In the field of machine vision, the multi-solution problem of the perspective-three-point (P3P) camera pose estimation problem has been widely researched. Many researchers have tried to find unique solutions that will enable the use of the P3P method in practical applications such as the calibration of external parameters of a camera. Gao found a special case that is very simple and intuitive, but can only be used for a camera with a very large field of view. Therefore, it did not attract much attention. The purpose of this study was to analyse Gao's special case and use it for calibrating the external parameters of an omnidirectional camera, which is used widely because of its very large field of view. We first verify Gao's special case and extend its application. We then propose an iterative method for finding the unique solution. After this, we perform a simulation experiment to determine the effect of the configuration of the three control points on the accuracy of the unique solution. Finally, we use an application to examine the efficiency of the method.