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Optimal Filtering for Polynomial States over Polynomial Observations

Basin, Michael and Calderon-Alvarez, Dario and Shi, Peng (2008) Optimal Filtering for Polynomial States over Polynomial Observations. In: Proceedings of the 47th IEEE Conference on Decision and Control. IEEE, pp. 5128-5133.

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Abstract

In this paper, the optimal filtering problem for polynomial system states over polynomial observations is studied proceeding from the general expression for the stochastic Ito differentials of the optimal estimate and the error variance. In contrast to the previously obtained results, the paper deals with the general case of nonlinear polynomial states and observations. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state over observations with any polynomial drift is then established. In the example, the obtained optimal filter is applied to solve the optimal third order sensor filtering problem for a quadratic state, assuming a Gaussian initial condition for the extended third order state vector. The simulation results show that the designed filter yields a reliable and rapidly converging estimate.

Item Type: Book Section
ISBN: 9781424431236, e9781424431243
Uncontrolled Keywords: ResPubID18943, Gaussian processes, filtering theory, polynomials, sensors
Subjects: Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
FOR Classification > 0199 Other Mathematical Sciences Information Systems
Depositing User: VUIR
Date Deposited: 18 Jan 2014 07:03
Last Modified: 16 Dec 2014 03:33
URI: http://vuir.vu.edu.au/id/eprint/6199
DOI: 10.1109/CDC.2008.4738916
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Citations in Scopus: 0 - View on Scopus

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