This paper is concerned with optimal trajectory control for two unmanned aerial vehicles (UAVs) in a multisource localization environment. The received signal strength (RSS) at the UAVs in specified time intervals permits passive differential RSS (DRSS)-based localization of multiple radio frequency (RF) sources with unknown transmit powers. A steering algorithm is proposed to update the UAV waypoints in order to minimize the summation of the uncertainty of the source locations. The UAV paths are optimized by maximizing the determinant of the Fisher Information Matrix (FIM). The FIM is approximated at successive waypoints using the estimated locations of the sources. In addition to maximizing the localization accuracy, the objectives of the proposed trajectory control are to minimize the number of UAVs, the mission time and the path length. As the DRSS is a non-linear measurement, an extended Kalman filter (EKF), which is a non-linear filtering technique, is considered in this paper. The efficiency of the approach is depicted through simulations.