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The GPS-type broadcast ephemerides are currently used by BDS constellation. However, a 5°-rotation added on the original orbital inclination is needed in the GEOs ephemeris parameters fitting algorithm as well as in the user satellite position computation because of the singularity due to small inclination. Besides, the phenomena of exceeding the given boundary happen occasionally for some ephemeris parameters of GEOs. In order to unify the user ephemerides algorithm for the hybrid constellation, a two-step GEO broadcast ephemerides fitting algorithm was analyzed based on the first class nonsingular orbital elements. After the investigation on the reason for the variations of some ephemeris parameters out of limited range, a reduced fitting parameter set was adopted by giving the underlying one or two parameters with fixed values. Fit simulations for 5 GEOs during both eclipsing and non-eclipsing periods show that the two-step fitting algorithm has considerable robustness to ensure the success rate and fitting accuracy. The mean fitting user range error of GEOs with 2 h for NAV and 3 h data set for CNAV are better than 3 mm. For specific fit arcs with the boundary-exceeding problem, it can be fully avoided by using the fitting algorithm with a reduced fitting parameter set. However, the fitting URE will increase to 2 cm.

The satellite shadow parameters can be numerically calculated with high accuracy from the positions of the sun, the earth and the specific satellite. Unfortunately, it is difficult for the numerical calculation to give a general profile of the variations and distributions of these parameters for some certain types of orbital spacecraft. A satellite shadow model was presented based on the spatial view at the altitude of the satellite and the correlative geometry amongst the sun, the earth and the satellite. Firstly, the size and location of the satellite shadow were determined by the semi-major axis of the satellite orbit and the annual motion of the apparent sun, respectively. Secondly, the computing formulae of the satellite shadow parameters were derived, together with the correction formulae for the long-term prediction of the parameters due to oblateness perturbation, etc. Examinations on the three types of orbits for the BeiDou navigation constellation show that the proposed satellite shadow model and its shadow parameters computing formulae can provide a prompt profile of the eclipse parameters for the medium-high altitude circular orbit satellites.

A set of reliable LEO (low earth orbit) broadcast ephemerides is required to be designed specifically if LEOs, with current GEOs, are also utilized as navigation augmentation satellites. The classical nine state parameters-based GLONASS-type broadcast ephemerides model can only represent precisely the 30-minute orbital motions of the medium and high earth orbiters. To directly deal with LEOs, a modified 21-parameter broadcast ephemerides model is proposed. First, the short-term variations of the main perturbation forces of LEOs are analyzed. Then a set of simple quadratic polynomials and harmonic functions is adopted to compensate mathematically atmospheric drag perturbation and other effects. A thoroughly simulation for the LEOs of altitude 500~1200 km is given to demonstrate the impact of the numbers of ephemerides parameters, the length of the fitting arcs and the sample rates on the fitting precision. The results of 20-minute fitting arc (approximately 1/5 of orbital period) show that the average RMS of the fitting user range error (FURE) is less than 0.05 m for LEOs higher than 700 km and within 0.03 m for LEOs of altitude 1000 km.

Low earth orbit satellites, with unique advantages, are prosperous types of navigation augmentation satellites for the GNSS satellites constellations. The broadcast ephemeris element needs to be designed as an important index of the augmented LEOs. The GPS ephemerides of 16/18 elements cannot be directly applied to the LEOs because of the poor fitting accuracies in along-track positional component. Besides, the ill-conditioned problem of the normal-matrix exists in fitting algorithm due to the small eccentricity of the LEO orbits. Based on the nonsingular orbital elements, 5 sets of ephemerides with element numbers from 16 to 19 were designed respectively by adding or modifying orbital elements magnifying the along-track and radial positional components. The fitting experiments based on the LEO of 300 to 1500 km altitudes show that the fitting UREs of the proposed 16/17/18/18*/19-element ephemerides are better than 10/6/4/5/2.5 cm, respectively. According to the dynamical range of the fitting elements, the interfaces were designed for the 5 sets of ephemerides. The effects of data truncation on fitting UREs are at millimeter level. The total bits are 329/343/376/379/396, respectively. 29/15 bits are saved for the 16/17-element ephemerides compared with the GPS16 ephemeris, while 64/61/41 bits can be saved for the 18/18*/19-element ephemerides compared with the GPS18 elements ephemeris.