The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the uncertainty of prediction and avoid over-fitting. Traditional GPSSMs, however, are based on Gaussian transition model, thus often have difficulty in describing a more complex transition model, e.g. aircraft motions. To resolve the challenge, this thesis proposes a framework using multiple GP transition models which is capable of describing multi-modal dynamics. Furthermore, this thesis extend the model to the 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 simple Dubins vehicle and high-fidelity flight simulator are presented to demonstrate the performance and interpretability of the proposed model. Finally, this thesis introduces a framework using InfoSSM with Bayesian filtering for airplane tracking.