Multiple-step prediction using a two stage Gaussian Process model

A two stage probabilistic prediction model is presented that uses nonparametric Gaussian Process (GP) regression to model continuous complex actions combined with a parametric model for known system dynamics. This two stage model is applied to the case of anticipating driver behavior and vehicle motion. The cross covariances between the initial state distribution and the control action distributions given by the GP regression model are computed analytically, allowing for a closed form evaluation of the joint distribution over the initial state and the GP outputs. Computing these cross covariances is necessary to capture important state dependent behavior in the GP data such as lane keeping for road vehicles. The proposed prediction model is evaluated using driving data collected from three human subjects navigating a standard four-way intersection in a driving simulation.