For the Oxford Aerial Tracking System (OATS) we are developing a robot helicopter that can track moving ground objects. Here we describe algorithms for the device to perform path planning and trajectory prediction. The path planner uses superquadratic potential fields and incorporates a height change mechanism that is triggered where necessary and in order to avoid local minima traps. The goal of the trajectory prediction system is to reliably predict the target trajectory during occlusion caused by ground obstacles. For this we use two artificial neural networks in parallel whose retraining is automatically triggered if major changes in the target behaviour pattern are detected. Simulation results for both systems are presented.