Mathematical and experimental analysis of GNSS horizontal and vertical errors

Recent progress in the field of the satellite navigation systems (GNSS, SBAS) supports effort to use it for the determination of train position for the railway safety-related systems. The key feature of localization from the point of view of safety-related applications in transportation is integrity. Currently available SBAS systems were developed in order to satisfy the aviation requirements, but the safety concept on the railways is very different from the aviation safety concept. The integrity level of these systems is not suitable for the safety-related railway applications. A method for increasing integrity was proposed in previous works. The method is based on relation between horizontal and vertical GNSS errors. Verification of applicability of the method by mathematical model is necessary In this paper a mathematical model of GNSS position determination is developed in order to investigate the relation between GNSS errors in horizontal plane and vertical direction. The position computed by this model is compared to the results of the simulations based on real GNSS data.