A New Suboptimal Approach to the Filtering Problem for Bilinear Stochastic Differential Systems

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 stateestimates 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. Key words. square integrable martingales, wide-sense Wiener processes, stochastic bilinear systems, Kronecker algebra, Kalman

• Type: Journal
• Year: 2000
• Where: SIAMCO
• Authors: Francesco Carravetta, Alfredo Germani, Marat K. Shuakayev
• Keywords: Finite-dimensional Filter, Finite-dimensional Optimal Linear, Polynomial Finite-dimensional Filters, SIAMCO 2000