Sparse Bayesian Learning Method Research Articles

Robust Tensor-Based DOA and Polarization Estimation in Conformal Polarization Sensitive Array with Bad Data.

Partially impaired sensor arrays pose a significant challenge in accurately estimating signal parameters. The occurrence of bad data is highly probable, resulting in random loss of source information and substantial performance degradation in parameter estimation. In this paper, a tensor variational sparse Bayesian learning (TVSBL) method is proposed for the estimate of direction of arrival (DOA) and polarization parameters jointly based on a conformal polarization sensitive array (CPSA), taking into account scenarios with the partially impaired sensor array. First, a sparse tensor-based received data model is developed for CPSAs that incorporates bad data. Then, a column vector detection method is proposed to diagnose the positions of the impaired sensors. In scenarios involving partially impaired sensor arrays, a low-rank matrix completion method is employed to recover the random loss of signal information. Finally, variational sparse Bayesian learning (VSBL) and minimum eigenvector methods are utilized sequentially to obtain the DOA and polarization parameters estimation, successively. Furthermore, the Cramér-Rao bound is given for the proposed method. Simulation results validated the effectiveness of the proposed method.

Direction-of-Arrival Estimation via Sparse Bayesian Learning Exploiting Hierarchical Priors with Low Complexity.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

Sparse Bayesian Deep Learning for Cross Domain Medical Image Reconstruction

Cross domain medical image reconstruction aims to address the issue that deep learning models trained solely on one source dataset might not generalize effectively to unseen target datasets from different hospitals. Some recent methods achieve satisfactory reconstruction performance, but often at the expense of extensive parameters and time consumption. To strike a balance between cross domain image reconstruction quality and model computational efficiency, we propose a lightweight sparse Bayesian deep learning method. Notably, we apply a fixed-form variational Bayes (FFVB) approach to quantify pixel-wise uncertainty priors derived from degradation distribution of the source domain. Furthermore, by integrating the uncertainty prior into the posterior sampled through stochastic gradient Langevin dynamics (SGLD), we develop a training strategy that dynamically generates and optimizes the prior distribution on the network weights for each unseen domain. This strategy enhances generalizability and ensures robust reconstruction performance. When evaluated on medical image reconstruction tasks, our proposed approach demonstrates impressive performance across various previously unseen domains.

DOA estimation based on sparse Bayesian learning with moving synthetic virtual array

AbstractIn scenarios with constrained physical aperture sizes, aiming to enhance the resolution and accuracy of Direction of Arrival (DOA) estimation, this paper proposes a novel approach that integrates a moving synthetic virtual array with Sparse Bayesian Learning (SBL) for DOA estimation. Initially, a virtual array is constructed based on the motion characteristics of the target. Subsequently, the SBL method is employed to estimate the DOA of the target. Simulation experiments validate the effectiveness of this approach, demonstrating comparable DOA estimation performance to synthetic aperture methods with larger aperture sizes, even in situations with limited aperture expansion. Furthermore, under constant virtual aperture expansion, this method surpasses non‐SBL methods regarding DOA resolution.

Source localization by Matching the Multipath Arrival Angles based on Sparse Bayesian Learning

In the deep-sea direct arrival region, a significant multipath characteristic is presented by the propagation of acoustic signals. This characteristic is closely linked to the distance and depth of the sound source and can be utilized for source localization. In this study, the changes in incidence angle characteristics of multipath signals at different distances and depths are analysed initially. Subsequently, the high-resolution azimuthal spectra are obtained using the Sparse Bayesian Learning (SBL) method. The azimuthal spectra are then matched with multiple incidence angles using the Gaussian kernel function, facilitating the localization of sound sources. Throughout this paper, the impacts of different distance, depth, and SNR conditions on the model are assessed through simulations. Furthermore, the model’s validity is confirmed by utilizing experimental data from an explosion sound source.

