LAUSR

In this simulation study, the operational GNSS satellites of global positioning system (GPS), Galileo, global navigation satellite system (GLONASS), and BeiDou navigation satellite system (BDS), which are currently in service, are used to transmit signals for global navigation satellite system reflectometry (GNSS-R) measurement. low Earth orbit (LEO) constellations composed of 8, 16, and 24 satellites and with two different patterns, the 2-D-lattice flower constellation (2-D-LFC) and the 3-D-lattice flower constellation (3-D-LFC), are designed considering the tradeoff among three objectives, namely the visited coverage (VC), the revisited coverage (RC) and the total cost of the constellation. Two multiobjective evolutionary algorithms (MOEAs), the nondominated sorting genetic algorithm II (NSGA-II) and the multiobjective evolutionary algorithm based on decomposition (MOEA/D), are applied to solve this multiobjective optimization problem (MOP). The optimal constellations meeting the best tradeoff for the three objectives are picked out, and the distributions of the reflected points observed by them are presented and compared. It is found that NSGA-II generally performs better with respect to the convergence and the diversity of the Pareto solutions. The optimal tradeoff constellations are generally with inclinations of around 67° to 77° and orbital altitudes of nearly 1000 km. For certain number of satellites, the latitudinal and longitudinal distributions of the number of the reflected points observed by the optimal 2-D-LFC and 3-D-LFC are highly similar to each other. Moreover, with the resolution of $0.25^{\circ }\,\,\times \,\,0.25^{\circ }$ , the VCs of the optimal 8-satellite and 16-satellite 3-D-LFCs reach 58.30% and 79.59%, respectively, and the optimal 24-satellite 2-D-LFC and 3-D-LFC can achieve an average revisit time of about 11.0 and 10.2 h, respectively.