Multi-Restriction Satellite Visibility Prediction (MRSVP) problem is of great significance in space missions such as Earth observation and space surveillance. This paper presents a numerical method to rapidly and accurately compute site-satellite and satellite-satellite in-view periods, taking multiple restrictions into account. A novel curve fitting method named Adaptive Piecewise Cubic Hermite Interpolation (APCHI) technique is introduced to approximate waveforms of visibility functions derived for corresponding restrictions, featured with autonomous searching for the best interpolation points to guarantee accuracy. Test results obtained from this approach are almost the same with those from conventional trajectory check method. However, this new approach reduces more than 90% of computation time. As this numerical method can apply to all kinds of orbit types and propagators, it proves to be a good choice for satellite constellation design and mission planning.
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