Broadcast ephemerides for LEO augmentation satellites based on nonsingular elements

Low earth orbit (LEO) satellite constellations have the potential to augment global navigation satellite system services. Among the ongoing tasks of LEO-based navigation, providing broadcast ephemerides that satisfy the accuracy requirement for positioning, navigation, and timing is one of the most critical prerequisites. Singularities can occur when fitting broadcast ephemeris parameters in the case of a small eccentricity or small or large inclination. We choose an improved nonsingular element set for the LEO broadcast ephemeris design. We establish suitable broadcast ephemeris models, considering the fit accuracy, number of parameters, orbital altitude, and inclination. The fit accuracy using different orbital altitudes, orbital inclinations, and eccentricities suggests that the optimal parameters are $$\dot{n}$$ , $$\ddot{n}$$ , Crc3, Crs3, $$C_{\lambda c3}$$ , and $$C_{\lambda s3}$$ , together with the basic broadcast ephemeris model. After adding these six parameters, a fit accuracy of better than 10 cm can be achieved with a 20 min arc length and 500–1400 km orbital altitudes. The effects of the number of parameters, orbital altitude, inclination, and eccentricity on the fit accuracy are discussed in detail. Finally, the performance is validated with real LEO satellites to confirm the effectiveness of the proposed method.