One-Second GPS Orbits: A Comparison Between Numerical Integration and Interpolation

Precise positioning using the Global Positioning System (GPS) requires accurate knowledge of the satellite orbits. The International GNSS Service (IGS) distributes post-processed GPS satellite orbits that give the satellite positions at 15 minutes interval. For GPS applications involving high-rate (1 Hz) GPS, it is necessary to know the satellite positions at one second intervals. One approach of doing this is to interpolate the IGS precise orbit using a polynomial or trigonometric function. An alternative approach is to use the precise ephemeris distributed by the IGS to obtain the satellite position and velocity at the initial epoch and then perform numerical integration to determine the satellite position at one second intervals. JPL's GPS Inferred Positioning System/Orbit Analysis and Simulation Software (GIPSY/OASIS) is used to numerically integrate the orbit of a single GPS satellite in order to determine the position at one second intervals. A comparison of the numerically integrated positions and the interpolated positions shows that the numerically integrated satellite positions more closely match the IGS orbits than an orbit constructed using a trigonometric interpolation.