A technique for solving celestial fix problems is proposed in this study. This method is based on Particle Swarm Optimization from the field of swarm intelligence, utilizing its superior optimization and searching abilities to obtain the most probable astronomical vessel position. In addition to being applicable to two-body fix, multi-body fix, and high-altitude observation problems, it is also less reliant on the initial dead reckoning position. Moreover, by introducing spatial data processing and display functions in a Geographical Information System, calculation results and chart work used in Circle of Position graphical positioning can both be integrated. As a result, in addition to avoiding tedious and complicated computational and graphical procedures, this work has more flexibility and is more robust when compared to other analytical approaches.