with a two-layer convolutional neural network to better capture the sparse features of the signal. The input is... (from the posterior mean) Covariance Matrix (composed of diagonal elements) for OK The real-valued matrix of columns, For the first The two-dimensional input tensor, composed of the diagonal elements of the layer posterior mean vector and the posterior covariance matrix, can be used to learn the following convolutional neural network structure: First layer: 8 output channels Convolution kernel, Tangent Exponential Linear Unit (TeLU) activation function, same padding; Second layer: 1 output channel, Convolution kernel, no padding.

[0084] Residual connection is used, hyperparameters The update rules are as follows:

[0085] in, For the learnable weights and biases of CNN, For the first Adaptive learning rate of the layer For the first The hyperparameter vector of the layer, For the first The two-dimensional input tensor is composed of the diagonal elements of the layer posterior mean vector and the posterior covariance matrix.

[0086] 4. Off-grid error update module: Updates the off-grid error vector based on the sample entropy and adaptive learning rate.

[0087] in, For regularization parameters, ensure reversible, For the first The layer is used to update the coefficient matrix of the off-grid error. For the first Layer off-grid error vector For the first Adaptive learning rate of the layer It is the identity matrix. For the first The layer is used to update the right-hand term vector of the off-grid error.

[0088] In this embodiment, entropy-guided deep expansion variational sparse Bayesian learning network training is performed: Loss function: A composite loss function with entropy regularization is used. :

[0089] in, Number of Monte Carlo implementations for each mini-batch, and These are the true sparse coefficient vector and the deviation vector from the grid, respectively. and The regularization coefficient is . To estimate the differential entropy of a sparse vector, The number of spatial grid points, The posterior covariance matrix is... To estimate the sparse vector, To estimate the obtained deviation vector from the grid, The number of antenna elements is denoted by . The entropy regularization term forces the posterior covariance matrix to be sparse, enhancing the spatial resolution of DOA estimation.

[0090] Training dataset: Generate a dataset containing 100,000 unique samples, where the number of source samples is... Randomly selected from DOA is randomly distributed in Minimum angular spacing Worst-case noise power ratio (WNPR) range arrive Signal-to-noise ratio (SNR) range arrive Quick shot number Take 50, 100, 200 and 500.

[0091] Data augmentation: DOA near grid points Internal random perturbation.

[0092] The dataset is divided into training, validation, and test sets in an 8:1:1 ratio.

[0093] Training strategy: Adaptive Moment Estimation (Adam) optimizer is used, with an initial learning rate of... A cosine annealing learning rate scheduler is used, reducing the learning rate by 0.5 times every 20 training iterations across all data. The mini-batch size is set to 32, and the maximum number of training epochs is 100. An early stopping mechanism is enabled when the validation loss does not improve after 10 consecutive training iterations across all data. A cosine annealing learning rate scheduler is applied to the CNN layers. Regularization (weight decay coefficient) After each convolutional layer, a random dropout layer with a retention probability of 0.8 is inserted.

[0094] Network convergence analysis: Modeling the inter-layer propagation of the network as a discrete-time nonlinear dynamical system:

[0095] in, For the first Layer state variables, For the first Nonlinear mapping of layers, For the first Learnable parameters of the layer.

[0096] Because the composite loss function includes an entropy regularization term, the inter-layer mappings learned by the network will cause the state entropy to decrease strictly. State entropy has a lower bound (the entropy of a deterministic state is 0), therefore, as the number of layers increases... hour, For the direction, As the equation becomes infinite, the state variables converge to a deterministic fixed point. Simultaneously, the first two terms of the loss function minimize the estimation error, thus the fixed point... This is the optimal estimate.

[0097] In this embodiment, the hierarchical end-to-end training strategy is specifically as follows: An Adaptive Moment Estimation (Adam) optimizer is used, with an initial learning rate of... The cosine annealing learning rate scheduler is used to reduce the learning rate by 0.5 times every 20 training iterations of all data. The mini-batch size is set to 32, the maximum number of training rounds is 100, and the early stopping mechanism is enabled when the validation loss does not improve after 10 consecutive training iterations across all data. Apply to convolutional neural network layers Regularization, weight decay coefficient is To prevent overfitting, a random dropout layer with a retention probability of 0.8 is inserted after each convolutional layer.

