This paper considers the problem of choosing measurement locations of an aerial robot in an online manner in order to localize an animal with a radio collar. The aerial robot has a commercial, low-cost directional antenna and USB receiver to capture the signal. It uses its own movement to obtain a bearing measurement. The uncertainty in these measurements is assumed to be bounded and represented as wedges. The measurements are then merged by intersecting the wedges. The localization uncertainty is quantified by the area of the resulting intersection. The goal is to reduce the localization uncertainty to a value below a given threshold in minimum time. We present an online strategy to choose measurement locations during execution based on previous readings and analyze its performance with competitive analysis. The time required to localize a target is upper-bounded by the function of measurement noise, desired localization uncertainty and minimum step length. We also validate the strategy in extensive simulations and show its applicability through field experiments over a 5 hectare area using an autonomous aerial robot equipped with a directional antenna.