Filtering of differential nonlinear systems via a Carleman approximation approach

This paper deals with the state estimation problem for a stochastic nonlinear differential system driven by a standard Wiener process. The solution here proposed is a linear filtering algorithm and is achieved by means of the Carleman approximation scheme applied to both the state and the measurement nonlinear equations. Such a procedure allows to define an approximate representation by means of a suitable bilinear system for which a filtering algorithm is available from literature. Numerical simulations support the theoretical results and show a rather interesting improvement in terms of sampled error covariance of the proposed approach with respect to the classical Kalman-Bucy filter applied to the linearized differential system.