Joint Multi-Domain Channel Estimation Based on Sparse Bayesian Learning for OTFS System

Since orthogonal time-frequency space(OTFS)can effectively handle the problems caused by Doppler effect in high-mobility environment,it has gradually become a promising candidate for modulation scheme in the next generation of mobile communication.However,the inter-Doppler interference(IDI)problem caused by fractional Doppler poses great challenges to channel estimation.To avoid this problem,this paper proposes a joint time and delayDoppler(DD)domain based on sparse Bayesian learning(SBL)channel estimation algorithm.Firstly,we derive the original channel response(OCR)from the time domain channel impulse response(CIR),which can reflect the channel variation during one OTFS symbol.Compare with the traditional channel model,the OCR can avoid the IDI problem.After that,the dimension of OCR is reduced by using the basis expansion model(BEM)and the relationship between the time and DD domain channel model,so that we have turned the underdetermined problem into an overdetermined problem.Finally,in terms of sparsity of channel in delay domain,SBL algorithm is used to estimate the basis coefficients in the BEM without any priori information of channel.The simulation results show the effectiveness and superiority of the proposed channel estimation algorithm.

Vector Approximate Message Passing with Sparse Bayesian Learning for Gaussian Mixture Prior

Compressed sensing(CS)aims for seeking appropriate algorithms to recover a sparse vector from noisy linear observations.Currently,various Bayesian-based algorithms such as sparse Bayesian learning(SBL)and approximate message passing(AMP)based algorithms have been proposed.For SBL,it has accurate performance with robustness while its computational complexity is high due to matrix inversion.For AMP,its performance is guaranteed by the severe restriction of the measurement matrix,which limits its application in solving CS problem.To overcome the drawbacks of the above algorithms,in this paper,we present a low complexity algorithm for the single linear model that incorporates the vector AMP(VAMP)into the SBL structure with expectation maximization(EM).Specifically,we apply the variance auto-tuning into the VAMP to implement the E step in SBL,which decrease the iterations that require to converge compared with VAMP-EM algorithm when using a Gaussian mixture(GM)prior.Simulation results show that the proposed algorithm has better performance with high robustness under various cases of difficult measurement matrices.

DOA estimation based on multi-frequency joint sparse Bayesian learning for passive radar

This paper considers multi-frequency passive radar and develops a multi-frequency joint direction of arrival(DOA)estimation algorithm to improve estimation accuracy and resolution.The developed algorithm exploits the sparsity of targets in the spatial domain.Specifically,we first extract the required frequency channel data and acquire the snapshot data through a series of preprocessing such as clutter suppression,coherent integration,beamforming,and constant false alarm rate(CFAR)detection.Then,based on the framework of sparse Bayesian learning,the target’s DOA is estimated by jointly extracting the multi-frequency data via evidence maximization.Simulation results show that the developed algorithm has better estimation accuracy and resolution than other existing multi-frequency DOA estimation algorithms,especially under the scenarios of low signalto-noise ratio(SNR)and small snapshots.Furthermore,the effectiveness is verified by the field experimental data of a multi-frequency FM-based passive radar.

Sparse Bayesian learning in ISAR tomography imaging

Inverse synthetic aperture radar(ISAR) imaging can be regarded as a narrow-band version of the computer aided tomography(CT). The traditional CT imaging algorithms for ISAR, including the polar format algorithm(PFA) and the convolution back projection algorithm(CBP), usually suffer from the problem of the high sidelobe and the low resolution. The ISAR tomography image reconstruction within a sparse Bayesian framework is concerned. Firstly, the sparse ISAR tomography imaging model is established in light of the CT imaging theory. Then, by using the compressed sensing(CS) principle, a high resolution ISAR image can be achieved with limited number of pulses. Since the performance of existing CS-based ISAR imaging algorithms is sensitive to the user parameter, this makes the existing algorithms inconvenient to be used in practice. It is well known that the Bayesian formalism of recover algorithm named sparse Bayesian learning(SBL) acts as an effective tool in regression and classification,which uses an efficient expectation maximization procedure to estimate the necessary parameters, and retains a preferable property of the l0-norm diversity measure. Motivated by that, a fully automated ISAR tomography imaging algorithm based on SBL is proposed.Experimental results based on simulated and electromagnetic(EM) data illustrate the effectiveness and the superiority of the proposed algorithm over the existing algorithms.

