Striking a Balance: Performance and Cost Optimization of LEO-PNT Constellation for Hybrid Users Using a Meta-Heuristic Approach

The design process of a novel LEO-PNT constellation that can provide continuous global coverage to hybrid users (e.g., those who require the use of both GNSS and LEO systems) is predominantly governed by two key factors, namely the system's performance and cost. They play a decisive role in determining the optimal configuration of the constellation. The performance factors entail a comprehensive evaluation of the constellation's ability to meet the desired mission objectives and requirements, including, but not limited, to services' availability and continuity, and position and timing accuracies. On the other hand, the cost drivers encompass the expenses associated with designing, launching, and maintaining the constellation over its expected lifespan. As such, a delicate balance between the two factors must be struck to ensure that the design outcome is not only efficient and effective but also economically viable. The present study sought to address the LEO-PNT constellation design problem through a meta-heuristic approach and by formulating it as a multi-objective optimization problem. To solve this problem, a nondominated sorting-based Multi-Objective Evolutionary Algorithm (MOEA), specifically a variant of N ondominated Sorting Genetic Algorithm II (NSGA-II) was employed because they have been shown to be effective optimization means to search the complex trade-off spaces of satellite constellation design [1]. Four Figures of Merit (FoMs) are used as objectives to strive for a fast trade-off between the navigation performance and the space segment cost and deployment efficiency, namely the minimization of Global Dilution Of Precision (GDOP) both at Average User Location (AUL) and Worst User Location (WUL), plus the minimization of the total number of satellites and orbital planes. A ranking-based approach is used to select the best solution candidates and fine-tuning of the best constellation patterns set is performed to enhance the efficiency of the optimization process. This paper first introduces a tailored optimization strategy and methodology for the design of a new LEO-PNT constellation with global coverage. The implementation of this methodology is presented, starting from the assumption of a plausible but simplified set of mission scenarios and requirements. The resultant optimal design is then validated for compliance by carrying out a detailed analysis of the selected constellation baselines in high resolution, in terms of user grid points uniformly distributed on the Earth's surface and simulation time window.