This paper investigates unmanned aerial vehicle (UAV)-aided jamming technique for enabling physical layer keyless security in scenarios where the exact eavesdropper location is unknown. We assume that the unknown eavesdropper location is within an ellipse characterizing the coverage region of the transmitter. By sequentially optimizing the transmit power, the flight path of the UAV and its jamming power, we aim at maximizing the average secrecy rate with arbitrary eavesdropper location. Simulation results demonstrate that the optimal flight path obtains better secrecy rate performance compared to that using direct UAV flight path encasing the transmitter and the legitimate receiver. Most importantly, even with the unknown eavesdropper location, we obtained a secrecy rate that is comparable to a scenario when the eavesdropper's location is known. However, the average secrecy rate with the unknown eavesdropper location varies depending on the proximity of the eavesdropper to the known location of the transmitter. We also observe that due to the UAV-aided jamming, the average secrecy rate stabilizes at some point even though the average received envelope power of the eavesdropper increases. This essentially demonstrates the effectiveness of the proposed scheme.