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 ℓ1-norm 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) flexibility to encompass maximum a posteriori optimal estimators with reliable performance under nominal conditions; and iv) improved performance relative to competing alternatives at comparable complexity, as corroborated via simulated tests.
Bibliographical noteFunding Information:
Manuscript received January 11, 2011; revised April 27, 2011 and June 22, 2011; accepted June 22, 2011. Date of publication July 05, 2011; date of current version September 14, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Benoit Champagne. Work in this paper was supported by NSF Grants CCF 1016605 and CON 1002180.
- robust regression
- state-space modeling