Sparse Bayesian Learning Framework Research Articles

Sparse Bayesian Learning Based Multi Trajectory Tracking Algorithm For Direction of Arrival Trajectory Estimation

One of the applications of sequential sparse signal reconstruction is multi-target Direction of Arrival (DoA) trajectory estimation. In fact, each member of the support set is equivalent to the DoA of a moving target at each time instant. There is a mapping between the indices of the sparse vector and DoA values in continuous angle space. The key idea of this paper is to use the dynamic information of the continuous angular space to more accurately track sparse vectors and estimate the DoA trajectories of moving sources with time-varying acceleration based on the Sparse Bayesian Learning (SBL) framework. For this purpose, the members of the estimated support set are mapped to the continuous angular space at each instant. Then, the obtained DoAs are assigned to the available DoA trajectories using the Predictive-Description-Length (PDL) algorithm. In the following, the DoA of each source is predicted for the next time using the Kalman filter. Finally, the predicted DoAs are mapped to a sparse vector. The obtained sparse vector is used as the prior information for SBL-based sparse reconstruction. Simulation results show that the proposed algorithm, which is called SBL-MTT (Multi Trajectory Tracking), leads to an accurate reconstruction of successive sparse vectors in application of DoA trajectory estimation of moving sources.

Markov chain-based temporal correlation processing algorithm in reverberant environment by sparse Bayesian learning for acoustic imaging

Identifying sound sources is an important step in noise control, different sound source localization algorithms have been proposed and studied for almost a century. Most of the studies assume an ideal measurement environment, i.e., an anechoic or half-anechoic environment, but there are limited studies discussing localizing sound sources in a reverberation environment. This paper proposes an acoustic imaging method in a reverberation environment based on the sparse Bayesian learning framework. Initially, a sound propagation model was established by accounting for the multipath effects of the sound source in a reverberant environment. Based on the temporal correlation of a Markov chain, the algorithm is further improved in the sparse Bayesian learning framework. By leveraging the temporal correlation the algorithm provides, identifying the true source in a reverberant environment becomes more accurate. Numerical simulation results have shown that the proposed algorithm achieves real sound source localization and eliminates the influence of image sources in contour maps under realistic reverberant environments.

High-Resolution Identification of Sound Sources Based on Sparse Bayesian Learning with Grid Adaptive Split Refinement

Sound source identification technology based on a microphone array has many application scenarios. The compressive beamforming method has attracted much attention due to its high accuracy and high-resolution performance. However, for the far-field measurement problem of large microphone arrays, existing methods based on fixed grids have the defect of basis mismatch. Due to the large number of grid points representing potential sound source locations, the identification accuracy of traditional grid adjustment methods also needs to be improved. To solve this problem, this paper proposes a sound source identification method based on adaptive grid splitting and refinement. First, the initial source locations are obtained through a sparse Bayesian learning framework. Then, higher-weight candidate grids are retained, and local regions near them are split and updated. During the iteration process, Green’s function and the source strength obtained in the previous iteration are multiplied to get the sound pressure matrix. The robust principal component analysis model of the Gaussian mixture separates and replaces the sound pressure matrix with a low-rank matrix. The actual sound source locations are gradually approximated through the dynamically adjusted sound pressure low-rank matrix and optimized grid transfer matrix. The performance of the method is verified through numerical simulations. In addition, experiments on a standard aircraft model are conducted in a wind tunnel and speakers are installed on the model, proving that the proposed method can achieve fast, high-precision imaging of low-frequency sound sources in an extensive dynamic range at long distances.

Millimeter Wave Multi-mode OAM-MIMO Channel Capacity Study

This study examines the theoretical aspects of channel capacity for millimeter wave multi-mode Orbital Angular Momentum (OAM) Multiple Input Multiple Output (MIMO) systems. It begins with a theoretical analysis of these channels, highlighting their importance and potential applications in wireless communications. A Sparse Bayesian Learning (SBL) based Joint Uplink and Downlink Channel Estimation (JUDCE) approach is then employed to estimate the downlink channel using uplink training signals, while accounting for inactive receiving antennas. Exploiting the sparsity of millimeter wave channels, the downlink channel estimation is modeled as a compressed sensing problem using a binary mask matrix. An SBL framework is developed to efficiently tackle this problem. Theoretical and simulation results indicate the proposed method significantly improves channel estimation accuracy and spectral efficiency of downlink transmissions, underscoring its importance for the advancement of future communication technologies.

