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Finite‐time distributed block‐decomposed information filter for nonlinear systems with colored measurement noise
Author(s) -
Yang Yanbo,
Qin Yuemei,
Yang Yanting,
Li Zhi,
Pan Quan
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5437
Subject(s) - filter (signal processing) , filtering problem , autoregressive model , control theory (sociology) , gaussian noise , nonlinear system , mathematics , noise (video) , algorithm , information filtering system , fisher information , nonlinear filter , block (permutation group theory) , computer science , filter design , statistics , artificial intelligence , physics , geometry , control (management) , quantum mechanics , machine learning , image (mathematics) , computer vision
Abstract This paper considers the distributed filtering problem for discrete‐time nonlinear systems with colored measurement noise obeying a nonlinear autoregressive process in sensor networks. A novel block‐decomposed information‐type filter for such systems is proposed in a centralized fusion structure, by using the statistical linear regression to deal with model nonlinearities and the measurement difference approach to overcome the noise correlation caused by colored measurement noises. Meanwhile, with the help of block matrix inverse operation to realize the high‐dimensional block matrix decomposition, the information vector and information matrix of the original system state in the designed information filter is directly estimated recursively, so as to own good numerical stability. Then, the finite‐time distributed implementation of the proposed filter is put forward, where the final filtering estimate in each sensor node is consistent with the centralized filtering result, by ensuring that each sensor node directly obtains the average values of shared variables in the sensor network through finite iterations of average consensus. Finally, the posterior Cramér–Rao lower bound is derived to show the proposed filter reaches the optimal theoretical performance bound in the premise of statistical linear regression and Gaussian posterior probability density approximation. A target tracking example with colored measurement noise obeying a linear and a nonlinear autoregressive processes validates the proposed method.