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Circuits, Systems & Signal Processing

, Volume 28, Issue 2, pp 223–239 | Cite as

Optimal Filtering for Incompletely Measured Polynomial Systems with Multiplicative Noise

  • Michael Basin
  • Dario Calderon-Alvarez
New Trends in Optimum and Robust Filtering

Abstract

In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations with an arbitrary, not necessarily invertible, observation matrix is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. Thus, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. A transformation of the observation equation is introduced to reduce the original problem to the previously solved one with an invertible observation matrix. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of linear and bilinear state equations. In an example, the performance of the designed optimal filter is verified against those of the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman–Bucy filter.

Keywords

Filtering Stochastic system Nonlinear polynomial system Bilinear system 

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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  1. 1.Department of Physical and Mathematical SciencesAutonomous University of Nuevo LeonSan Nicolas de los GarzaMexico

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