Design Method of Robust Kalman Filter Based on Statistics and Its Application

In this paper, we propose a new design method of RKF via l1 regression for multi output systems. Parameters of conventional RKF are designed by heuristic methods, so the parameters have no physical meanings. It is shown that statistics of Gaussian measurement noise determine the parameters of RKF via a primal and dual problem of l1 optimization problem. We discuss a covariance matrix of updated state estimation error. The proposed parameters can design the parameters systematically. In addition, the parameters have physical meanings, and we need no prior information except Gaussian measurement noise. RKF with the proposed design method is applied to a two-wheeled vehicle control with outliers, and the effectiveness is demonstrated by numerical simulations.