Doubly Robust Smoothing of Dynamical Processes via Outlier Sparsity Constraints

TL;DR

This paper introduces robust smoothing algorithms for dynamical processes that effectively handle outliers in both measurements and state dynamics using sparsity-promoting regularization, with proven convergence and superior performance.

Contribution

It develops novel fixed-lag and fixed-interval smoothing algorithms that jointly estimate states and outliers, handling both types of outliers with a unified, convergent approach.

Findings

Algorithms are expressed in closed form per iteration.

Methods demonstrate improved performance over existing approaches.

Algorithms are robust to unknown noise and outlier distributions.

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 {\it 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 $\ell_1$-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.