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 high-gain 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