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

摘要

Abstract 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. Keywords: nonlinear systemstime-varying systemsmissing measurementsquantisation effectsmultiplicative noisesriccati-like difference equation Acknowledgements This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61273201, 61104125 and 11271103, National 973 Project under Grant 2009CB320600, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany.