The observer follower filter: A new approach to nonlinear suboptimal filtering

This paper investigates the state estimation problem for a class of stochastic nonlinear differential systems. A novel algorithm is proposed, denoted as Observer Follower Filter (OFF), based on a two-steps, mixed approach: the first step makes use of a high-gain observer-based estimator for nonlinear systems, applied to the system equations in order to provide the trajectory around which a ν-degree Carleman approximation of the stochastic differential system is achieved, second step. In principle, any other highgain estimator can be used, but in this note we prove that the one here proposed provides a bounded mean square error. Numerical simulations show the effectiveness of the proposed methodology, and the improvements of the OFF with respect to the standard Extended Kalman–Bucy Filter (EKBF) obtained by increasing the order of the Carleman approximation.