  Consistent state estimation is challenging, especially under the epistemic
uncertainties arising from learned (nonlinear) dynamic and observation models.
In this work, we propose a set-based estimation algorithm, named Gaussian
Process-Zonotopic Kalman Filter (GP-ZKF), 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 states are bounded by sets (zonotopes)
across all time steps, with high probability. We formally relate GP-ZKF 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, GP-ZKF
reduces to GP-EKF. We empirically demonstrate our method's efficacy in both a
simulated pendulum domain and a real-world robot-assisted dressing domain,
where GP-ZKF produced more consistent and less conservative set-based estimates
than all baseline stochastic methods.
