Error variance-constrained ℋ filtering for a class of nonlinear stochastic systems with degraded measurements: the finite horizon case

Lifeng Ma, Yuming Bo, Yuchen Zhou and Zhi Guo

International Journal of Systems Science, 2012, vol. 43, issue 12, 2361-2372

Abstract: This article is concerned with the robust ℋ∞ filtering problem for a class of time-varying nonlinear stochastic systems with error variance constraint. The stochastic nonlinearities considered are quite general, which contain several well-studied stochastic nonlinear systems as special cases. The purpose of the filtering problem is to design a filter which is capable of achieving the pre-specified ℋ∞ performance and meanwhile guaranteeing a minimised upper-bounded on the filtering error variance. By means of the adjoint system method, a necessary and sufficient condition for satisfying the ℋ∞ constraint is first given, expressed as a forward Riccati-like difference equation. Then an upper-bound on the variance of filtering error system is given, guaranteeing the error variance is not more than a certain value at each sampling instant. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time, hence is suitable for online computation. A numerical example is presented finally to show the effectiveness and applicability of the proposed method.

Date: 2012
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DOI: 10.1080/00207721.2011.577249

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