Many signal processing applications require estimation of time-varying sparse signals, potentially with the knowledge of an imperfect dynamics model. In this paper, we propose an algorithm for dynamic filtering of time-varying sparse signals based on the sparse Bayesian learning (SBL) framework. The key idea underlying the algorithm, termed SBL-DF, is the incorporation of a signal prediction generated from a dynamics model and estimates of previous time steps into the hyperpriors of the SBL probability model. The proposed algorithm is robust to imperfect dynamics models (due to the propagation of dynamics information through higher-order statistics), robust to certain undesirable dictionary properties such as coherence (due to properties of the SBL framework), allows the use of arbitrary dynamics models, and requires the tuning of fewer parameters than many other dynamic filtering algorithms do. We also extend the fast marginal likelihood SBL inference procedure to the informative hyperprior setting to create a particularly efficient version of the SBL-DF algorithm. Numerical simulations show that SBL-DF converges much faster and to more accurate solutions than standard SBL and other dynamical filtering algorithms. In particular, we show that SBL-DF outperforms state of the art algorithms when the dictionary contains challenging structure such as coherence and column scaling, as is found in many practical applications.
A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements
School of Engineering and Applied Science, Ahmedabad University（艾哈迈达巴德大学工程与应用科学学院）；Department of Electrical Engineering, Indian Institute of Technology (BHU) Varanasi（印度理工学院（BHU）瓦拉纳西分校电气工程系）；ELLIS Institute Finland（芬兰ELLIS研究所）；Department of Electrical Engineering and Automation, Aalto University（阿尔托大学电气工程与自动化系）
TrackDiffuser: Nearly Model-Free Bayesian Filtering with Diffusion Model
Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University（同济大学上海智能自主系统研究院）；School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）；School of Aeronautics and Astronautics, Shanghai Jiaotong University（上海交通大学航空航天学院）；Shanghai Zhangjiang Institute of Mathematics（上海张江数学研究院）；School of Computer Science and Technology, East China Normal University（华东师范大学计算机科学与技术学院）
