his paper deals with the state estimation problem for stochastic nonlinear differential systems, driven by standard Wiener processes, and presents a filter that is a generalization of the classical extended kalman-bucy filter (EKBF). While the EKBF is designed on the basis of a first order approximation of the system around the current estimate, the proposed filter exploits a Carleman-like approximation of a chosen degree v ges 1. The approximation procedure, applied to both the state and the measurement equations, allows to define an approximate representation of the system by means of a bilinear system, for which a filtering algorithm is available from the literature. Numerical simulations on an example show the improvement, in terms of sample error covariance, of the filter based on the first-order, second-order and third-order system approximations (v = 1,2,3).

Filtering of Stochastic Nonlinear Differential Systems via a Carleman Approximation Approach

GERMANI, Alfredo;MANES, COSTANZO;
2007-01-01

Abstract

his paper deals with the state estimation problem for stochastic nonlinear differential systems, driven by standard Wiener processes, and presents a filter that is a generalization of the classical extended kalman-bucy filter (EKBF). While the EKBF is designed on the basis of a first order approximation of the system around the current estimate, the proposed filter exploits a Carleman-like approximation of a chosen degree v ges 1. The approximation procedure, applied to both the state and the measurement equations, allows to define an approximate representation of the system by means of a bilinear system, for which a filtering algorithm is available from the literature. Numerical simulations on an example show the improvement, in terms of sample error covariance, of the filter based on the first-order, second-order and third-order system approximations (v = 1,2,3).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/18644
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