State-Space Inference for Non-Linear Latent Force Models with Application to Satellite Orbit Prediction
This work addresses the challenge of inference in non-linear latent force models for applications like satellite orbit prediction, representing an incremental improvement by adapting existing filtering methods to a specific bottleneck.
The authors tackled the problem of analytically intractable inference in non-linear latent force models by representing them as state-space models and using non-linear Kalman filtering for approximate inference, achieving efficient state and parameter estimation as demonstrated in simulated examples and a real-world application to GPS satellite orbit prediction.
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.