Multipole transfer matrix model-based sparse Bayesian learning approach for sound source identification

Accurate source identification is key to solving complex flow-induced noise problems, and sources often have non-uniform radiation patterns. At the same time, traditional methods have many application limitations, including the need for prior knowledge of the sound field, as well as inability to apply to coherent sources or coexisting multipoles. A multipole transfer matrix model-based sparse Bayesian learning approach for sound source identification (MT-SBL) is proposed. In this algorithm, the transfer relationship for the multipole radiation patterns of sound sources is established. Then, the signal sparse reconstruction is transformed into an iterative updating problem of the feature parameters under a sparse Bayesian learning (SBL) framework, which leads to the accurate identification of multipole sources. Numerical simulations and experiments on electric speakers in an anechoic environment validate the proposed algorithm. Compared with the existing methods, the algorithm is more advantageous in terms of accuracy, resolution, and computational efficiency. Further experiments were conducted on the identification of supersonic jet noise sources, verifying the effectiveness of the method for identifying strongly directional sound sources.

Sparse Bayesian Learning Approach for Compound Bearing Fault Diagnosis

Compound bearing fault diagnosis is an essentially challenging task due to the mutual interference among multiple fault components. The state-of-the-art methods usually take the potential fault characteristic frequencies as the prior knowledge and then try to recover every fault component by exploiting the impulse signal sparsity. However, they inevitably suffer from algorithmic degradation caused by energy leakage, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -norm approximation, and/or improper parameter selection. To handle these shortcomings, in this paper, we propose a novel sparse Bayesian learning (SBL)-based method for the compound bearing fault diagnosis. We first present a new categorical probabilistic model to efficiently capture the truly-occurred fault components with a truncated feasible domain, which can greatly reduce the energy leakage effect. Then, we devise a more general SBL framework to recover the compound sparse impulse signal under the new categorical probabilistic model. The newly proposed method successfully avoids the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -norm approximation and manual parameter selection, thus it can yield much higher accuracy and robustness. Both simulations and experiments demonstrate the superiority of the developed method.

Approximating the zero-norm penalized sparse signal recovery using a hierarchical Bayesian framework

Sparse Bayesian learning (SBL) with its self-regulation and uncertainty estimation features, has become a popular topic in the field of sparse signal recovery. However, it is a challenging problem to employ zero-norm penalty on signals in the hierarchical framework of SBL. In this paper, an SBL approach that approximates the zero-norm penalized spare signal recovery is proposed based on the idea that signals can be modeled using generalized Gaussian distribution (GGDs). It should be noted that the mean and variance of GGDs are related to its shape parameters, making the direct use of GGDs in Bayesian inference impractical. To solve this problem, we derives a proposition and further build a new hierarchical Bayesian framework (HrBayFw). The proposed HrBayFw is equivalent to assign ℓp-norm penalty to signals, and the parameter p can be designed to approximate 0. Thus, the zero-norm penalized spare signal recovery can be realized using SBL, and the use of the proposition enables tractable marginalization over all parameters. The main advantage of the proposed approach is that it achieves a lower reconstruction error than current Bayesian methods. Numerical simulations evidence that the proposed SBL approach achieves better accuracy performance in terms of normalized-mean-square-error comparing with other contemporary algorithms.

Sparse Bayesian Learning for End-to-End EEG Decoding.

Decoding brain activity from non-invasive electroencephalography (EEG) is crucial for brain-computer interfaces (BCIs) and the study of brain disorders. Notably, end-to-end EEG decoding has gained widespread popularity in recent years owing to the remarkable advances in deep learning research. However, many EEG studies suffer from limited sample sizes, making it difficult for existing deep learning models to effectively generalize to highly noisy EEG data. To address this fundamental limitation, this paper proposes a novel end-to-end EEG decoding algorithm that utilizes a low-rank weight matrix to encode both spatio-temporal filters and the classifier, all optimized under a principled sparse Bayesian learning (SBL) framework. Importantly, this SBL framework also enables us to learn hyperparameters that optimally penalize the model in a Bayesian fashion. The proposed decoding algorithm is systematically benchmarked on five motor imagery BCI EEG datasets ( N=192) and an emotion recognition EEG dataset ( N=45), in comparison with several contemporary algorithms, including end-to-end deep-learning-based EEG decoding algorithms. The classification results demonstrate that our algorithm significantly outperforms the competing algorithms while yielding neurophysiologically meaningful spatio-temporal patterns. Our algorithm therefore advances the state-of-the-art by providing a novel EEG-tailored machine learning tool for decoding brain activity.Code is available at https://github.com/EEGdecoding/Code-SBLEST.

Machine discovery of partial differential equations from spatiotemporal data: A sparse Bayesian learning framework.