[0098] S5, DOA estimation output: Input the radar received signal to be processed into the trained deep unfolded variational sparse Bayesian learning network to obtain the estimation results of sparse vector and off-grid error vector. The final DOA estimate is obtained through peak detection and off-grid error correction.

[0099] Sparse vectors output by a depth-unfolded variational sparse Bayesian learning network The former Identify from the elements The maximum peak value is used to obtain the corresponding grid index. Combining the off-grid error vector Calculate the final DOA estimate. :

[0100] in, The closest azimuth angle on the grid Angle, For the first The off-grid error vector of the layer (final output layer) of the variational sparse Bayesian learning network output by depth expansion. In the middle, corresponding to the first The grid index where each peak is located The elements are used to correct for mesh mismatch errors. For the first One peak.

[0101] In summary, this invention addresses the problems of large off-grid mismatch error, poor robustness to non-uniform noise, high computational complexity, and lack of strict convergence guarantees in existing technologies. First, this invention constructs a variational signal representation using joint tensor quantization of the noise and signal covariance manifolds. It then quantifies the statistical uncertainty of non-uniform noise through differential entropy, constructing an entropy-weighted sparse off-grid dictionary. Second, it proposes an entropy-guided real-valued variational sparse Bayesian learning (EG-RV-VSBL) algorithm, employing sample entropy (SampEn) as a quantitative measure of the dynamic stability of iterative inference to achieve adaptive hyperparameter modulation and accelerated convergence. Finally, this algorithm is expanded into an entropy-guided deep unfolding variational sparse Bayesian learning network. The network (EG-DU-VSBLnet) introduces entropy regularization into the end-to-end loss function to enhance the discriminative power of sparse features. Based on the state entropy evolution theory of discrete-time nonlinear dynamical systems, rigorous convergence analysis is performed on the iterative algorithm and the unfolded network. This invention, while ensuring DOA estimation accuracy is close to the Crammér-Rao Bound (CRB), reduces computational complexity by more than an order of magnitude. It exhibits excellent robustness to heterogeneous and non-uniform noise in unknown spaces, making it suitable for scenarios such as real-time radar target localization, autonomous driving perception, and millimeter-wave communication. Therefore, the core technical solution of this invention is as follows: 1. Signal preprocessing and coupling decoupling: The signal received by the asymmetric active-coupled radar array is subjected to an invertible linear transformation to decouple the coupling effect, the sample covariance matrix is ​​calculated and quantized to obtain the vectorized sample covariance vector.

[0102] 2. Construction of Entropy-Weighted Real-Value Off-Grid Sparse Model: A variational signal representation is constructed by jointly fusing noise and vectorized sample covariance vectors, eliminating the need for explicit noise power estimation; the statistical uncertainty of non-uniform noise is quantified using differential entropy, and an entropy weighting matrix is ​​designed to adaptively weight the variational signal representation; an off-grid sparse model is constructed based on the first-order Taylor series approximation, and the complex-valued model is converted into a real-valued Hilbert space representation to reduce computational complexity.

[0103] 3. Entropy-guided real-valued variational SBL iterative inference: A Bayesian inference framework is constructed based on an entropy-weighted real-valued off-grid sparse model, and the Expectation-Maximization (EM) algorithm is used for iterative solution. Sample entropy (SampEn) is introduced to quantitatively evaluate the dynamic stability of the iterative process, and an adaptive learning rate is designed to realize the dynamic updating of hyperparameters and off-grid errors. Based on the state entropy evolution theory of discrete-time nonlinear dynamic systems, the asymptotic convergence of the iterative process is rigorously proven.

[0104] 4. Entropy-Guided Deep Unfolding Variational Sparse Bayesian Learning Network Construction and Training: Each iteration of the Entropy-Guided Real-Valued Variational Sparse Bayesian Learning (EG-RV-VSBL) algorithm is mapped to a layer of a deep neural network to construct an Entropy-Guided Deep Unfolding Variational Sparse Bayesian Learning Network (EG-DU-VSBLnet). An entropy regularization term is introduced into the end-to-end composite loss function to enhance the sparse feature learning ability. A hierarchical end-to-end training strategy is adopted to optimize the network parameters, and the convergence of the network is proved based on the state entropy evolution theory.

