Bayesian Nonparametric State-Space Model for System Identification with Distinguishable Multimodal Dynamics

Abstract

The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics, Gaussian process (GP) has been widely used; GP can estimate the uncertainty of prediction. Traditional GP state-space models, however, are based on the Gaussian transition model, and thus they often have difficulty in describing more complex transition models, e.g., aircraft motions. To resolve the challenge, this paper proposes a framework using multiple GP transition models that is capable of describing multimodal dynamics. Furthermore, the model is extended to an information-theoretic framework, the so-called InfoSSM, by introducing a mutual information regularizer helping the model to learn interpretable and distinguishable multiple dynamics models. Two illustrative numerical experiments in a simple Dubins vehicle and high-fidelity flight simulator are presented to demonstrate the performance and interpretability of the proposed model. Finally, this paper further provides a use case of InfoSSM with Bayesian filtering for air traffic control tracking.