State-Space Inference for Non-Linear Latent Force Models with Application to Satellite Orbit Prediction

TL;DR

This paper introduces a novel state-space inference method for non-linear latent force models, combining physical and data-driven approaches, and demonstrates its effectiveness in satellite orbit prediction.

Contribution

It presents an efficient non-linear Kalman filtering approach for LFMs, enabling practical inference in complex physical systems like satellite orbits.

Findings

Effective in simulated examples

Accurate long-term GPS satellite orbit predictions

Outperforms traditional methods in non-linear settings

Abstract

Latent force models (LFMs) are flexible models that combine mechanistic modelling principles (i.e., physical models) with non-parametric data-driven components. Several key applications of LFMs need non-linearities, which results in analytically intractable inference. In this work we show how non-linear LFMs can be represented as non-linear white noise driven state-space models and present an efficient non-linear Kalman filtering and smoothing based method for approximate state and parameter inference. We illustrate the performance of the proposed methodology via two simulated examples, and apply it to a real-world problem of long-term prediction of GPS satellite orbits.