This paper discusses the problem of stabilizing a multicopter over a tethered high-altitude platform by using visual analysis systems to determine the position and orientation of the target platform. We propose a neural network architecture to solve the problem of backup local navigation system of tethered unmanned aerial vehicles in GPS-Denied and GLONASS-Denied environments. The input of the system is a video frame from the multicopter's onboard camera, and the output is the estimates of displacement and rotation of the tethered high-altitude platform. This research proposes a technique for synthesizing training examples based on the application of 3D graphics tools. Thus, the neural network is trained on synthetic data generated in a virtual environment.