Characteristics of Probability Distribution and Fitting Accuracy for LEO Satellite Ephemeris

Low Earth Orbit (LEO) satellites have nowadays shown great potential to enhance the existing GNSSs for better Positioning, Navigation, and Timing (PNT) services. Despite the requirements for high-accuracy real-time orbits, the distribution of various LEO satellite ephemeris is of concern, yet rarely studied for efficient broadcasting of the LEO satellite ephemeris. This is especially important for setting proper thresholds when broadcasting the LEO satellite ephemeris. In this study, the probability distribution of the LEO satellite ephemeris parameters is investigated together with the corresponding fitting accuracies. Twelve LEO satellites flying at different altitudes with different orbital characteristics are tested for 16-, 18-, 20-, and 22-parameter ephemeris fitting. The results reveal that an increase in orbital altitude does not only lead to improved fitting accuracy, but also results in a more concentrated distribution of orbital elements. Reducing the fitting interval and increasing the number of ephemeris parameters contribute positively to improving the fitting accuracy, where an accuracy of 1~2 cm or serval millimeters can be achieved with 10-min fitting interval and 20/22-parameter ephemeris for a 300~1400 km orbital altitude. This, however, comes at the cost of dispersed distribution of the orbital elements, i.e., with wider ephemeris threshold required. It was also found that the mean values of certain crucial ephemeris parameters, e.g., the mean motion correction, the right ascension of ascending node rate, and the second-order harmonic coefficients Cus2 and Crc2, are highly correlated with the orbital altitudes and inclinations.