Efficient Online Inference and Learning in Partially Known Nonlinear State-Space Models by Learning Expressive Degrees of Freedom Offline

TL;DR

This paper introduces a method for efficient online inference and learning in nonlinear state-space models by offline conditioning of Gaussian Processes, enabling faster convergence and reduced computational complexity in real-world systems.

Contribution

It proposes a data-driven offline conditioning approach for Gaussian Processes that restricts online learning to a subspace, simplifying inference and improving convergence.

Findings

Enables rapid convergence with fewer particles in simulations.

Reduces computational complexity compared to existing methods.

Provides theoretical bounds on the error due to subspace restriction.

Abstract

Intelligent real-world systems critically depend on expressive information about their system state and changing operation conditions, e.g., due to variation in temperature, location, wear, or aging. To provide this information, online inference and learning attempts to perform state estimation and (partial) system identification simultaneously. Current works combine tailored estimation schemes with flexible learning-based models but suffer from convergence problems and computational complexity due to many degrees of freedom in the inference problem (i.e., parameters to determine). To resolve these issues, we propose a procedure for data-driven offline conditioning of a highly flexible Gaussian Process (GP) formulation such that online learning is restricted to a subspace, spanned by expressive basis functions. Due to the simplicity of the transformed problem, a standard particle filter can be employed for Bayesian inference. In contrast to most existing works, the proposed method enables online learning of target functions that are nested nonlinearly inside a first-principles model. Moreover, we provide a theoretical quantification of the error, introduced by restricting learning to a subspace. A Monte-Carlo simulation study with a nonlinear battery model shows that the proposed approach enables rapid convergence with significantly fewer particles compared to a baseline and a state-of-the-art method.