Fast Determination of Satellite-to-Moon Visibility Using an Adaptive Interpolation Method Based on Vertex Protection

Fast determination of satellite visibility with respect to a target area is important for satellite navigation and positioning. In this paper, we propose an adaptive interpolation algorithm based on vertex protection to solve the satellite visibility period problem more accurately and quickly, where "vertex" refers to the local extremum point. The algorithm can avoid the error in the visibility period calculation caused by skimming the vertices when fitting the multi-hump visibility function under certain fitting accuracy requirements with the traditional adaptive interpolation method. The algorithm does not need to construct a cubic polynomial in each subinterval to determine whether the satellite is visible or not; it only constructs a cubic polynomial to solve the problem if the visibility function of that subinterval is judged to have a solution from the existence theorem of zero points, which can improve the computational efficiency. For the lunar navigation problem, a solution to satellite-Moon visibility calculations based on a vertex-protected adaptive interpolation is given, and the experimental results show that the computation time of the algorithm can be reduced by approximately 98% compared with the brute force method and by approximately 30% compared with the traditional adaptive interpolation algorithm.