Recursive Gaussian process state space model

Learning dynamical models of mechanical systems from data is fundamental and holds great promise for system behavior analysis, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models (GPSSMs) have recently gained significant attention due to their combination of flexibility and interpretability. However, for online learning, the field lacks an efficient method suitable for scenarios where prior information regarding data distribution and model function is limited. To address this issue, this paper proposes a recursive GPSSM method with adaptive capabilities for both operating domains and Gaussian process (GP) hyperparameters. Specifically, linearization approximation is first applied to derive a Bayesian update equation for the joint distribution between the system state and the GP model, enabling operating domain-independent online GPSSMs learning. Second, an online selection algorithm for inducing points is developed based on informative criteria to achieve lightweight learning. Third, to support online hyperparameter optimization, historical measurement information is recovered from the current filtering distribution. Comprehensive evaluations on synthetic and real-world datasets demonstrate the effectiveness of the proposed method, achieving about 70% higher accuracy than state-of-the-art online GPSSM methods with comparable computational cost in the benchmark test.