Wasserstein Distributionally Robust Kalman Filtering
This work addresses model risk in Kalman filtering for applications like control or signal processing, but it is incremental as it builds on existing distributionally robust optimization methods.
The authors tackled the problem of distributionally robust mean square error estimation over a nonconvex Wasserstein ambiguity set of normal distributions, proving it is equivalent to a tractable convex program and introducing a robust Kalman filter that hedges against model risk.
We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the estimation problem is equivalent to a tractable convex program. We further devise a Frank-Wolfe algorithm for this convex program whose direction-searching subproblem can be solved in a quasi-closed form. Using these ingredients, we introduce a distributionally robust Kalman filter that hedges against model risk.