Robust Sparse Bayesian Two-Dimensional Direction-of-Arrival Estimation with Gain-Phase Errors

To reduce the influence of gain-phase errors and improve the performance of direction-of-arrival (DOA) estimation, a robust sparse Bayesian two-dimensional (2D) DOA estimation method with gain-phase errors is proposed for L-shaped sensor arrays. The proposed method introduces an auxiliary angle to transform the 2D DOA estimation problem into two 1D angle estimation problems. A sparse representation model with gain-phase errors is constructed using the diagonal element vector of the cross-correlation covariance matrix of two submatrices of the L-shaped sensor array. The expectation maximization algorithm derives unknown parameter expression, which is used for iterative operations to obtain off-grid and signal precision. Using these parameters, a new spatial spectral function is constructed to estimate the auxiliary angle. The obtained auxiliary angle is substituted into a sparse representation model with gain and phase errors, and then the sparse Bayesian learning method is used to estimate the elevation angle of the incident signal. Finally, according to the relationship of the three angles, the azimuth angle can be estimated. The simulation results show that the proposed method can effectively realize the automatic matching of the azimuth and elevation angles of the incident signal, and improves the accuracy of DOA estimation and angular resolution.

Non-Circular Signal DOA Estimation with Nested Array via Off-Grid Sparse Bayesian Learning.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

Feature fusion and distillation embedded sparse Bayesian learning model for in-situ foreknowledge of robotic machining errors

In recent years, robotic machining of complex surface has become a research hotspot for intelligent manufacture. Considering the weak rigidity characteristics of industrial robot structure, the machining errors will be generated during the robotic machining process, which will further induce the undesirable impact on machining quality and production cycles. Therefore, this work proposes an in-situ foreknowledge model for robotic machining errors of complex curved parts. The static and dynamic features during the robotic manufacture process are obtained, where the robots’ stiffness concerning end effect operator is extracted as the static features, as well as the dynamic features of the monitored dynamic cutting forces. Furthermore, the structured fusion features are utilized as the dataset to train the foreknowledge model based on sparse Bayesian learning method. In order to adapt to the rapid response in the industrial field, the principal component analysis strategy is adopted to reduce feature dimension, by which the complexity of fusion features is reduced by 50.51 %. In addition, based on the adjustment of sparse weights, the complexity of the sparse Bayesian foreknowledge model is reduced by 74.31 %. According to the validation experiment on the blade shaped workpiece of marine propeller, the results indicate that the prediction accuracy of the proposed in-situ foreknowledge model is in the range of 60.03–87.07 µm, meeting the engineering requirements of robotic machining errors. The proposed in-situ foreknowledge sparse model displays the potential prospects for robotic machining errors prediction and control in the industrial application field.

A Sparse Bayesian Learning Method for Direction of Arrival Estimation in Underwater Maneuvering Platform Noise

The underwater maneuvering platform generates self-noise when sailing, which shows spatial directionality to the arrays fixed on the platform. In this paper, it is called spatially colored noise (SCN). The direction of arrival (DOA) estimation results are often influenced by this self-noise, leading to a decrease in estimation accuracy and to the appearance of spurious peaks. To resolve this problem, a sparse Bayesian learning (SBL) method adapted to underwater maneuvering platform noise is proposed in this paper. The SBL framework with unknown SCN is established first. Then, the SCN covariance matrix is estimated by projecting the received data covariance matrix into the noise subspace, and the DOA estimation results are finally obtained through multiple iterations. The simulation results show that the proposed method avoids spurious peaks, and compared to the existing methods, the proposed method achieves a higher accuracy in the case of low SNRs and small snapshot numbers. The sea trial data processing results show that the proposed method provides lower and flatter noise spectrum levels without spurious peaks.

High-resolution DOA estimation achieved by a single acoustic vector sensor under anisotropic noise

The acoustic vector sensor (AVS) has a wide application in the direction of arrival (DOA) estimation of sound sources including aircraft, underwater or on-land vehicles, search-and-rescue efforts, etc. The performance of only one acoustic vector sensor can compare favorably with a traditional acoustic array in DOA estimation. The anisotropic noise problem of the vector sensor has had a severe affective on the estimation accuracy and has caused little attention until now. In this paper, an AVS measurement system is designed, and an Anisotropic Sparse Bayesian Learning (SBL) method (the A-SBL method) is proposed to model and estimate the anisotropic noise of the AVS system. A high-resolution DOA estimation method is also introduced based on the noise estimation algorithm. The experimental results exhibit the necessity of modeling the anisotropic noise, and the estimation accuracy of the proposed A-SBL method based on the noise model is verified. The comparison of DOA methods shows the superiority of the proposed method, in which the DOA estimation error is not more than 1°. The proposed method’s utility may be found in applications for localization or tracking of targets with prominent acoustic characteristics when the environment is complicated.

