Shen Li, Theodoros Stouraitis, Michael Gienger, Sethu Vijayakumar, Julie Shah, "Set-based State Estimation with Probabilistic Consistency Guarantee under Epistemic Uncertainty", Research and Automation Letters, 2022.

Consistent state estimation is challenging, especially when both dynamic and observation models are nonlinear and learned from data. In this work, we develop a set-based estimation algorithm, that produces zonotopic state estimates that respect the epistemic uncertainties in the learned mod- els, in addition to the aleatoric uncertainties. Our algorithm guarantees probabilistic consistency, in the sense that the true state is always bounded by the zonotopes, with a high probability. We formally relate our set-based approach and a corresponding probabilistic approach (GP-EKF) in the case of learned non-linear models. In particular, when linearization errors and aleatoric uncertainties are omitted, and epistemic uncertainty is simplified, our set-based approach reduces to the probabilistic approach. The improved consistency is empirically demonstrated in both a simulated pendulum domain and a real-world robot-assisted dressing domain, where the robot estimates the configuration of the human arm utilizing the force measurements at its end effector.