Fast Algorithm of Robust Kalman Filter via l_1 Regression by a Closed Form Solution

摘要

Robust Kalman filter (RKF) via l_1 regression is a linear filter for non-Gaussian measurement noise, and it can be formulated as a l_1 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 l_1 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.