Orbit fitting based on Helmert transformation

Abstract

Orbit fitting is used in many GPS applications. For example, in Precise Point Positioning (PPP), GPS orbits (SP3 orbits) are normally retrieved either from IGS or from one of its Analysis Centers (ACs) with 15 minutes’ sampling, which is much bigger than the normal observation sampling. Therefore, algorithms should be derived to fit GPS orbits to the observation time. Many methods based on interpolation were developed. Using these methods the orbits fit well at the sampling points. However, these methods ignore the physical motion model of GPS satellites. Therefore, the trajectories may not fit the true orbits at the periods in between 2 sampling epochs. To solve this problem, we develop a dynamic approach, in which a model based on Helmert transformation is developed in GPS orbit fitting. In this orbit fitting approach, GPS orbits at sampling points are treated as pseudo-observations. Thereafter, Helmert transformation is built up between the pseudo-observations and dynamically integrated orbits at each epoch. A set of Helmert parameters together with corrections of GPS initial orbits are then modeled as unknown parameters. Results show that the final fit orbits have the same precision as the IGS final orbits.