A Marginal Distributionally Robust Kalman Filter for Sensor Fusion

Weizhi Chen, Yaowen Li, Yu Liu, You He

Abstract: This paper proposes a moment-constrained marginal distributionally robust Kalman filter (MC-MDRKF) for centralized state estimation in multi-sensor systems with unknown sensor noise correlations. We first derive a robust static estimator and then extend it to dynamic systems for the MC-MDRKF algorithm. The static estimator defines a marginal distributional uncertainty set using moment constraints and formulates a minimax optimization problem to robustly address unknown correlations. We prove that this minimax problem admits an equivalent convex optimization formulation, enabling efficient numerical solutions. The resulting MC-MDRKF algorithm recursively updates state estimates in dynamic state-space models. Simulation results demonstrate the superiority and robustness of the proposed method in a multi-sensor target tracking scenario.

External IDs:dblp:journals/spl/ChenLLH25