{"ID":2832181,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.06286","arxiv_id":"2512.06286","title":"Distributionally Robust Kalman Filter","abstract":"We study state estimation for discrete-time linear stochastic systems under distributional ambiguity in the initial state, process noise, and measurement noise. We propose a noise-centric distributionally robust Kalman filter (DRKF) based on Wasserstein ambiguity sets imposed directly on these distributions. This formulation excludes dynamically unreachable priors and yields a Kalman-type recursion driven by least-favorable covariances computed via semidefinite programs (SDP). In the time-invariant case, the steady-state DRKF is obtained from a single stationary SDP, producing a constant gain with Kalman-level online complexity. We establish the convergence of the DR Riccati covariance iteration to the stationary SDP solution, together with an explicit sufficient condition for a prescribed convergence rate. We further show that the proposed noise-centric model induces a priori spectral bounds on all feasible covariances and a Kalman filter sandwiching property for the DRKF covariances. Finally, we prove that the steady-state error dynamics are Schur stable, and the steady-state DRKF is asymptotically minimax optimal with respect to worst-case mean-square error.","short_abstract":"We study state estimation for discrete-time linear stochastic systems under distributional ambiguity in the initial state, process noise, and measurement noise. We propose a noise-centric distributionally robust Kalman filter (DRKF) based on Wasserstein ambiguity sets imposed directly on these distributions. This formu...","url_abs":"https://arxiv.org/abs/2512.06286","url_pdf":"https://arxiv.org/pdf/2512.06286v3","authors":"[\"Minhyuk Jang\",\"Astghik Hakobyan\",\"Insoon Yang\"]","published":"2025-12-06T04:30:39Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}