Design method of robust Kalman filter via ℓ1 regression and its application for vehicle control with outliers

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. Many reduction methods of the outliers have been proposed. One of the methods 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. However, parameters of the method are designed by heuristic methods. In this paper, we propose a design method of RKF via ℓ₁ regression. We show that statistics of Gaussian noise determine the parameters of RKF, and we can design the parameters systematically. Then, we apply the method to a velocity estimation and control of a two-wheeled vehicle with outliers. Effectiveness is demonstrated by some numerical simulations.