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.

Probabilistic outlier detection for sparse multivariate geotechnical site investigation data using Bayesian learning

Various uncertainties arising during acquisition process of geoscience data may result in anomalous data instances(i.e.,outliers)that do not conform with the expected pattern of regular data instances.With sparse multivariate data obtained from geotechnical site investigation,it is impossible to identify outliers with certainty due to the distortion of statistics of geotechnical parameters caused by outliers and their associated statistical uncertainty resulted from data sparsity.This paper develops a probabilistic outlier detection method for sparse multivariate data obtained from geotechnical site investigation.The proposed approach quantifies the outlying probability of each data instance based on Mahalanobis distance and determines outliers as those data instances with outlying probabilities greater than 0.5.It tackles the distortion issue of statistics estimated from the dataset with outliers by a re-sampling technique and accounts,rationally,for the statistical uncertainty by Bayesian machine learning.Moreover,the proposed approach also suggests an exclusive method to determine outlying components of each outlier.The proposed approach is illustrated and verified using simulated and real-life dataset.It showed that the proposed approach properly identifies outliers among sparse multivariate data and their corresponding outlying components in a probabilistic manner.It can significantly reduce the masking effect(i.e.,missing some actual outliers due to the distortion of statistics by the outliers and statistical uncertainty).It also found that outliers among sparse multivariate data instances affect significantly the construction of multivariate distribution of geotechnical parameters for uncertainty quantification.This emphasizes the necessity of data cleaning process(e.g.,outlier detection)for uncertainty quantification based on geoscience data.

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.

OTFS系统SBL-Turbo压缩感知信道估计算法

针对正交时频空调制(OTFS)系统由多普勒频移引起的信道估计准确度下降的问题,本文提出了一种联合无线信道在时延-多普勒域稀疏特性的SBL-Turbo压缩感知信道估计算法。首先,对时延-多普勒域稀疏信道建模,使其服从以噪声功率为条件的高斯先验分布,利用稀疏贝叶斯学习模块估计得到稀疏信道的均值与方差,并结合期望最大化算法更新高斯先验模型中的参数。其次,引入了LMMSE(线性最小均方误差)估计器模块,该模块对稀疏信道的后验分布进行再估计,提高估计的准确度。通过对每个模块估计得到的信道后验分布进行数据处理,使得模块的输入值与输出值解耦,进而减少模块间的错误传播。最后,两个模块采用Turbo结构迭代估计信道的后验分布,得到信道状态信息。实验结果表明,相较于其他估计方法,该算法能够显著提高信道估计的精度,并且改善系统的误码率性能,能够有效地解决OTFS系统中由多普勒频移引起的信道估计问题。

Learning Bayesian networks by constrained Bayesian estimation

Bayesian networks (BNs) have become increasingly popular in recent years due to their wide-ranging applications in modeling uncertain knowledge. An essential problem about discrete BNs is learning conditional probability table (CPT) parameters. If training data are sparse, purely data-driven methods often fail to learn accurate parameters. Then, expert judgments can be introduced to overcome this challenge. Parameter constraints deduced from expert judgments can cause parameter estimates to be consistent with domain knowledge. In addition, Dirichlet priors contain information that helps improve learning accuracy. This paper proposes a constrained Bayesian estimation approach to learn CPTs by incorporating constraints and Dirichlet priors. First, a posterior distribution of BN parameters is developed over a restricted parameter space based on training data and Dirichlet priors. Then, the expectation of the posterior distribution is taken as a parameter estimation. As it is difficult to directly compute the expectation for a continuous distribution with an irregular feasible domain, we apply the Monte Carlo method to approximate it. In the experiments on learning standard BNs, the proposed method outperforms competing methods. It suggests that the proposed method can facilitate solving real-world problems. Additionally, a case study of Wine data demonstrates that the proposed method achieves the highest classification accuracy.

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 l0 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.

一种基于稀疏贝叶斯学习的离网DOA估计算法

本文提出一种基于稀疏贝叶斯学习的改进离网DOA估计算法,以提升非理想测向环境下在低信噪比、低快拍数时的DOA估计性能,称之为MOGSBL算法。本算法将信号源方位区间进行离散化,得到方位离散网格。为阵列接收信号建立稀疏贝叶斯模型,将网格节点修正量设为模型超参数。采用期望最大化算法迭代更新网格节点修正量,使更新后的网格节点更接近真实源信号方位。为了检验MOGSBL算法的性能,本文进行了大量的数值实验,并将MOGSBL算法的DOA估计结果与RSBL算法、OGSBL算法和L1-SVD算法进行对比。在不同信噪比和不同快拍数时,MOGSBL算法均能清晰分辨方位很接近的两个信号源,角度分辨率明显高于RSBL算法、OGSBL算法和L1-SVD算法。随着信噪比和快拍数的增加,4种算法的RMSE均逐渐减小。但MOGSBL算法的RMSE明显低于RSBL算法、OGSBL算法和L1-SVD算法,且RSBL算法、OGSBL算法优于L1-SVD算法。实验还分析了方向测试范围的离散网格节点数对DOA估计的影响,发现细密的离散网格可以提高DOA估计精度,但DOA估计的计算量会增加。且在任意网格节点数时,相比于RSBL算法、OGSBL算法和L1-SVD算法,本文的MOGSBL算法均具有最低的RMSE和最短的计算时间。

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.