EARLY CATARACT DETECTION BY DYNAMIC LIGHT SCATTERING WITH SPARSE BAYESIAN LEARNING

Dynamic light scattering(DLS)is a promising technique for early cataract detection and for studying cataractogenesis.A novel probabilistic analysis tool,the sparse Bayesian learning(SBL)algorithm,is described for reconstructing the most-probable size distribution ofα-crystallin and their aggregates in an ocular lens from the DLS data.The performance of the algorithm is evaluated by analyzing simulated correlation data from known distributions and DLS data from the ocular lenses of a fetal calf,a Rhesus monkey,and a man,so as to establish the required efficiency of the SBL algorithm for clinical studies.

Off-Grid Sparse Bayesian Inference with Biased Total Grids for Dense Time Delay Estimation

For dense time delay estimation(TDE),when multiple time delays are located within a grid interval,it is dificult for the existing sparse Bayesian learning/inference(SBL/SBI)methods to obtain high estimation accuracy to meet the application requirements.To solve this problem,this paper proposes a method named off-grid sparse Bayesian inference-biased total grid(OGSBI-BTG),where a mesh evolution process is conducted to move the total grids iteratively based on the position of the off-grid between two grids.The proposed method updates the off-grid dictionary matrix by further reconstructing an optimum mesh and offsetting the off-grid vector.Experimental results demonstrate that the proposed approach performs better than other state-of-the-art SBI methods and multiple signal classification even when the grid interval is larger than the gap of true time delays.In this paper,the time domain model and frequency domain model of TDE are studied.

Online identification of time-varying dynamical systems for industrial robots based on sparse Bayesian learning

Nowadays, industrial robots have been widely used in manufacturing, healthcare, packaging, and more. Choosing robots in these applications mainly attributes to their repeatability and precision. However, prolonged and loaded operations can deteriorate the accuracy and efficiency of industrial robots due to the unavoidable accumulated kinematical and dynamical errors. This paper resolves these aforementioned issues by proposing an online time-varying sparse Bayesian learning(SBL) method to identify dynamical systems of robots in real-time. The identification of dynamical systems for industrial robots is cast as a sparse linear regression problem. By constructing the dictionary matrix, the parameters of the robot dynamics are effectively estimated via a re-weighted1-minimization algorithm. Online recursive methods are integrated into SBL to achieve real-time system identification. By including sparsity and promoting online learning, the proposed method can handle time-varying dynamical systems and therefore improve operational stability and accuracy. Experimental results on both simulated and real selective compliance assembly robot arm(SCARA) robots have demonstrated the effectiveness of the proposed method for industrial robots.

On fast estimation of direction of arrival for underwater acoustic target based on sparse Bayesian learning

The Direction of Arrival （DOA） estimation methods for underwater acoustic target using Temporally Multiple Sparse Bayesian Learning （TMSBL） as the reconstructing algorithm have the disadvantage of slow computing speed. To solve this problem, a fast underwater acoustic target direction of arrival estimation was proposed. Analyzing the model characteristics of block-sparse Bayesian learning framework for DOA estimation, an algorithm was proposed to obtain the value of core hyper-parameter through MacKay＇s fixed-point method to estimate the DOA. By this process, it will spend less time for computation and provide more superior recovery performance than TMSBL algorithm. Simulation results verified the feasibility and effectiveness of the proposed algorithm.

DOA Estimation Based on Root Sparse Bayesian Learning Under Gain and Phase Error

The direction of arrival(DOA)is approximated by first-order Taylor expansion in most of the existing methods,which will lead to limited estimation accuracy when using coarse mesh owing to the off-grid error.In this paper,a new root sparse Bayesian learning based DOA estimation method robust to gain-phase error is proposed,which dynamically adjusts the grid angle under coarse grid spacing to compensate the off-grid error and applies the expectation maximization(EM)method to solve the respective iterative formula-based on the prior distribution of each parameter.Simulation results verify that the proposed method reduces the computational complexity through coarse grid sampling while maintaining a reasonable accuracy under gain and phase errors,as compared to the existing methods.

基于吉布斯采样的稀疏水声信道估计方法

The estimation of sparse underwater acoustic(UWA)channels can be regarded as an inference problem involving hidden variables within the Bayesian framework.While the classical sparse Bayesian learning(SBL),derived through the expectation maximization(EM)algorithm,has been widely employed for UWA channel estimation,it still differs from the real posterior expectation of channels.In this paper,we propose an approach that combines variational inference(VI)and Markov chain Monte Carlo(MCMC)methods to provide a more accurate posterior estimation.Specifically,the SBL is first re-derived with VI,allowing us to replace the posterior distribution of the hidden variables with a variational distribution.Then,we determine the full conditional probability distribution for each variable in the variational distribution and then iteratively perform random Gibbs sampling in MCMC to converge the Markov chain.The results of simulation and experiment indicate that our estimation method achieves lower mean square error and bit error rate compared to the classic SBL approach.Additionally,it demonstrates an acceptable convergence speed.

