Random Fibonacci sampling and region division: A numerical analysis of constellation coverage

Coverage analysis serves as the foundation for designing the communication or remote sensing satellite constellations. The classical numerical method, grid-point approach (GPA), is widely utilized in constellation coverage analysis, yet it encounters challenges such as uneven grid distribution and substantial computational demands. In this paper, we introduce a random Fibonacci sampling method (RFSM) to achieve a more balanced distribution of sampling points, alongside a k-means region division method (KRDM) to enhance computational efficiency. In the RFSM, discrete sampling points replace grids for evaluating coverage performance. By incorporating randomness into the Fibonacci lattices method, we ensure that the sampling points exhibit a random uniform distribution. This allows for the amalgamation of coverage data from different sets of sampling points and the dynamic adjustment of the number of sampling points during computation. In the KRDM, we divide the whole target region into several sub-regions using the k-means algorithm, followed by calculating their respective visible windows. Numerical simulations demonstrate that the proposed method significantly enhances computational efficiency without compromising accuracy, achieving speed improvements of one or two orders of magnitude compared to the classical GPA. These findings suggest that the proposed method holds considerable promise for expediting constellation coverage performance calculations on a broader scale.