Doubly Robust Smoothing of Dynamical Processes via Outlier Sparsity Constraints

Abstract—Coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice. In this context, the present paper develops novel fixed-lag and fixed-interval smoothing algorithms that are robust to outliers simultaneously present in the measurements and in the state dynamics. Outliers are handled through auxiliary unknown variables that are jointly estimated along with the state based on the least-squares criterion that is regularized with the 1norm of the outliers in order to effect sparsity control. The resultant iterative estimators rely on coordinate descent and the alternating direction method of multipliers, are expressed in closed form per iteration, and are provably convergent. Additional attractive features of the novel doubly robust smoother include: i) ability to handle both types of outliers; ii) universality to unknown nominal noise and outlier distributions; iii) flex...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Shahrokh Farahmand, Georgios B. Giannakis, Daniele Angelosante
• Keywords: CORR 2011, Education, Outlier, Posteriori Optimal Estimators, Unknown Nominal Noise