Abstract: For the increasingly complex space environment，space-based observations have attracted more and more attention due to their flexible distribution and all-weather observation，which is a typical above-the-horizon（ATH）observation problem.Based on the concept of segmental integration，a quantitative calculation method of the coverage region for ATH observations was proposed，which includes all possibilities of 10 integral forms of the problem for scenarios with any observation constraints.Not only has the two-dimensional planar coverage problem been verified with existing methods，but also the quantitative analytical calculation problem of the coverage volume of ATH in three-dimensional space has been solved for the first time.The simulation results show that there is a significant difference between the optimal orbit altitude corresponding to the maximization of planar and spatial coverage.The proposed approaches are more accurate and efficient in coverage performance，providing reference for constellation design.

Key words: spaceborne observation, space situational awareness, observations above the horizon, coverage, coverage calculation