Improving GPS satellite orbit prediction with Bayesian latent force Gaussian process models

Abstract

This thesis applies and extends a Bayesian latent-force Gaussian Process framework for improving Global Navigation Satellite System satellite orbit prediction. The work addresses a central limitation of conventional physics-based orbit propagation: unmodelled accelerations, especially those caused by solar radiation pressure and other non-conservative forces, can degrade prediction accuracy and are difficult to handle with purely deterministic models. The proposed approach augments the orbital dynamics with latent stochastic forces modelled as Gaussian processes in state-space form, which enables computationally efficient inference through continuous-discrete Gaussian filtering and smoothing. The thesis reviews the theoretical foundations of Gaussian processes, state-space representations, Kalman filtering, and latent force modelling, and then formulates a methodological framework for radial-along-track-cross-track orbit prediction using precise satellite orbit observations. In the GPS G01 January 2025 case study, the quasi-periodic resonator latent-force model achieved a 3D position RMSE of 97.7 m at 24 h and 243.2 m at 120 h, compared with 1,730,959.9 m and 8,243,307.2 m for the deterministic baseline.