This paper considers the use of non-parametric system models for sequential state estimation. In particular, motion and observation models are learned from training examples using Gaussian process (GP) regression. The state estimator is an unscented Kalman filter (UKF). The resulting GP-UKF algorithm has a number of advantages over standard (parametric) UKFs. These include the ability to estimate the state of arbitrary nonlinear systems, improved tracking quality compared to a parametric UKF, and graceful degradation with increased model uncertainty. These advantages stem from the fact that GPs consider both the noise in the system and the uncertainty in the model. If an approximate parametric model is available, it can be incorporated into the GP; resulting in further performance improvements. In experiments, we show how the GP-UKF algorithm can be applied to the problem of tracking an autonomous micro-blimp.