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Camera calibration is an important step for vision-based stabilization of unmanned aerial vehicles (UAV). The goal of this paper is to develop a method for automatic calibration of a catadioptric camera so that it can be easily run before mounting the camera on the UAV or even during the flight to deal with vibrations or shocks. Whereas existing works can provide interesting results, they suffer from several practical limitations (manual line extraction, inaccurate conic fitting, calibration pattern, camera motion, execution time, etc...) and therefore cannot be applied in our application. The proposed algorithm aims to determine the most probable calibration that verifies some geometric constraints induced by catadioptric projection. In order to efficiently maximize this probability, we use a particle filtering approach. Experimental results have demonstrated the effectiveness of the proposed method.