Robust unscented Kalman filter via l1 regression and design method of its parameters

In this paper, we propose a robust unscented Kalman filter (RUKF) using l₁ regression and a new design method of its regularization parameters. Generally, the regularization parameters in l₁ regression are designed by heuristic methods, so the parameters have no physical senses. However, in our design method, it is shown that statistics of Gaussian measurement noise determine the parameters of the RUKF, and we can design the parameters systematically. The proposed RUKF is applied to a state estimation of a two-link manipulator with outliers, and the effectiveness is demonstrated by numerical simulations.