Laplace l_1 Robust Kalman Smoother Based on Majorization Minimization

摘要

In this paper, a cubature Rauch-Tung-Striebel Kalman smoother is proposed to provide robust estimation for nonlinear stochastic systems in which measurements are contaminated by outliers. Considering the heavy-tailed property of the measurement noise caused by outliers, we employ a Laplace distribution to model this underlying non-Gaussian measurement noise. The robust smoothing problem is formulated in a sense of maximum a posterior, which involves a computationally prohibitive l_1 minimization optimization. We utilize a majorization-minimization approach to solve the robust smoothing problem. Specifically, with the help of several introduced auxiliary parameters and Young's inequality, the f minimization problem is converted into an l_2 one. The auxiliary parameters and state estimates associated with the resulting l_2 norm problem are updated in an iterative manner. In each iteration, the l'i minimization problem is efficiently implemented in the conventional cubature Kalman smoothing framework. The robustness of the proposed robust smoother is demonstrated by numerical simulation results.