Laplace ℓ1 robust kalman smoother based on majorization minimization

Hongwei Wang, Hongbin Li, Wei Zhang, Junyi Zuo, Heping Wang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publicationAIAA Scitech 2019 Forum
DOIs
StatePublished - 2019
EventAIAA Scitech Forum, 2019 - San Diego, United States
Duration: 7 Jan 201911 Jan 2019

Publication series

NameAIAA Scitech 2019 Forum

Conference

ConferenceAIAA Scitech Forum, 2019
Country/TerritoryUnited States
CitySan Diego
Period7/01/1911/01/19

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