We proposed an extended geometry and probability model (EGAPM) to analyze the performance of various kinds of (Global Navigation Satellite System) GNSS+ constellation design scenarios in terms of satellite visibility and dilution of precision (DOP) et al. on global and regional scales. Different from conventional methods, requiring real or simulated satellite ephemerides, this new model only uses some basic parameters of one satellite constellation. Verified by the reference values derived from precise satellite ephemerides, the accuracy of visible satellite visibility estimation using EGAPM gets an accuracy better than 0.11 on average. Applying the EGAPM to evaluate the geometry distribution quality of the hybrid GNSS+ constellation, where highly eccentric orbits (HEO), quasi-zenith orbit (QZO), inclined geosynchronous orbit (IGSO), geostationary earth orbit (GEO), medium earth orbit (MEO), and also low earth orbit (LEO) satellites included, we analyze the overall performance quantities of different constellation configurations. Results show that QZO satellites perform slightly better in the Northern Hemisphere than IGSO satellites. HEO satellites can significantly improve constellation geometry distribution quality in the high latitude regions. With 5 HEO satellites included in the third-generation BeiDou navigation satellite system (BDS-3), the average VDOP (vertical DOP) of the 30° N–90° N region can be decreased by 16.65%, meanwhile satellite visibility can be increased by 38.76%. What is more, the inclusion of the polar LEO constellation can significantly improve GNSS service performance. When including with 288 LEO satellites, the overall DOPs (GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP) are decreased by about 40%, and the satellite visibility can be increased by 183.99% relative to the Global Positioning System (GPS) constellation.
A System Engineering Tool for the Optimisation of a GNSS Constellation Design
