Doubly robust Kalman smoothing by controlling outlier sparsity

Coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice. This paper develops a novel smoothing algorithm that is 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 regularized with the ℓ₁-norm to effect sparsity control. Attractive features of the novel doubly robust Kalman 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, and also exhibit reliable performance under nominal conditions; and iv) improved performance relative to competing alternatives, as corroborated via simulated tests.