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Vehicle-to-vehicle communications via dedicated-short-range-communication (DSRC) devices will enable safety applications such as cooperative collision warning. These devices use the IEEE 802.11p standard to support low-latency vehicle-to-vehicle and vehicle-to-infrastructure communications. However, a major challenge for the cooperative collision warning is to accurately determine the location of vehicles. In this paper, we present a novel cooperative-vehicle-position-estimation algorithm which can achieve a higher accuracy and more reliability than the existing global-positioning-system-based positioning solutions by making use of intervehicle-distance measurements taken by a radio-ranging technique. Our algorithm uses signal-strength-based intervehicle-distance measurements, vehicle kinematics, and road maps to estimate the relative positions of vehicles in a cluster. We have analyzed our algorithm by examining its performance-bound, computational-complexity, and communication-overhead requirements. In addition, we have shown that the accuracy of our algorithm is superior to previously proposed localization algorithms.