Design of Nonlinear Global Filter with Nonlinear Constraints

O. Straka, M. Šimandl, and J. Duník (Czech Republic)


State estimation; Nonlinear filtering; Constrained estimation; Gaussian sum method; Stochastic system


The paper deals with state estimation of nonlinear stochastic systems, where the state is subject to a nonlinear equal ity constraint reflecting some physical or technological limitations. Usually, local and global filters are designed with out considering any constraint. However, recently some local filters with constraints either linear or nonlinear have emerged. The aim of the paper is to improve estimate quality by considering constraints within design of a nonlinear global filter. As a basis for the proposed constrained global filtering method, the Gaussian sum approximation technique has been chosen together with the two-step projection method for constraint application, which was originally used in the Kalman filtering framework only. The performance of the novel method compared to a standard constrained local filtering method is illustrated in a numerical example.

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