# Wasserstein Distributionally Robust Kalman Filtering

arXiv: https://arxiv.org/abs/1809.08830 · HTML: https://mlsanity.com/paper/1809.08830/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2018.

## Built on by (most cited first, 17 of 17)

- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [A Finite Sample Complexity Bound for Distributionally Robust Q-learning](https://mlsanity.com/paper/2302.13203/) (2023)
- [Outlier-Robust Wasserstein DRO](https://mlsanity.com/paper/2311.05573/) (2023)
- [Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts](https://mlsanity.com/paper/2106.00322/) (2021)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Topology-aware Robust Optimization for Out-of-distribution Generalization](https://mlsanity.com/paper/2307.13943/) (2023)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [An Inexact Halpern Iteration with Application to Distributionally Robust Optimization](https://mlsanity.com/paper/2402.06033/) (2024)
- [A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set](https://mlsanity.com/paper/2405.20124/) (2024)
- [Towards Backwards-Compatible Data with Confounded Domain Adaptation](https://mlsanity.com/paper/2203.12720/) (2022)
- [Minimax Statistical Estimation under Wasserstein Contamination](https://mlsanity.com/paper/2308.01853/) (2023)
- [Tempering the Bayes Filter towards Improved Model-Based Estimation](https://mlsanity.com/paper/2512.02823/) (2025)
- [Propagating Kernel Ambiguity Sets in Nonlinear Data-driven Dynamics Models](https://mlsanity.com/paper/2304.14057/) (2023)
- [Distributionally Robust K-Means Clustering](https://mlsanity.com/paper/2604.11118/) (2026)
- [Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk](https://mlsanity.com/paper/2604.18546/) (2026)
- [Adversarial observations in probabilistic State-Space Models for robust Reinforcement Learning](https://mlsanity.com/paper/2606.20880/) (2026)
- [Learning Perturbation Robust Policies for LLM Agents with Stable Optimization](https://mlsanity.com/paper/2609.34064/) (2026)

## Abstract (arXiv)

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.