A Minimum Variance Filter for Discrete-Time Linear Systems Perturbed by Unknown Nonlinearities

This paper investigates the problem of state estimation for discrete-time stochastic systems with linear dynamics perturbed by unknown nonlinearities. The Extended Kalman Filter (EKF) can not be applied in this framework, because the lack of knowledge on the nonlinear terms forbids a reliable linear approximation of the perturbed system. Following the idea to compensate this lack of knowledge suitably exploiting the information brought by the measured output, a recursive linear filter is developed according to the minimum error variance criterion. Differently from what happens for the EKF, the gain of the proposed filter can be computed off-line. Numerical simulations show the effectiveness of the proposed filter.