This study presents a general framework, namely, Sparse Spatiotemporal System Discovery (S3d), for discovering dynamical models given by Partial Differential Equations (PDEs) from spatiotemporal data. S3d is built on the recent development of sparse Bayesian learning, which enforces sparsity in the estimated PDEs. This approach enables a balance between model complexity and fitting error with theoretical guarantees. The proposed framework integrates Bayesian inference and a sparse priori distribution with the sparse regression method. It also introduces a principled iterative re-weighted algorithm to select dominant features in PDEs and solve for the sparse coefficients. We have demonstrated the discovery of the complex Ginzburg-Landau equation from a traveling-wave convection experiment, as well as several other PDEs, including the important cases of Navier-Stokes and sine-Gordon equations, from simulated data.

Structural damage detection with two-stage modal information and sparse Bayesian learning

Sparse Bayesian learning (SBL) has been proved to be an effective damage detection strategy. In this research, a structural damage detection technique with two-stage modal information is incorporated into the SBL framework. As an approximate representative, the equivalent damage factor requires sufficient sparsity for damage locating in the first stage. To content this, the mode shape energy (MSE) with SBL is performed in the model updating. With limited sensors, more accurate elemental damage will be estimated using mode shapes in the second stage. For further simplified process of damage detection, model reduction method is conducted to decrease both the calculation of eigenvalue and the second derivative corresponding to damage factors. The performance of SBL in damage detection is significantly improved. The accuracy and efficiency of the proposed method is verified by a bridge numerical simulation and a simply supported beam test.

Joint channel and impulse noise estimation based on compressed sensing and Kalman filter for OFDM system

Impulse noise (IN) widely exists in many communication systems, which seriously affects the performance of OFDM communication systems. A joint channel and IN estimation method based on all subcarriers is designed. This method uses a sparse Bayesian learning (SBL) algorithm incorporating forward–backward Kalman filter (FB-Kalman) to tackle the problem of joint channel and IN estimation and data detection for OFDM systems. Firstly, the channel impulse response and IN are regarded as unknown sparse vectors, and a SBL framework using all subcarriers is proposed to estimate the unknown vector. The SBL theory is used based on the prior distribution of variables, and then the forward–backward joint system is established, which applies the data detection simultaneously. We also propose the FB-Kalman implementation algorithm by using the expectation maximization updates. Explicit expressions of mean and covariance matrix of the posterior distribution are derived in the E-step. Simulation results show that the proposed algorithm improves the normalized mean square error and bit error rate performance of OFDM system in the presence of IN communication environment.

Passive localization of wideband near-field sources using Sparse Bayesian learning and envelope alignment

Most studies about passive localization of near-field signals are limited to narrowband sources. In this paper, a novel efficient algorithm is developed for direction of arrival (DOA) and range estimation of wideband near-field sources. Using the specific structure of symmetric linear array, the direction information is extracted and the off-grid Sparse Bayesian learning (SBL) framework is established for DOA estimation. The generalized approximate message passing (GAMP) strategy is applied for fast implementation. Then the envelope aligned approach is proposed for the range estimation in time domain and the linear searching concept is applied to accelerate the computation. Compared with the existing wideband near-field localization methods, the proposed algorithm has better performance of accuracy and resolution probability. Simulation results validate the feasibility and effectiveness of the proposed algorithm.

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.

A novel sparse recovery‐based space‐time adaptive processing algorithm based on gridless sparse Bayesian learning for non‐sidelooking airborne radar

AbstractNon‐sidelooking airborne radar encounters significant non‐stationary and heterogeneous clutter environments, resulting in a severe shortage of samples. Sparse recovery‐based space‐time adaptive processing (SR‐STAP) methods can achieve good clutter suppression performance with limited samples. Nonetheless, grid‐based SR‐STAP algorithms encounter off‐grid effects in non‐sidelooking arrays, which can severely degrade the clutter suppression performance. In this study, the authors propose a novel gridless SR‐STAP method in the continuous spatial‐temporal domain to address the issue of off‐grid effects. Inspired by the fact that sparse Bayesian learning (SBL) framework implicitly performs a structured covariance matrix estimation, the authors reparameterise its cost function to directly estimate the block‐Toeplitz structured matrix from the measurements in a gridless manner. Since the proposed cost function is non‐convex, we utilise a majorisation‐minimisation‐based iterative procedure to estimate the clutter covariance matrix. Finally, using the standard concept of semidefinite programming, the authors derive a convex gridless implementation of the SBL cost function for uniformly sampled radar systems. Extensive simulation experiments demonstrate the exceptional clutter suppression and target detection performance of the proposed algorithm.

Multitask Sparse Bayesian Channel Estimation for Turbo Equalization in Underwater Acoustic Communications

In this article, a multitask sparse Bayesian learning channel estimation based on factor graphs (MT-SBL-FG) for turbo equalization (TEQ) in underwater acoustic (UWA) communications is proposed. Based on the framework of multitask sparse Bayesian learning, the received data are divided into subblocks and the channel estimation (CE) of each subblock is regarded as a task. Considering the time-varying channel in UWA communications and the CE error in turbo equalization, a factor graph is proposed for the multitask CE of the subblocks. Based on the factor graph, a message-passing algorithm with weighting factor is derived. The performance of channel estimation is improved by utilizing the temporal correlation between the subblocks and the sparsity of the UWA channel. The proposed algorithm has been tested by the underwater trial data collected in an experiment conducted in Qiandao Lake, Hangzhou, China, in May 2016. We have verified that the proposed algorithm outperforms other CE algorithms in terms of the bit error rate (BER).

