Spherical Circle Fitting Algorithm and Its Application on Azimuth Determination by Observing the Moon

The Moon is the brightest body in the night sky, and it is of great value to be used to determine the azimuth. However, the key problem is how to solve the center of the apparent Moon accurately. This paper puts forward a new method called spherical circle fitting algorithm to determine the center of the apparent Moon. It has such many merits as strictness, briefness and little calculation in contrast to the existing algorithm. Simulated observation data is processed to understand the relationship between the attitude of the phase of the Moon and fitting accuracy. An experiment based on real observations was used to testify the correctness of the algorithm, and a comparison is made between the spherical circle fitting algorithm and the old algorithm. The results show that while the inner precision is almost the same, the outer accuracy of our algorithm improves by 0.5″. These results suggest that spherical circle fitting algorithm is more suitable for engineering applications.