In this paper, a single Unmanned-Aerial-Vehicle (UAV)-aided localization algorithm which uses both Doppler and Time of Arrival (ToA) measurements is presented. In contrast to Doppler-based localization algorithms which are based on non-convex functions, exploiting ToA measurements in a Least-Square (LS) Doppler-based cost function, leads to a quadratic convex function whose minimizer lies on a line. Utilizing the ToA measurements in addition to the linear equation of minimizer, a closed form solution is obtained for the emitter location using a constrained LS optimization. In addition, a trajectory design of the UAV is provided which has also closed-form solution. Simulation experiments demonstrate the effectiveness of the proposed algorithm in comparison to some others in the literature.