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In contrast to carrier-phase measurements, receiver-generated Doppler measurements have much better availability, even in severe urban canyons or high-dynamic movement applications, while providing centimeter-level precision. Thus, the Doppler-aided approach may improve the positioning accuracy of the receiver. Some Kalman-filter-based applications have been developed in recent years, but the theoretical error analysis is still missing. In this paper, we propose a model-free Doppler-aided position estimation approach. The Doppler measurements are modeled together with the code pseudoranges and then solved as a weighted least square (WLS) problem. In addition, we analyze the lower bound of errors of the approach based on the Cramér-Rao bound (CRB). Simulation results and the error analysis show that the proposed approach may improve accuracy in position estimation.