Gaussian Processes with Noisy Regression Inputs for Dynamical Systems

This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are typically noisy, which implies that both the regression inputs and outputs are corrupted by noise. However, most of the literature considers only noise in the regression outputs. In this paper, we show how to account for the noise in the regression inputs in an extended Gaussian process framework to approximate scalar and multidimensional systems. We demonstrate the potential of our framework by comparing it to different state-of-the-art methods in several simulation examples.