Latent force models in autonomous GNSS satellite orbit prediction

In this paper, we present a method for improving autonomous GNSS satellite orbit prediction accuracy by including latent forces, i.e. forces that are estimated with broadcast ephemeris data. The purpose of autonomous prediction is to reduce the Time to First Fix of a stand-alone positioning device. Our orbit model includes gravity and solar radiation forces and initial state estimation algorithm. We present a state-space model for the latent forces, which are meant to correct the deficiencies of our force model, and we describe how latent forces are incorporated as a part of our prediction algorithm. Using a novel algorithm, where multiple ephemerides are used to estimate the latent forces, the orbit prediction accuracy for GPS, GLONASS and Beidou is significantly improved. For example, for 7-day prediction of GPS satellites, the 68% quantile of SISRE, which is an estimate of positioning accuracy, reduced 37.1%.