Relative positioning among vehicles is a fundamental parameter for advanced applications of intelligent transportation systems such as collision avoidance and road safety. However, the level of positioning accuracy achievable using Global Navigation Satellite Systems does not meet the requirements of these applications. Cooperative positioning (CP) techniques can be used for improving the performance of absolute or relative positioning in a vehicular ad hoc network (VANET). The tight integration of Global Positioning System (GPS) data among communicating vehicles has already been introduced by the authors as a tight CP approach with specific advantages over differential GPS (DGPS) for relative positioning. In this paper, we propose an enhanced tight CP technique adding low-cost inertial navigation sensors and GPS Doppler shifts. Based on analytical and experimental results, the new method outperforms its predecessor and DGPS by 10% and 24%, respectively.