Commercial operation of unmanned aerial vehicles (UAVs) would benefit from an onboard ability to sense and avoid (SAA) potential mid-air collision threats. In this paper we present a new approach for detection of aircraft below the horizon. We address some of the challenges faced by existing vision-based SAA methods such as detecting stationary aircraft (that have no relative motion to the background), rejecting moving ground vehicles, and simultaneous detection of multiple aircraft. We propose a multi-stage, vision-based aircraft detection system which utilises deep learning to produce candidate aircraft that we track over time. We evaluate the performance of our proposed system on real flight data where we demonstrate detection ranges comparable to the state of the art with the additional capability of detecting stationary aircraft, rejecting moving ground vehicles, and tracking multiple aircraft.