Adaptive Grid Refinement Method for DOA Estimation via Sparse Bayesian Learning

In sparse signal recovery methods for direction of arrival (DOA) estimation, a set of uniform angular grid points is usually predefined. Dense grid points will improve the resolution and precision, but increase computational workload distinctly. To improve the efficiency and performance when using coarse initial grid points, an adaptive grid refinement (AGR) sparse Bayesian learning (SBL) method is proposed. The key idea of the proposed method is to adaptively insert new grid points based on the spatial spectrum learned from SBL iterations, as a result, grid points become denser and denser around the potential DOAs. The number of total grid points in the AGR process is much smaller than that of traditional uniform grid points, which enhances the computation efficiency. After the improved on-grid estimation of the AGR process, a post-processing DOA search procedure is implemented to reduce the off-grid DOA error. Furthermore, the proposed method is extended into the wideband case. Simulation results demonstrate that the proposed method has higher computation efficiency and precision than the classical off-grid SBL methods in scenarios of low SNR and limited snapshots. The effectiveness of the proposed method is also validated using the data of the SWellEx-96 ocean acoustic experiment.

A robust sparse Bayesian learning method for the structural damage identification by a mixture of Gaussians

Sparse Bayesian learning methods have been successfully applied to the community of structural damage identification, which commonly assumes that the uncertainties from modeling errors and measurement noises follow Gaussian distribution. However, this assumption typically compromises the accuracy of damage identification because these real uncertainties may not follow a Gaussian distribution. A mixture of Gaussian distributions can more accurately quantify the real uncertainties of damage identification than a Gaussian distribution because it can theoretically approximate any continuous distribution. Motivated by this, we utilized a robust sparse Bayesian learning method to investigate the problem of structural damage identification and further improve the accuracy of damage identification. This method includes a sparse Bayesian learning model with a mixture of Gaussians and an expectation–maximization algorithm based on the Laplace approximation technique. The numerical and experimental results illustrate that our method improves the damage identification accuracy by 6.78% and 11.92% than the existing two sparse Bayesian learning ones, respectively.

A Novel Fast Sparse Bayesian Learning STAP Algorithm for Conformal Array Radar

Space-time adaptive processing (STAP) is an important method of clutter suppression that requires adequate training samples. For an airborne conformal array radar, conventional STAP methods do not have enough training samples to acquire good performance due to the range dependent clutter caused by geometry and the problem of polarization. Sparse-recovery-based STAP (SR-STAP) methods have garnered significant attention in the past few decades because they only require a small number of training samples. Sparse Bayesian Learning (SBL) methods have seen increasing amounts of development due to its robust, self-regularizing nature and because it is not sensitive to user parameters, but it converges slowly. In this paper, a novel fast SBL (NFSBL) method is put forward to increase the rate of convergence. To minimize the SBL penalty function, the proposed method introduces the conjugate function to construct a surrogate function. Additional solution sparsity will be achieved through iteratively minimizing the surrogate function. Then, from the proposed method, we could obtain a more accurate clutter plus noise covariance matrix. Numerical simulation results express that this method could acquire better performance of STAP and improvement in convergence and computational complexity for a conformal array.

Fast estimation of direction of arrival based on sparse Bayesian learning for towed array sonar during manoeuvring

AbstractFor improving performance of the towed array sonar during the manoeuvring period, a processing framework is proposed based on joint estimation of direction of arrival (DOA) and the array shape. The sparse Bayesian learning (SBL) algorithm is utilised to accurately estimate the DOAs of interesting targets. Meanwhile, the towed array shape is modelled as a parabola array, and the array element positions are estimated using the bow of the parabola. Then, an approximate posterior covariance is implemented to the SBL for a fast converging speed required by practical applications. Besides, the co‐prime array structure is considered for the uniform linear array to further reduce the computational load. The numerical simulations have verified the effectiveness of the fast converging SBL method. MAPEX2000 experimental data processing results have shown that the proposed framework performs well in detection of weak targets during slow turns.

A Clutter Suppression Algorithm via Enhanced Sparse Bayesian Learning for Airborne Radar

The traditional space-time adaptive processing (STAP) method based on sparse Bayesian learning (SBL) has the problems of low computational efficiency and slow convergence speed. In this paper, a novel SBL approach based on statistical threshold is proposed to address these issues. To discriminate between the active and inactive atoms of the dictionary, we first develop an adaptive decision test. Next, the adaptive decision test is integrated into the SBL method, which increases its accuracy and convergence rate. Additionally, the detection threshold has an important property that is independent of signal and noise power. Therefore, the adaptive decision test is robust to external changes. Numerous simulations demonstrate that the proposed algorithm has excellent clutter suppression performance and fast convergence rate.

