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Low Earth orbit (LEO) satellites located at altitudes of 500 km~1500 km can carry much stronger signals and move faster than medium Earth orbit (MEO) satellites at about a 20,000 km altitude. Taking advantage of these features, LEO satellites promise to make contributions to navigation and positioning where global navigation satellite system (GNSS) signals are blocked as well as the rapid convergence of precise point positioning (PPP). In this paper, LEO-based optimal global navigation and augmentation constellations are designed by a non-dominated sorting genetic algorithm III (NSGA-III) and genetic algorithm (GA), respectively. Additionally, a LEO augmentation constellation with GNSS satellites included is designed using the NSGA-III. For global navigation constellations, the results demonstrate that the optimal constellations with a near-polar Walker configuration need 264, 240, 210, 210, 200, 190 and 180 satellites with altitudes of 900, 1000, 1100, 1200, 1300, 1400 and 1500 km, respectively. For global augmentation constellations at an altitude of 900 km, for instance, 72, 91, and 108 satellites are required in order to achieve a global average of four, five and six visible satellites for an elevation angle above 7 degrees with one Walker constellation. To achieve a more even coverage, a hybrid constellation with two Walker constellations is also presented. On this basis, the GDOPs (geometric dilution of precision) of the GNSS with and without an LEO constellation are compared. In addition, we prove that the computation efficiency of the constellation design can be considerably improved by using master–slave parallel computing.

Optimal Walker Constellation Design of LEO-Based Global Navigation and Augmentation System