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.

系统识别的目的是了解时间序列数据背后的潜在物理动力学。为了模拟概率和非参数动力学，高斯过程（GP）已被广泛使用。GP可以估计预测的不确定性。然而，传统的GP状态空间模型基于高斯过渡模型，因此，它们通常难以描述更复杂的过渡模型，例如飞机运动。为了解决这一挑战，本文提出了一个使用多个GP过渡模型的框架，该模型能够描述多峰动力学。此外，该模型已扩展到信息理论框架，即所谓的InfoSSM，通过引入互信息正则器帮助模型学习可解释和可区分的多种动力学模型。提出了在简单的杜宾斯飞行器和高保真飞行模拟器中进行的两个说明性数值实验，以证明所提出模型的性能和可解释性。最后，本文进一步提供了带有贝叶斯滤波的InfoSSM的用例，用于空中交通管制跟踪。