Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements

• Published in: International journal of control Vol. 86; no. 4; pp. 650 - 663
• Main Authors: Hu, Jun, Wang, Zidong, Shen, Bo, Gao, Huijun
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.04.2013; Taylor & Francis Ltd
• Subjects: Algorithms; Design engineering; Dynamical systems; Filtering; Filtration; Mathematical models; missing measurements; multiplicative noises; Noise measurement; Nonlinear systems; quantisation effects; Recursive; riccati-like difference equation; Studies; time-varying systems; Upper bounds
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2012.756149

This article is concerned with the recursive finite-horizon filtering problem for a class of nonlinear time-varying systems subject to multiplicative noises, missing measurements and quantisation effects. The missing measurements are modelled by a series of mutually independent random variables obeying Bernoulli distributions with possibly different occurrence probabilities. The quantisation phenomenon is described by using the logarithmic function and the multiplicative noises are considered to account for the stochastic disturbances on the system states. Attention is focused on the design of a recursive filter such that, for all multiplicative noises, missing measurements as well as quantisation effects, an upper bound for the filtering error covariance is guaranteed and such an upper bound is subsequently minimised by properly designing the filter parameters at each sampling instant. The desired filter parameters are obtained by solving two Riccati-like difference equations that are of a recursive form suitable for online applications. Finally, two simulation examples are exploited to demonstrate the effectiveness and applicability of the proposed filter design scheme.