In the intelligent transportation systems (ITS) field, the number of applications that demand a high integrity positioning system is growing. In order to improve the integrity of localization systems, GPS is usually hybridized with additional proprioceptive sensors. In this paper, a new hybridization algorithm based on GPS plus odometry and a gyro is proposed as an improvement of the most common extended Kalman filter (EKF) approach. In concrete, these investigations focus on the performance of the system under bad initial conditions. Results show the suitability of the proposed system for navigation under bad initial values of heading, and its benefits as compared to two state-of-the-art methods of the literature: an EKF, and a particle filter based solution.