Sparse Bayesian Learning with hierarchical priors for duct mode identification of tonal noise

Fan noise has become an important noise component of civil aviation engines with the increasing bypass ratio. The mode identification method is the key to in-duct fan noise testing. The number of modes that can propagate through the duct increases dramatically for high-frequency in-duct fan noise, which requires a large number of microphones to measure the sound field in the duct. Since the number of modes is usually larger than the number of microphones, it is difficult to realize mode identification. A Sparse Bayesian Learning algorithm for mode identification is proposed to solve this problem in this paper. The in-duct sound field is described by a statistical model, and the inverse problem of mode identification is expressed in a Bayesian framework. The non-convex optimization problem of the cost function is considered, iteratively achieving the sparsest solution via a block coordinate descent algorithm in a majorization-minimization framework. The mode identification method based on Sparse Bayesian Learning has high sparsity and can achieve parameter adaptation. The effectiveness of the Sparse Bayesian Learning method for duct mode identification is verified by numerical simulations and experimental tests. The results show that the mode identification method of Sparse Bayesian Learning can accurately identify the target mode using fewer microphones.

A novel sparse Bayesian learning and its application to fault diagnosis for multistation assembly systems

This article addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause excessive dimensional variation of the product using dimensional measurements. For such problems, the challenge is solving an underdetermined system caused by a common phenomenon in practice; namely, the number of measurements is less than that of the process errors. To address this challenge, this article attempts to solve the following two problems: (i) how to utilize the temporal correlation in the time series data of each process error and (ii) how to apply prior knowledge regarding which process errors are more likely to be process faults. A novel sparse Bayesian learning method is proposed to achieve the above objectives. The method consists of three hierarchical layers. The first layer has parameterized prior distribution that exploits the temporal correlation of each process error. Furthermore, the second and third layers achieve the prior distribution representing the prior knowledge of process faults. Since posterior distributions of process faults are intractable, this article derives approximate posterior distributions via Variational Bayes inference. Numerical and simulation case studies using an actual autobody assembly process are performed to demonstrate the effectiveness of the proposed method.

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion.

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli-Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

Off-grid DOA estimation using improved root sparse Bayesian learning for non-uniform linear arrays

This paper concerns direction of arrival (DOA) estimation based on a sparse Bayesian learning (SBL) approach. We address two inherent problems of this class of DOA estimation methods: (i) a predefined dictionary can generate off-grid problems to a SBL DOA estimator; (ii) a parametric prior generally enforces the solution to be sparse, but the existence of noise can greatly affect the sparsity of the solution. Both of these issues may have a negative impact on the estimation accuracy. In this paper, we propose an improved root SBL (IRSBL) method for off-grid DOA estimation that adopts a coarse grid to generate an initial dictionary. To reduce the bias caused by dictionary mismatch, we integrate the polynomial rooting approach into the SBL method to refine the spatial angle grid. Then, we integrate a constant false alarm rate rule in the SBL framework to enforce sparsity and improve computational efficiency. Finally, we generalize the IRSBL method to the case of non-uniform linear arrays. Numerical analysis demonstrates that the proposed IRSBL method provides improved performance in terms of both estimation accuracy and computational complexity over the most relevant existing method.

Data-Drive Site Characterization for Benchmark Examples: Sparse Bayesian Learning versus Gaussian Process Regression

In this paper, two data-drive site characterization methods, the sparse Bayesian learning (SBL) method and the Gaussian process regression (GPR) method, are benchmarked by a set of virtual ground examples and a real ground example of cone penetration test (CPT) data. The two methods both assume a zero-mean prior Gaussian random field model for the spatial trend, but the strategies of maintaining model simplicity are different. The SBL method produces a simple trend model by adopting sparse basis functions, whereas the GPR method produces a simple trend model by adopting a kernel function governed by few hyperparameters. The accuracy of the two methods in predicting the cone tip resistance (qt) of CPT was quantified by the root-mean square prediction error (RMSE), whereas the accuracy in identifying soil layers was quantified by the identification rate (IR). It was found that the GPR method in general outperforms the SBL method. Further accuracy improvement for the GPR method can be obtained if a clustering analysis based on the Robertson’s soil behavior index (Ic) is conducted.