[0105] 5. DOA Estimation Output: The radar received signal to be processed is input into the trained entropy-guided depth expansion variational sparse Bayesian learning network EG-DU-VSBLnet to obtain the estimation results of sparse vector and off-grid error vector; the grid point corresponding to DOA is determined by peak detection, and the final high-precision DOA estimate is obtained by combining off-grid error correction.

[0106] Example 2

[0107] like Figure 2 As shown, this invention provides an off-grid DOA estimation system for asymmetric active-coupled radar arrays, used to execute the off-grid DOA estimation method for asymmetric active-coupled radar arrays described in Example 1, comprising: The signal preprocessing module is used to perform coupling and decoupling transformation on the signals received by the asymmetric active coupling radar array, calculate the sample covariance matrix and quantize it to obtain the vectorized sample covariance vector. The sparse model building module is used to construct a variational signal representation by jointly fusing noise and vectorized sample covariance vectors. It uses differential entropy to quantify the statistical uncertainty of non-uniform noise, designs an entropy weighting matrix to weight the variational signal representation, and converts it into a real-valued Hilbert space representation. The iterative inference module is used to construct a Bayesian inference framework based on an entropy-weighted real-valued off-grid sparse model. It uses sample entropy to quantitatively evaluate the dynamic stability of the iterative process and designs an adaptive learning rate based on sample entropy to achieve dynamic updates of hyperparameters and off-grid errors. It also proves the asymptotic convergence of the iterative process based on the state entropy evolution theory. The Deep Unfolded Variational Sparse Bayesian Learning Network module is used to map each iteration of the entropy-guided real-valued variational sparse Bayesian learning algorithm to a layer of a deep neural network based on the inference results, constructing an entropy-guided deep unfolded variational sparse Bayesian learning network. An entropy regularization term is introduced into the end-to-end loss function to enhance the sparse feature learning ability. A hierarchical end-to-end training strategy is adopted to optimize the parameters of the entropy-guided deep unfolded variational sparse Bayesian learning network. The output module is used to input the radar received signal to be processed into the trained deep unfolded variational sparse Bayesian learning network to obtain the estimation results of sparse vector and off-grid error vector. The final DOA estimate is obtained through peak detection and off-grid error correction.

[0108] like Figure 2 The asymmetric active coupling radar array off-grid DOA estimation system provided in the embodiment shown can execute the technical solution shown in the method embodiment 1 above. Its implementation principle and beneficial effects are similar, and will not be repeated here.

[0109] In this embodiment, the functional units can be divided according to the off-grid DOA estimation method for asymmetric active coupled radar arrays. For example, each function can be divided into its own functional units, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this invention is illustrative and represents only a logical division; other division methods may be used in actual implementation.

[0110] In this embodiment, the asymmetric active-coupled radar array off-grid DOA estimation system, in order to achieve the principle and beneficial effects of the method in Embodiment 1, includes hardware structures and / or software modules corresponding to the execution of various functions. Those skilled in the art should readily recognize that, in conjunction with the illustrative units and algorithm steps described in the embodiments disclosed herein, this invention can be implemented in hardware and / or a combination of hardware and computer software. Whether a function is executed in a hardware or computer software driven manner depends on the specific application and design constraints of the technical solution. Different methods can be used to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

Claims

1. A method for estimating the off-grid DOA of an asymmetric actively coupled radar array, characterized in that, Includes the following steps: S1. Signal preprocessing: Perform coupling and decoupling transformation on the signal received by the asymmetric active coupled radar array, calculate the sample covariance matrix and quantize it to obtain the vectorized sample covariance vector. S2. Construction of Entropy-Weighted Real-Valued Off-Grid Sparse Model: By jointly fusing noise and vectorized sample covariance vectors, a variational signal representation is constructed. The statistical uncertainty of non-uniform noise is quantified using differential entropy. An entropy weighting matrix is ​​designed to weight the variational signal representation, which is then converted into a real-valued Hilbert space representation. S3. Entropy-guided real-valued variational SBL iterative inference: A Bayesian inference framework is constructed based on an entropy-weighted real-valued off-grid sparse model. Sample entropy is used to quantitatively evaluate the dynamic stability of the iterative process. An adaptive learning rate based on sample entropy is designed to realize the dynamic update of hyperparameters and off-grid errors. The asymptotic convergence of the iterative process is proved based on the state entropy evolution theory. S4. Construction and Training of Deep Unfolded Variational Sparse Bayesian Learning Network: Based on the inference results, each iteration of the entropy-guided real-valued variational sparse Bayesian learning algorithm is mapped to a layer of a deep neural network to construct an entropy-guided deep unfolded variational sparse Bayesian learning network. An entropy regularization term is introduced into the end-to-end loss function to enhance the sparse feature learning ability. A hierarchical end-to-end training strategy is adopted to optimize the parameters of the entropy-guided deep unfolded variational sparse Bayesian learning network. S5, DOA estimation output: Input the radar received signal to be processed into the trained deep unfolded variational sparse Bayesian learning network to obtain the estimation results of sparse vector and off-grid error vector. The final DOA estimate is obtained through peak detection and off-grid error correction.

