In this paper, a Bayesian approach is proposed for the early detection of a drone threatening or anomalous behaviour in a surveyed region. This is in relation to revealing, as early as possible, the drone intent to either leave a geographical area where it is authorised to fly (e.g. to conduct inspection work) or reach a prohibited zone (e.g. runway protection zones at airports or a critical infrastructure site). The inference here is based on the noisy sensory observations of the target state from a non-cooperative surveillance system such as a radar. Data from Aveillant's Gamekeeper radar from a live drone trial is used to illustrate the efficacy of the introduced approach.