Design method of robust Kalman filter for multi output systems based on statistics

In many cases, outliers are contained in sensor signals, and these deteriorate performances of control systems, e.g., UAV and UGV using non-contact sensors. One of reduction methods of the outliers is robust Kalman filter (RKF) via l₁ regression. The method is easy to implement and compute due to a simple structure and convex optimization problem, so the method attracts many attentions. In this paper, we propose a new design method of RKF via l₁ regression for multi output systems. It is shown that statistics of Gaussian noise determine the parameters of RKF, and we can design the parameters systematically. RKF with the proposed design method is applied to a two-wheeled vehicle control with outliers, and the effectiveness is demonstrated by numerical simulations.