Synthetic aperture radar imaging based on attributed scatter model using sparse recovery techniques

The sparse recovery algorithms formulate synthetic aperture radar （SAR） imaging problem in terms of sparse representation （SR） of a small number of strong scatters＇ positions among a much large number of potential scatters＇ positions, and provide an effective approach to improve the SAR image resolution. Based on the attributed scatter center model, several experiments were performed with different practical considerations to evaluate the performance of five representative SR techniques, namely, sparse Bayesian learning （SBL）, fast Bayesian matching pursuit （FBMP）, smoothed 10 norm method （SL0）, sparse reconstruction by separable approximation （SpaRSA）, fast iterative shrinkage-thresholding algorithm （FISTA）, and the parameter settings in five SR algorithms were discussed. In different situations, the performances of these algorithms were also discussed. Through the comparison of MSE and failure rate in each algorithm simulation, FBMP and SpaRSA are found suitable for dealing with problems in the SAR imaging based on attributed scattering center model. Although the SBL is time-consuming, it always get better performance when related to failure rate and high SNR.

Mutation detection and fast identification of switching system based on data-driven method

In the engineering field,switching systems have been extensively studied,where sudden changes of parameter value and structural form have a significant impact on the operational performance of the system.Therefore,it is important to predict the behavior of the switching system,which includes the accurate detection of mutation points and rapid reidentification of the model.However,few efforts have been contributed to accurately locating the mutation points.In this paper,we propose a new measure of mutation detection—the threshold-based switching index by analogy with the Lyapunov exponent.We give the algorithm for selecting the optimal threshold,which greatly reduces the additional data collection and the relative error of mutation detection.In the system identification part,considering the small data amount available and noise in the data,the abrupt sparse Bayesian regression(abrupt-SBR)method is proposed.This method captures the model changes by updating the previously identified model,which requires less data and is more robust to noise than identifying the new model from scratch.With two representative dynamical systems,we illustrate the application and effectiveness of the proposed methods.Our research contributes to the accurate prediction and possible control of switching system behavior.

Data-Driven Discovery of Stochastic Differential Equations

Stochastic differential equations(SDEs)are mathematical models that are widely used to describe complex processes or phenomena perturbed by random noise from different sources.The identification of SDEs governing a system is often a challenge because of the inherent strong stochasticity of data and the complexity of the system’s dynamics.The practical utility of existing parametric approaches for identifying SDEs is usually limited by insufficient data resources.This study presents a novel framework for identifying SDEs by leveraging the sparse Bayesian learning(SBL)technique to search for a parsimonious,yet physically necessary representation from the space of candidate basis functions.More importantly,we use the analytical tractability of SBL to develop an efficient way to formulate the linear regression problem for the discovery of SDEs that requires considerably less time-series data.The effectiveness of the proposed framework is demonstrated using real data on stock and oil prices,bearing variation,and wind speed,as well as simulated data on well-known stochastic dynamical systems,including the generalized Wiener process and Langevin equation.This framework aims to assist specialists in extracting stochastic mathematical models from random phenomena in the natural sciences,economics,and engineering fields for analysis,prediction,and decision making.

Multimode Process Monitoring Based on the Density-Based Support Vector Data Description

Complex industry processes often need multiple operation modes to meet the change of production conditions. In the same mode,there are discrete samples belonging to this mode. Therefore,it is important to consider the samples which are sparse in the mode.To solve this issue,a new approach called density-based support vector data description( DBSVDD) is proposed. In this article,an algorithm using Gaussian mixture model( GMM) with the DBSVDD technique is proposed for process monitoring. The GMM method is used to obtain the center of each mode and determine the number of the modes. Considering the complexity of the data distribution and discrete samples in monitoring process,the DBSVDD is utilized for process monitoring. Finally,the validity and effectiveness of the DBSVDD method are illustrated through the Tennessee Eastman( TE) process.

Data-driven discovery of linear dynamical systems from noisy data

In modern science and engineering disciplines,data-driven discovery methods play a fundamental role in system modeling,as data serve as the external representations of the intrinsic mechanisms within systems.However,empirical data contaminated by process and measurement noise remain a significant obstacle for this type of modeling.In this study,we have developed a data-driven method capable of directly uncovering linear dynamical systems from noisy data.This method combines the Kalman smoothing and sparse Bayesian learning to decouple process and measurement noise under the expectation-maximization framework,presenting an analytical method for alternate state estimation and system identification.Furthermore,the discovered model explicitly characterizes the probability distribution of process and measurement noise,as they are essential for filtering,smoothing,and stochastic control.We have successfully applied the proposed algorithm to several simulation systems.Experimental results demonstrate its potential to enable linear dynamical system discovery in practical applications where noise-free data are intractable to capture.

