Integrity bounds for rail and road applications based on local hazard maps

Current high accuracy positioning systems for transport applications require high safety and high accuracy. Considering that some of the most relevant errors leading to a loss of integrity are multipath and interferences this paper introduces the use of a set of digital maps for mitigating the presence of such hazards. Moreover, relevant statistical modelling of multipath and interference errors is provided. More in details, three maps are introduced: the satellite visibility map, the multipath map and the interference map. The satellite visibility map, through a piecewise constant function, allows the receiver determining, for each azimuth, the minimum elevation of a satellite to consider it suitable for PVT. Moreover, a quantized version of such parameters allows designing an optimized version of the data to be transmitted. Concerning the interference map, it is constituted by a list of the prevailing radio frequency interferences and their spectral characteristics. As for the multipath map, a statistical model where the variance of the multipath error is considered as a random variable with a discrete distribution is considered. More in details, the multipath variance is modelled as the product of a geometrical factor, depending on the satellite elevation, and the C/N0, and a stochastically modeled inflating factor. These assumptions result in a distribution of the multipath error which follows a Gaussian Mixture. Therefore, a Mean Square receiver position solution, and the application of Solution Separation for satellite fault determination and PL calculation under the Gaussian Mixture distribution hypothesis, is derived. A Monte Carlo simulation is carried out for determining the estimation error, with respect to a Weighted Least Square solution and a classical Gaussian distribution of the multipath error with inflating factor equal to 1. Thanks to the better matching of the measurement error distribution, larger errors are attenuated and accounted for by the protection level. A consistent reduction in misleading information is demonstrated through a Stanford Plot analysis.