Detecting and tracking moving objects in real-time from an airborne infrared (IR) camera offers interesting possibilities in video surveillance, remote sensing and computer vision applications, such as monitoring large areas simultaneously, quickly changing the point of view on the scene and pursuing objects of interest. To fully exploit such a potential, versatile solutions are needed, but, in the literature, the majority of them works only under specific conditions about the considered scenario, the characteristics of the moving objects or the aircraft movements. In order to overcome these limitations, we propose a novel approach to the problem, based on the use of a cheap inertial navigation system (INS), mounted on the aircraft. To exploit jointly the information contained in the acquired video sequence and the data provided by the INS, a specific detection and tracking algorithm has been developed. It consists of three main stages performed iteratively on each acquired frame. The detection stage, in which a coarse detection map is computed, using a local statistic both fast to calculate and robust to noise and self-deletion of the targeted objects. The registration stage, in which the position of the detected objects is coherently reported on a common reference frame, by exploiting the INS data. The tracking stage, in which the steady objects are rejected, the moving objects are tracked, and an estimation of their future position is computed, to be used in the subsequent iteration. The algorithm has been tested on a large dataset of simulated IR video sequences, recreating different environments and different movements of the aircraft. Promising results have been obtained, both in terms of detection and false alarm rate, and in terms of accuracy in the estimation of position and velocity of the objects. In addition, for each frame, the detection and tracking map has been generated by the algorithm, before the acquisition of the subsequent frame, proving its capability to work in real-time.