Residual-Aware Distributionally Robust EKF: Absorbing Linearization Mismatch via Wasserstein Ambiguity
This work addresses state estimation challenges for robotics and tracking systems, offering an incremental improvement over standard EKF methods.
The paper tackles the performance limitations of the extended Kalman filter (EKF) due to noise-model mismatch and linearization errors by developing a residual-aware distributionally robust EKF that absorbs linearization residuals into a Wasserstein ambiguity set, resulting in improved estimation accuracy and safety in simulations on target tracking and robot navigation.
The extended Kalman filter (EKF) is a cornerstone of nonlinear state estimation, yet its performance is fundamentally limited by noise-model mismatch and linearization errors. We develop a residual-aware distributionally robust EKF that addresses both challenges within a unified Wasserstein distributionally robust state estimation framework. The key idea is to treat linearization residuals as uncertainty and absorb them into an effective uncertainty model captured by a stage-wise ambiguity set, enabling noise-model mismatch and approximation errors to be handled within a single formulation. This approach yields a computable effective radius along with deterministic upper bounds on the prior and posterior mean-squared errors of the true nonlinear estimation error. The resulting filter admits a tractable semidefinite programming reformulation while preserving the recursive structure of the classical EKF. Simulations on coordinated-turn target tracking and uncertainty-aware robot navigation demonstrate improved estimation accuracy and safety compared to standard EKF baselines under model mismatch and nonlinear effects.