2. The method for estimating the off-grid DOA of an asymmetric actively coupled radar array according to claim 1, characterized in that, The coupling-decoupling transformation in S1 specifically refers to: For including A uniform linear asymmetric active-coupled radar array with n antenna elements has the following received signal matrix: Through invertible linear transformation Decoupling the coupling effect yields the decoupled received signal matrix. Among them, the active coupling matrix For block diagonal composite operators, For the number of snapshots, The statement belongs to, for OK A complex matrix of columns, Invert a matrix; Calculate the sample covariance matrix And the sample covariance matrix Column-major vectorization yields the vectorized sample covariance vector. ,in, This is the Hermitian transpose operator.

3. The method for estimating the off-grid DOA of an asymmetric actively coupled radar array according to claim 1, characterized in that, The construction of the entropy-weighted real-valued sparse grid model in S2 is specifically as follows: Through noise and vectorized sample covariance vector Constructing variational signal representation ,in, To augment the guiding matrix, The tensor product of column vectors is the guiding matrix. For column vector tensor product operations, For complex conjugate operators, This is the original guiding vector matrix. The noise basis matrix, To augment sparse vectors, For signal power vector, For noise power vector, For the rank transformation operator, To estimate the error vector; Calculate the estimation error vector Differential entropy ,in, To estimate the error vector The covariance matrix, For Kronecker product, It is the determinant of a matrix. For logarithmic operations with base 10, Pi For natural index, The theoretical covariance matrix, This refers to the number of antenna elements; Quantization using differential entropy Statistical uncertainty of non-uniform noise; Design an entropy weighted matrix ,in, Estimate the error vector within the current noise power range. The maximum possible entropy, It is an exponential function. For matrix This operation; entropy weighting matrix The weights of data dimensions are adaptively adjusted based on uncertainty. Using entropy weighting matrix For variational signal representation Entropy weighting is performed to obtain the weighted variational signal. And convert it into a real-valued Hilbert space representation. ,in, For real-valued mesh orientation matrices, and These are the operators for taking the real part and the imaginary part, respectively. Let be the real-valued estimation error vector. It is a sparse vector. This is the weighted, undefined dictionary.

4. The method for estimating the off-grid DOA of an asymmetric actively coupled radar array according to claim 1, characterized in that, The specific design method for the sample entropy adaptive learning rate in S3 is as follows: During iterative inference, a time series consisting of the Euclidean norm of the posterior mean vector is constructed. ,in, For the number of iterations, Denotes the Euclidean norm; Calculate time series Sample entropy ,in, For embedded dimensions, For the natural index Logarithmic operations with base 0. For similarity threshold, for The average probability of vector similarity in a dimensional embedding space. for The average probability of vector similarity in a dimensional embedding space; Design a sample entropy adaptive learning rate. ,in, This refers to the sensitivity parameter.

5. The method for estimating the off-grid DOA of an asymmetric actively coupled radar array according to claim 1, characterized in that, The convergence proof based on the state entropy evolution theory in S3 is as follows: The iterative process of the entropy-guided real-valued variational sparse Bayesian learning algorithm is modeled as a discrete-time nonlinear dynamical system. Among them, state variables , For hyperparameter vectors, This is the distance from the grid error vector. It is a nonlinear mapping. The weighted variational signal in Hilbert space; Define the system in the first The state entropy of the next iteration is Its change is ,in, Let be the probability density function of the state variable. The integral symbol is used. For differential elements, Let Jacobian matrix be the result of the iterative mapping. For partial derivative operators, In the first The state entropy of the next iteration; Prove that when the array manifold matrix is ​​full rank, the source signal and noise are statistically independent, and the sample entropy adaptive learning rate satisfies... Under the condition that the spectral radius of the Jacobian matrix is ​​less than 1, the state entropy Strictly decreasing and bounded, the iterative process converges to a unique fixed point, where, The learning rate is adapted to minimize sample entropy. The learning rate is adapted to the sample entropy. The adaptive learning rate is the maximum sample entropy.

