Fast Algorithm of Robust Kalman Filter via l1 Regression by a Closed Form Solution

Abstract

Robust Kalman filter (RKF) via l1 regression is a linear filter for non-Gaussian measurement noise, and it can be formulated as a l1 optimization problem. Generally, the optimization problem cannot be solved analytically, and some numerical iterative methods are needed. This paper proposes a closed form solution of RKF via l1 regression by an approximation of its optimal solution and it gives a fast algorithm. The approximated solution can be calculated by upper and lower bounds of the optimal solution. Moreover, a bound of an estimation error of the approximated solution can be analyzed. Some numerical simulations demonstrate the effectiveness of the proposed algorithm.