  We propose a principled algorithm for robust Bayesian filtering and smoothing
in nonlinear stochastic dynamic systems when both the transition function and
the measurement function are described by non-parametric Gaussian process (GP)
models. GPs are gaining increasing importance in signal processing, machine
learning, robotics, and control for representing unknown system functions by
posterior probability distributions. This modern way of "system identification"
is more robust than finding point estimates of a parametric function
representation. In this article, we present a principled algorithm for robust
analytic smoothing in GP dynamic systems, which are increasingly used in
robotics and control. Our numerical evaluations demonstrate the robustness of
the proposed approach in situations where other state-of-the-art Gaussian
filters and smoothers can fail.
