Precise Orbit Determination of the Kepler Navigation System - a Simulation Study

The paper deals with precise orbit determination (POD) of a future satellite navigation system called Kepler consisting of 24 Galileo-like Medium Earth Orbit (MEO) and 6 Low Earth Orbit (LEO) satellites connected by two-way optical inter-satellite links (ISLs) for communication, constellation-wide clock synchronization and precise ranging. The Kepler GNSS space-borne (6 LEOs) and ground data for 18 Galileo Sensor Stations are simulated with noise typical for real data including multipath, the ISL ranges are simulated with 1 mm Gaussian noise. The data are subsequently used for orbit determination in daily batches. It is demonstrated, that the POD of the Kepler system with ISL ranges and synchronized satellite clocks defining the reference time scale could be performed with just one ground station. The POD results are compared to MEO-only Galileo-like solutions. The Kepler MEO radial orbit accuracy is better than the Galileo one by a factor of 1000 in case of perfect models. To obtain more realistic results, a number of modeling errors was introduced leading to significant degradations of the orbit accuracy. However with the Kepler system, an efficient handling of the modeling errors by empirical accelerations is possible, resulting in orbit accuracies of 5 cm in 3D and 0.24 cm in radial direction. In the Kepler POD pseudo-range hardware delays and biases in the ISL ranges are additionally considered. It turns out that the estimation of the code hardware delay differences (receiver-transmitter) does not impact POD accuracy. Estimation of the ISL range biases in the presence of significant modeling errors, in turn, was found to have a rather dramatic impact, increasing the radial orbit error by an order of magnitude from 0.24 to 2 cm. ISL range biases of up to 5 mm, when not estimated, have a much smaller impact, radial orbit accuracy stays below 1 cm. It was also found, that removing the satellite fixed clocks assumption in the Kepler system with precise ISL ranges has no impact on the radial orbit component, but significantly increases the orbit error in along- and cross-track direction.