Paper H. Analytic Moment-based Gaussian Process Filtering. Edited version of the paper: M. P. Deisenroth, M. F. Huber, and U. D. Hanebeck. Analytic Momentbased Gaussian Process Filtering. In Proceedings of the 26th International Conference onMachine Learning (ICML),Montreal, Canada, June 2009

We propose an analytic moment-based filter for nonlinear stochastic dynamic systems modeled by Gaussian processes. Exact expressions for the expected value and the covariance matrix are provided for both the prediction step and the filter step, where an additional Gaussian assumption is exploited in the latter case. Our filter does not require further approximations. In particular, it avoids finite-sample approximations. We compare the filter to a variety of Gaussian filters, that is, the EKF, the UKF, and the recent GP-UKF proposed by [7].