Probability-Guaranteed Envelope-Constrained Filtering for Nonlinear Systems Subject to Measurement Outliers

• Published in: IEEE transactions on automatic control Vol. 66; no. 7; pp. 3274 - 3281
• Main Authors: Ma, Lifeng, Wang, Zidong, Hu, Jun, Han, Qing-Long
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> H_\infty</tex-math> </inline-formula> filtering; Algorithms; Computational geometry; Constraints; Convexity; envelope-constraint in probability; Estimation error; Filtration; finite-horizon filtering; Horizon; Linear matrix inequalities; Mathematical model; measurement outliers; Nonlinear systems; Optimization; Outliers (statistics); Performance indices; Saturation; Signal processing algorithms; Stochastic systems; Technological innovation; Time-varying systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3016767

This article deals with the recursive filtering problem for nonlinear time-varying stochastic systems subject to possible measurement outliers. In order to mitigate the effects from possible abnormal measurements, we construct a filter with a saturation constraint imposed on the innovations where the saturation level is adaptively determined according to the estimation errors. Two performance indices, namely, the finite-horizon <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula> specification and the envelope-constraint criterion with a prescribed probability, are put forward to describe the transient characteristics of the filtering error dynamics over a specified time interval. The purpose of the addressed problem is to design a filter capable of guaranteeing both the finite-horizon <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula> performance index and the probability-guaranteed envelope-constraint. Sufficient conditions are derived for the existence of the desired filter via certain convex optimization algorithms. Finally, an illustrative numerical example is proposed to demonstrate the effectiveness of the developed algorithm.