Set-based State Estimation with Probabilistic Consistency Guarantee under Epistemic Uncertainty

Consistent state estimation is challenging, especially under the epistemic uncertainties arising from learned (nonlinear) dynamic and observation models. This work proposes a set-based estimation algorithm that produces zonotopic state estimates while respecting both the epistemic uncertainties in the learned models and aleatoric uncertainties. Our method 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 with the corresponding stochastic approach (GP-EKF) in the case of learned (nonlinear) models. In particular, when linearization errors and aleatoric uncertainties are omitted, and epistemic uncertainties are simplified, our set-based approach reduces to its stochastic counterpart (GP-EKF). We empirically demonstrate our method in both a simulated pendulum domain and a real-world robot-assisted dressing domain. Our method has produced not only more consistent but also less conservative set-based estimates than all baseline stochastic methods.