An architecture for vehicle position estimation is introduced in this paper to tackle the issue of vehicles positioning in traffic congestion of intelligent transportation system (ITS). The introduced architecture is related to three unmanned aerial vehicles (UAVs) equipped with uniform linear array (ULA), ITS center and the terminal of position estimation, in which the UAV collect data from the ULA, the ITS center store data and the terminal is responsible for executing the corresponding direction of arrival (DOA) estimation algorithm to estimate the vehicle position. In the introduced architecture, DOA estimation is the crucial issue, hence a robust sparse recovery framework based on the optimal weighted subspace fitting is put forward for DOA estimation in the presence of direction-dependent unknown mutual coupling. Firstly, a data model can be obtained by a new transformation approach. Then, a sparse recovery algorithm based on the weighted subspace fitting is used to estimate the desired DOAs. The proposed DOA estimation algorithm can achieve superior performance in both coherent and incoherent signals in the environment of direction-dependent mutual coupling, and this environment often occurs in traffic congestion. Based on the DOA estimation results obtained from the proposed efficient regularized sparse recovery algorithm, the position of vehicles is final estimated by a weighted three-points cross-positioning method. The results of various simulation experiments fully demonstrate the robustness and superiority of the proposed architecture and algorithm.