A new suboptimal approach to the filtering problem for bilinear stochastic differential systems

Francesco Carravetta, Alfredo Germani, М.К. Shuakayev

2002

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DOI 10.1109/cdc.2001.914569
Data confidence 70 medium
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Abstract

The aim of this paper is to present a new approach to the filtering problem for the class of bilinear stochastic multivariable systems, consisting in searching for suboptimal state-estimates instead of the conditional statistics. As a first result, a finite-dimensional optimal linear filter for the considered class of systems is defined. Then, the more general problem of designing polynomial finite-dimensional filters is considered. The equations of a finite-dimensional filter are given, producing a state-estimate which is optimal in a class of polynomial transformations of the measurements with arbitrarily fixed degree. Numerical simulations show the effectiveness of the proposed filter.