基于频率着色的稀疏贝叶斯宽带波达角估计方法

为了提升稀疏贝叶斯(Sparse Bayesian Learning,SBL)算法在干扰环境下对目标信号的检测能力,提出将频率着色技术(Frequency Coloring,FC)推广至SBL算法中。在SBL-FC算法中,首先将阵列接收信号通过傅里叶变换转换至各个子带,在各子带内利用SBL算法进行波达角估计,输出功率谱。不同于常规的SBL算法仅将各子带的功率谱进行简单地叠加,算法考虑干扰和目标频谱结构的差异性,对各子带进行不同的着色,使得干扰和目标轨迹在方位时间历程图上对应于不同的颜色,从而使得目标轨迹更易被提取。数值仿真和实验数据分析表明,利用目标和干扰频谱结构的差异性可有效提升SBL算法在干扰环境下对目标信号的检测能力。

基于共同稀疏贝叶斯学习的多频等效源近场声全息方法

现有基于压缩感知的等效源近场声全息方法通常采用基于单频处理的单测量向量模型进行声场重建,此模型存在噪声鲁棒性较差以及重建精度不足的问题。实际中噪声源往往具有宽频特征,同一位置处不同频率的等效源源强聚集从而呈现共同稀疏特性,若充分利用源强的共同稀疏特性,可以改善重建性能。因此,提出一种基于共同稀疏贝叶斯学习的多频等效源近场声全息方法。在该方法中,首先采用多频协同处理,构建多频等效源近场声全息模型;然后为等效源源强施加共同稀疏约束,并使用共同稀疏贝叶斯学习方法求解等效源源强。与单频等效源近场声全息方法相比,所提方法可以获得更高的重建精度和更好的噪声鲁棒性。通过单极子声源仿真和小音箱试验验证了所提方法的优越性。

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BSBL-BO算法的DME脉冲干扰抑制方法

针对测距仪(distance measure equipment,DME)信号干扰L频段数字航空通信系统1(L-band digital aeronautical communication system 1,L-DACS1)正交频分复用(orthogonal frequency-division multiplexing,OFDM)接收机的问题,提出基于块稀疏贝叶斯学习边界优化(block sparsEbayesian learning-thEbound optimization,BSBL-BO)算法的DME脉冲干扰抑制方法。首先,利用OFDM接收机空子载波不传输有用信号的特点构造针对DME脉冲干扰信号的压缩感知模型;然后基于BSBL-BO算法重构DME脉冲干扰信号;最后在时域进行干扰消除。仿真结果表明,该方法比已有的脉冲干扰抑制方法具有更高的重构精度和更快的运算速度,进一步降低了OFDM接收机的误比特率,提高了L-DACS1系统前向链路传输性能。

一种联合SBL和DTW的叠前道集剩余时差校正方法

基于动态时间规整的叠前道集剩余时差校正方法存在动态时间规整算法对噪声敏感,准确计算规整路径困难;算法采用逐点搬家法,直接对地震道作剩余时差校正容易引起地震波形畸变的问题。提出一种联合稀疏贝叶斯学习(Sparse Bayesian Learning,SBL)和动态时间规整(Dynamic Time Warping,DTW)的叠前道集剩余时差校正方法,采用SBL对地震道集进行稀疏表示,再利用DTW对稀疏表示结果进行剩余时差校正,处理后重构地震记录。结果表明,SBL具有良好的噪声鲁棒性,较少的局部最小值,以及全局最优解同时也是最稀疏解,稀疏分解后得到地下地层单位冲击响应,消除了子波影响,再进行时差校正就能避免波形畸变,同时实现了高保真剩余时差校正和随机噪声压制。数值模拟和实际资料处理结果表明该方法具有良好的应用效果。

基于EBSBL-BO算法的L-DACS系统干扰抑制方法

L频段数字航空通信系统(L-band digital aviation communication system,L-DACS)是未来面向航路阶段的空地数据链路,其工作频段部署在两个测距仪(distance measure equipment,DME)工作频段之间,为了消除测距仪产生的高功率脉冲信号对L-DACS系统前向链路正交频分复用接收机的干扰,本文提出基于扩展稀疏贝叶斯-边界优化(extended block sparse Bayesian learning-boundary optimization,EBSBL-BO)算法的高功率DME脉冲干扰抑制方法。首先,利用L-DACS系统正交频分复用接收机的空子载波建立DME干扰信号压缩感知模型;然后,基于EBSBL-BO算法对DME信号进行重构;最后将高功率DME脉冲信号在时域消除。仿真结果显示:本文算法与其他稀疏贝叶斯重构算法相比,本文算法DME脉冲信号重构精度更高,正交频分复用接收机误码率更低,可有效改善L-DACS系统正交频分复用接收性能。

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.

基于广义模式耦合稀疏Bayesian学习的1-Bit压缩感知

在1-Bit压缩感知(compressive sensing,CS)框架下,将信号的稀疏结构先验引入广义稀疏Bayesian学习(generalized sparse Bayesian learning,Gr-SBL),研究基于Gr-SBL的1-Bit CS重构。将广义线性模型与模式耦合稀疏Bayesian学习相结合,提出了一种基于广义模式耦合稀疏Bayesian学习1-Bit CS重构算法,简称为1-Bit Gr-PC-SBL算法。该算法将1-Bit CS重构问题迭代地分解成一系列标准CS重构问题,在信号稀疏模式未知的情况下,基于模式耦合稀疏Bayesian学习实现信号重构。进而,引入阈值自适应的二进制量化,设计了自适应阈值的1-Bit Gr-PC-SBL算法,进一步提升了算法的信号重构性能。