Online Bayesian inference and learning of Gaussian-process state–space models

This paper addresses the recursive joint inference (state estimation) and learning (system identification) problem for nonlinear systems admitting a state–space formulation. We model the system as a Gaussian-process state–space model (GP-SSM) and leverage a recently developed reduced-rank formulation of GP-SSMs to enable efficient, online learning. The unknown dynamical system is expressed as a basis-function expansion, where a connection to the GP makes it possible to systematically assign priors to the basis-function weights. The approach is formulated within the sequential Monte Carlo framework, wherein each particle retains its own weights of the basis functions, which are updated recursively as measurements arrive. We report competitive results when compared to a state-of-the art offline Bayesian learning method. We also apply the method to a case study concerning tire-friction estimation. The results indicate that our method can accurately learn the tire friction using automotive-grade sensors in an online setting, and quickly detect sudden changes on the road surface.