LEO navigation systems have gained significant attention in recent years as an opportunity to enhance and complement existing GNSS systems relying on MEO satellites. To achieve these goals, the LEO satellites shall broadcast their ephemeris to allow the users locating them in the space at any point of time. These ephemerides are a parametrisation of the underlying orbits, and the nature of the LEO orbits is substantially different from the MEO one. Therefore, although the GPS/Galileo ephemeris model is a good starting point, it needs to evolve to cope with LEO orbit dynamics. This paper addresses the selection and justification of parameters to be included in the LEO navigation message, in order to ensure high-accuracy ephemeris.

To identify the relevant ephemeris parameters, the temporal evolution of the instantaneous LEO orbital elements has been analysed, characterising this evolution into linear, quadratic and harmonic trends, complemented with a Fourier analysis to characterise the harmonic frequency and power. Additionally, a software tool has been developed for LEO ephemeris computation. This tool is capable of fitting ephemeris to a given input orbit for different subsets of parameters, allowing to systematically test the most convenient combinations to minimise the ephemeris fitting error.

If the adequate parameters are added on top of the GPS/Galileo ephemeris model, the fitting error tends to reduce. Beyond the ephemeris parametrisation, other factors, such as the length of the fitting interval, significantly influence the achievable accuracy. As shown in the figure below, for a reference orbit at an altitude of 510 km, the best results in terms of Signal-In-Space Ranging Error (SISRE) at Worst-User-Location (WUL) are in the order of 1 cm for a 21-parameter set and a fitting interval of 10 minutes, or even close to 1 mm for a 5-minute interval and a 19-parameter set.