Underdetermined direction of arrival estimation for multiple input and multiple outputs sparse channel based on Bayesian learning framework

Direction of arrival (DOA) estimation for a sparse channel has attracted serious attention recently. Better signal analysis and denoising achieve accuracy in DOA determination. This paper proposes an underdetermined DOA estimation for multiple input and multiple outputs (MIMO) sparse channels. A novel multi-kernel-based non-negative sparse Bayesian learning (MK NNSBL) framework is implemented using the multiplied form of basis vector within the manifold matrix for a defined grid. Meanwhile, virtual antenna locations are reconfigured by exploiting the conventional cuckoo search algorithm (CCSA) for the fine reception of incoming signals on a nonuniform linear array (NULA). The simulated results reveal that the novel approach outperforms in its optimal root mean square error (RMSE) for various signal-to-noise ratio (SNR) limits and the compilation time. The convergence comparative graph indicates the improved performance in the proposed framework over existing algorithms.

Sparse Bayesian learning approach for discrete signal reconstruction

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL framework. To overcome this challenge, we introduce a novel discretization enforcing prior to exploit the knowledge of the discrete nature of the signal-of-interest. By integrating the discretization enforcing prior into the SBL framework and applying the variational Bayesian inference (VBI) methodology, we devise an alternating optimization algorithm to jointly characterize the finite-alphabet feature and reconstruct the unknown signal. When the measurement matrix is i.i.d. Gaussian per component, we further embed the generalized approximate message passing (GAMP) into the VBI-based method, so as to directly adopt the ideal prior and significantly reduce the computational burden. Simulation results demonstrate substantial performance improvement of the two proposed methods over existing schemes. Moreover, the GAMP-based variant outperforms the VBI-based method with i.i.d. Gaussian measurement matrices but it fails to work for non i.i.d. Gaussian matrices.

Sparse Bayesian learning for sparse signal recovery using [formula omitted]-norm

Sparse signal recovery is an important technique for acoustic direction-of-arrival (DOA) estimation which is widely used in applications such as humanoid robots and voice control loudspeakers. However, the estimation accuracy performance is limited by the size of platform and the sound wavelength. To improve the accuracy performance, we propose a sparse signal recovery approach for acoustic DOA estimation based on a hierarchical formulation of the generalized Gaussian prior with a shape parameter q=1/2. Specifically, a sparse Bayesian learning (SBL) framework is built using ℓ1/2-norm priors to efficiently utilize the space sparsity nature of acoustic sources. The priors, built primarily based on a hierarchical structure with a couple of layers, are used for modeling the sparse signals. Then, an expectation–maximization algorithm is proposed for inference and parameter learning. The estimation accuracy performance of the proposed approach is verified in terms of sparse signal recovery and acoustic DOA estimation. The experimental results exhibit that the proposed method achieves the highest recovery accuracy performance and has the lowest root mean square error (RMSE) in contrast with the state-of-the-art sparse signal recovery methods.

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.

Markov chain-based frequency correlation processing algorithm for wideband DOA estimation

For wideband direction-of-arrival (DOA) estimation, a Markov Chain-based frequency correlation processing algorithm is proposed in the sparse Bayesian learning (SBL) framework, called the MC-FC-SBL algorithm. The algorithm adopts a new frequency-domain structural correlation prior model, which can be adaptively changed to accommodate multi-wideband sources scenarios with different frequency characteristics. Specifically, the MC-FC-SBL algorithm separates the amplitudes and supports of the sparse coefficients through the spike-and-slab model, and judges the frequency correlation by the consistency of the supports at adjacent frequency points. The support prior is represented by a Gaussian mixture model, and the switching between the supports at adjacent frequency points is simulated by a Markov chain. The MC-FC-SBL algorithm performs the DOA estimation in the SBL framework to determine the adaptive prior of each coefficient by evaluating the appropriate frequency-correlation structural pattern. In addition, the MC-FC-SBL algorithm is processed in the real-domain, and the real and imaginary parts of complex signal are regarded as multi-snapshot data to implement joint sparse constraints, which can reduce the computational complexity and improve the algorithm performance. Numerical simulations demonstrate that the MC-FC-SBL algorithm is superior to the existing algorithms for wideband DOA estimation, and the results of field experiments show that this algorithm is still effective when the source is weak.