Mathematical aspects of transit photometry for small UAV detection in video

Abstract

The pervasiveness of small Unmanned Aerial Vehicles (UAVs), due to low cost, ease of control, and portability, opens the possibility of their use in urban environments for illegal or adversarial purposes. Such use includes unauthorized surveillance, reconnaissance, and weaponization. Detecting adversarial UAVs in urban environments is difficult. Urban canyons provide shielding from visibility. The small size of quadcopter-type UAVs limits the number of object pixels available for processing, which reduces standoff detection performance. UAVs fly against a background of ground motion clutter which can mask their motion. One possible solution to small UAV detection in urban environments uses low-cost UAV surveillance platforms, equipped with optical sensors, together with computer vision algorithms to detect adversarial UAVs in video data. In this paper we adapt the astronomical technique of transit photometry to detect small UAVs, operating in urban environments, in video data. Transit photometry, typically used for exo-planet discovery, detects small changes in background brightness due to a transiting object. As the UAV traverses across a bright background region, for example, the vehicle occludes the background and reduces the perceived brightness. This brightness dip may be used to infer the existence of a potential UAV passing across the background. The transit photometry curve, resulting from this brightness dip, reveals information about the traversing vehicle. We investigate mathematical properties of the transit photometry curve and derive a closed-form expression for it. We present numerical results demonstrating the technique on real video data acquired from a small UAV operating in an urban environment.