A theoretical analysis of the Extended Kalman Filter for data fusion in vehicular positioning

Global Navigation Satellite Systems (GNSS) offer a great value for many location-based services and applications. However, due to their limitations in terms of coverage, continuity, accuracy and integrity, GNSS are often fused with some extra aiding sensors. To perform the data fusion of multiple sensors it is possible to find in the literature of the field a large number of approaches that claim better accuracy, efficiency in computational terms or robustness than a reference one that is given for comparison. Normally, this reference is the Extended Kalman Filter (EKF), the most common version of the Kalman Filter for non-linear systems. However, because sensors, tests, filter tunings, etc. vary largely from one publication to another, it is not possible in many occasions to have a clear idea of the real benefits of the different methods in fair terms. This paper presents a theoretical analysis of the goodness of the EKF in loosely coupled data fusion architectures. The methodology presented can be applied to understand the limitations of different approaches for fusing multiple sensors in non-linear systems. Illustrations depict a real case with a sensor-set consisting of a GNSS, a gyro and the odometry of a road vehicle.