Variational System Identification for Nonlinear State-Space Models

TL;DR

This paper introduces a variational inference method for estimating parameters in nonlinear state-space models, offering a deterministic, tractable optimization-based approach that improves robustness and compares favorably to existing methods.

Contribution

It develops a novel variational inference framework tailored for nonlinear state-space models, enhancing parameter estimation robustness and computational efficiency.

Findings

The method performs well on simulated data.

It shows robustness to initial parameter guesses.

Favorable comparisons with state-of-the-art methods.

Abstract

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulated and real examples focusing on the robustness to parameter initialisation; additionally, favourable comparisons are performed against state-of-the-art alternatives.