Robust Estimation and Filtering for Poorly Known Models

This letter addresses the estimation and filtering problems of systems when only a rough model is available. Based on a modified version of the classic regularized least square problem, a new design criterion for estimation is proposed that considers measurements and innovations as a possible source of uncertainty. Under Gaussian assumption, it performs as an upper bound for the maximum a posteriori Bayesian estimator. The optimal solution is obtained by exploiting non-smooth analysis tools and the optimal solution reveals a region in the residue space for which the non-variation of the estimate is optimal. The approach provides robust estimators from a stochastic point of view in recursive form. To illustrate, a Kalman-like filter is derived and comparison with classic worst-case robust design filters are made.