6. The method for estimating the off-grid DOA of an asymmetric actively coupled radar array according to claim 1, characterized in that, The specific structure of the entropy-guided deep unfolded variational sparse Bayesian learning network in S4 is as follows: Entropy-guided deep expansion variational sparse Bayesian learning networks include Each of the cascaded layers corresponds to one iteration of the entropy-guided real-valued variational sparse Bayesian learning algorithm, and each layer contains: The Bayesian inference module is used to infer the hyperparameters of the input. Off-grid error and real-valued Hilbert space representation Calculate the posterior mean Covariance Matrix , where the posterior mean vector The sparse vectors estimated by the nth layer depth expansion variational sparse Bayesian learning network. The sparse vector output by the deep unfolded variational sparse Bayesian learning network. The posterior mean vector output by the Nth layer Bayesian inference module N represents the total number of layers in the deep unfolded variational sparse Bayesian learning network. The sample entropy adaptive adjustment module is used to calculate the sample entropy during the iterative process and generate an adaptive learning rate based on the sample entropy. ; A learnable convolutional neural network hyperparameter update module is used to replace the fixed maximization step update rule with a two-layer convolutional neural network, wherein the input is the posterior mean. Covariance Matrix A two-dimensional tensor composed of diagonal elements is output as hyperparameters. The amount of correction; The off-grid error update module is used to update the off-grid error vector based on the sample entropy and the adaptive learning rate.

7. The method for estimating the off-grid DOA of an asymmetric actively coupled radar array according to claim 1, characterized in that, The specific composite loss function with entropy regularization in S4 is as follows: in, For composite loss function, Number of Monte Carlo implementations for each mini-batch, and These are the true sparse coefficient vector and the deviation vector from the grid, respectively. and All are regularization coefficients. To estimate the differential entropy of a sparse vector, The number of spatial grid points, The posterior covariance matrix is... To estimate the sparse vector, To estimate the obtained deviation vector from the grid, This represents the number of antenna elements.

8. An off-grid DOA estimation system for an asymmetric active-coupled radar array, used to execute the off-grid DOA estimation method for an asymmetric active-coupled radar array as described in any one of claims 1-7, characterized in that, include: The signal preprocessing module is used to perform coupling and decoupling transformation on the signals received by the asymmetric active coupling radar array, calculate the sample covariance matrix and quantize it to obtain the vectorized sample covariance vector. The sparse model building module is used to construct a variational signal representation by jointly fusing noise and vectorized sample covariance vectors. It uses differential entropy to quantify the statistical uncertainty of non-uniform noise, designs an entropy weighting matrix to weight the variational signal representation, and converts it into a real-valued Hilbert space representation. The iterative inference module is used to construct a Bayesian inference framework based on an entropy-weighted real-valued off-grid sparse model. It uses sample entropy to quantitatively evaluate the dynamic stability of the iterative process and designs an adaptive learning rate based on sample entropy to achieve dynamic updates of hyperparameters and off-grid errors. It also proves the asymptotic convergence of the iterative process based on the state entropy evolution theory. The Deep Unfolded Variational Sparse Bayesian Learning Network module is used to map each iteration of the entropy-guided real-valued variational sparse Bayesian learning algorithm to a layer of a deep neural network based on the inference results, constructing an entropy-guided deep unfolded variational sparse Bayesian learning network. An entropy regularization term is introduced into the end-to-end loss function to enhance the sparse feature learning ability. A hierarchical end-to-end training strategy is adopted to optimize the parameters of the entropy-guided deep unfolded variational sparse Bayesian learning network. The output module is used to input the radar received signal to be processed into the trained deep unfolded variational sparse Bayesian learning network to obtain the estimation results of sparse vector and off-grid error vector. The final DOA estimate is obtained through peak detection and off-grid error correction.

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