Even though the wireless positioning in sensor networks has been extensively studied in the past decades, there is no contribution discussing positioning the receiver that belongs to another system, i.e., the third-party receiver. In this paper, we propose a new scheme to solve the problem by full-duplex rtechnique. In our scheme, we let the sensors conduct the full-duplex relay for the target receiver. By measuring the power variation of the corresponding transmitter, the sensors are able to position the receiver. Under the proposed scheme, we develop two methods. The first one is based on angle estimation, which requires multiple sensors. The second one is based on angle and time-difference-of-arrival (TDOA) estimations, which requires only one sensor. The simulation results demonstrate the performance of the proposed methods.