Combined UAMP and MF Message Passing Algorithm for Multi-Target Wideband DOA Estimation with Dirichlet Process Prior

When estimating the direction of arrival (DOA) of wideband signals from multiple sources, the performance of sparse Bayesian methods is influenced by the frequency bands occupied by signals in different directions. This is particularly true when multiple signal frequency bands overlap. Message passing algorithms (MPA) with Dirichlet process (DP) prior can be employed in a sparse Bayesian learning (SBL) framework with high precision. However, existing methods suffer from either high complexity or low precision. To address this, we propose a low-complexity DOA estimation algorithm based on a factor graph. This approach introduces two strong constraints via a stretching transformation of the factor graph. The first constraint separates the observation from the DP prior, enabling the application of the unitary approximate message passing (UAMP) algorithm for simplified inference and mitigation of divergence issues. The second constraint compensates for the deviation in estimation angle caused by the grid mismatch problem. Compared to state-of-the-art algorithms, our proposed method offers higher estimation accuracy and lower complexity.

ESTIMATION AND UNCERTAINTY QUANTIFICATION FOR PIECEWISE SMOOTH SIGNAL RECOVERY

This paper presents an application of the sparse Bayesian learning(SBL)algorithm to linear inverse problems with a high order total variation(HOTV)sparsity prior.For the problem of sparse signal recovery,SBL often produces more accurate estimates than maximum a posteriori estimates,including those that useℓ1 regularization.Moreover,rather than a single signal estimate,SBL yields a full posterior density estimate which can be used for uncertainty quantification.However,SBL is only immediately applicable to problems having a direct sparsity prior,or to those that can be formed via synthesis.This paper demonstrates how a problem with an HOTV sparsity prior can be formulated via synthesis,and then utilizes SBL.This expands the class of problems available to Bayesian learning to include,e.g.,inverse problems dealing with the recovery of piecewise smooth functions or signals from data.Numerical examples are provided to demonstrate how this new technique is effectively employed.

Multi-dimensional scenario forecast for generation of multiple wind farms

A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed.In the proposed approach,support vector machine(SVM)is applied for the spot forecast of wind power generation.The probability density function(PDF)of the SVM forecast error is predicted by sparse Bayesian learning(SBL),and the spot forecast result is corrected according to the error expectation obtained.The copula function is estimated using a Gaussian copula-based dynamic conditional correlation matrix regression(DCCMR)model to describe the correlation among the errors.And the multidimensional scenario is generated with respect to the estimated marginal distributions and the copula function.Test results on three adjacent wind farms illustrate the effectiveness of the proposed approach.

Deep adaptive control with online identification for industrial robots

Derivation of control equations from data is a critical problem in numerous scientific and engineering fields.The inverse dynamic control of robot manipulators in the field of industrial robot research is a key example.Traditionally,researchers needed to obtain the robot dynamic model through physical modeling methods before developing controllers.However,the robot dynamic model and suitable control methods are often elusive and difficult to tune,particularly when dealing with real dynamical systems.In this paper,we combine an enhanced online sparse Bayesian learning(OSBL)algorithm and a model reference adaptive control method to obtain a data-driven modeling and control strategy from data containing noise;this strategy can be applied to dynamical systems.In particular,we use a sparse Bayesian approach,relying only on some prior knowledge of its physics,to extract an accurate mechanistic model from the measured data.Unmodeled parameters are further identified from the modeling error through a deep neural network(DNN).By combining the identification model with a model reference adaptive control approach,a general deep adaptive control(DAC)method is obtained,which can tolerate unmodeled dynamics.The adaptive update law is derived from Lyapunov’s stability criterion,which guarantees the asymptotic stability of the system.Finally,the Enhanced OSBL identification method and DAC scheme are applied on a six-degree-of-freedom industrial robot,and the effectiveness of the proposed method is verified.

Application of kernel methods in signals modulation classification

A new approach to common signals classification of relevance vector machine （RVM） was presented and two signal classifiers based on kernel methods of support vector machine （SVM） and RVM were compared and analyzed. First several robust features of signals were extracted as the input of classifiers, then the kernel thought was used to map feature vectors impliedly to the high dimensional feature space, and multi-class RVM and SVM classifiers were designed to complete AM, CW, SSB, MFSK and MPSK signals recognition. Simulation result showed that when chose proper parameter, RVM and SVM had comparable accuracy but RVM had less learning time and basis functions. The classification speed of RVM is much faster than SVM.