Residual-Aware Distributionally Robust EKF: Absorbing Linearization Mismatch via Wasserstein Ambiguity

TL;DR

This paper introduces a residual-aware distributionally robust EKF that effectively manages linearization errors and noise-model mismatches using Wasserstein ambiguity sets, improving accuracy and safety in nonlinear estimation tasks.

Contribution

It proposes a novel Wasserstein-based robust EKF framework that incorporates linearization residuals as uncertainty, providing deterministic error bounds and a tractable SDP reformulation.

Findings

Enhanced estimation accuracy in simulations with model mismatch.

Deterministic bounds on estimation errors are derived.

Improved safety and robustness over standard EKF in nonlinear scenarios.

Abstract

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.