TY - GEN
T1 - Laplace ℓ1 robust kalman smoother based on majorization minimization
AU - Wang, Hongwei
AU - Li, Hongbin
AU - Zhang, Wei
AU - Zuo, Junyi
AU - Wang, Heping
N1 - Publisher Copyright:
� 2019 by German Aerospace Center (DLR). Published by the American Institute of Aeronautics and Astronautics, Inc.
PY - 2019
Y1 - 2019
N2 - 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 out-liers, 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 ℓ1 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 ℓ1 minimization problem is converted into an ℓ2 one. The auxiliary parameters and state estimates associated with the resulting ℓ2 norm problem are updated in an iterative manner. In each iteration, the ℓ2 mini-mization problem is efficiently implemented in the conventional cubature Kalman smoothing framework. The robustness of the proposed robust smoother is demonstrated by numerical simulation results.
AB - 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 out-liers, 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 ℓ1 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 ℓ1 minimization problem is converted into an ℓ2 one. The auxiliary parameters and state estimates associated with the resulting ℓ2 norm problem are updated in an iterative manner. In each iteration, the ℓ2 mini-mization problem is efficiently implemented in the conventional cubature Kalman smoothing framework. The robustness of the proposed robust smoother is demonstrated by numerical simulation results.
UR - http://www.scopus.com/inward/record.url?scp=85083943078&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85083943078&partnerID=8YFLogxK
U2 - 10.2514/6.2019-1932
DO - 10.2514/6.2019-1932
M3 - Conference contribution
AN - SCOPUS:85083943078
SN - 9781624105784
T3 - AIAA Scitech 2019 Forum
BT - AIAA Scitech 2019 Forum
T2 - AIAA Scitech Forum, 2019
Y2 - 7 January 2019 through 11 January 2019
ER -