Abstract: Accurate determination of whether a satellite is in the South Atlantic Anomaly (SAA) region is very important for protecting on-board important instruments, extending the service life of the satellite, and planning observations. This is essentially the so-called point positioning problem, which is in brief how to solve whether a point P is in a spherical polygon R. Traditional methods are to approximate the relevant sphere as a plane and to study the positioning of P relative to R as on the plane. The SAA is a spherical region so curved that using an approximating plane to judge position results in large errors. This paper proposes an algorithm to determine the relative position between a spherical polygon and a point. It can handle potential singular cases and can realize accurate positioning of a point within a spherical region.