A Stability Guaranteed Distributionally Robust Adaptive Kalman Filter for Dual Uncertainties in Model and Noise

This paper presents a distributionally robust adaptive Kalman filter (DRAKF) to address the dual challenges of model uncertainty and unknown time-varying noise in linear state estimation. A sliding window variational Bayesian (VB) module is employed to actively infer the true noise covariances online. Based on this information, a distributionally robust state estimator (DRSE) is constructed to guarantee worst-case performance under model mismatch. Under bounded model uncertainty and bounded front-end covariance perturbations, the estimation error covariance of the proposed hybrid filter is shown to be uniformly bounded in the mean-square sense via stochastic Lyapunov analysis. Monte Carlo simulations in typical target tracking scenarios demonstrate that DRAKF significantly outperforms existing adaptive and robust filters, while effectively resolving the uncertainty confounding issue. These results highlight the proposed method’s ability to deliver enhanced estimation accuracy and robustness in uncertain and dynamic environments.