Filtering of Stochastic Nonlinear Differential Systems via a Carleman Approximation Approach
Alfredo Germani, Costanzo Manes, Pasquale J Palumbo · IEEE Transactions on Automatic Control · 2007
This 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$ u\ge 1$. The approximation procedure, applied to both the state and the measurement equations, allows to define an approximate representation of the system by means of a bilinear system, for which a filtering algorithm is available from the literature. Numerical simulations on an example show the improvement, in terms of sample error covariance, of the filter based on the first-order, second-order and third-order system approximations$( u=1,2,3)$.