An update-resilient Kalman filtering approach

TL;DR

The paper tackles robust state estimation when model mismatch is confined to the observation model. It introduces a KL-divergence–based ambiguity set for the observation density and derives the update-resilient Kalman filter (U-RKF) with resilience in the update step. It provides a complete characterization of the least-favorable model via forward-backward recursions and proves filter stability under bounded tolerance, with comparative results showing improved accuracy and substantial computational efficiency over existing minimax and Wasserstein-based methods. It also extends to an update-risk-sensitive filter (U-RSF) with analogous robustness properties and meets practical performance gains in sensor-rich scenarios.

Abstract

We propose a new robust filtering paradigm considering the situation in which model uncertainty, described through an ambiguity set, is present only in the observations. We derive the corresponding robust estimator, referred to as update-resilient Kalman filter, which appears to be novel compared to existing minimax game-based filtering approaches. Moreover, we characterize the corresponding least favorable state space model and analyze the filter stability. Finally, some numerical examples show the effectiveness of the proposed estimator.

Figures (10)

• Figure 1: Minimum eigenvalue of $\mathbf R_k$ as a function of $\phi_k$ with $k=10$. The largest value of $\phi_k$ such that $\mathbf R_k$ is positive definite is approximately equal to 0.095.
• Figure 2: Variance of the estimation error when KF (black line), P-RKF (red line) and U-RKF (blue line) are applied to the least favorable model with $c=5\cdot 10^{-2}$.
• Figure 3: Variance of the estimation error when KF (black line), P-RKF (red line) and U-RKF (blue line) are applied to the least favorable model with $c= 10^{-2}$.
• Figure 4: Risk sensitivity parameter $\theta_t$ of P-RKF (red line) and U-RKF (blue line) when $c=5\cdot10^{-2}$.
• Figure 5: Mass-spring-damper system.