Protection Level Calculation in the Presence of Heavy Tail Errors Using Measurement Residuals

In safety-of-life applications of satellite navigation, the Protection Level (PL) equation translates what is known about the pseudorange errors into a reliable limit on the positioning error. The current PL equations for Satellite based augmentation systems are based on Gaussian statistics: all errors are characterized by a zero mean Gaussian distribution which is an upper bound of the true distribution in a certain sense. This approach is very practical: the calculations are simple and the receiver computing load is small. However, when the true distributions are far from Gaussian, such characterization forces an inflation of the protection levels that damages performance. This happens for example with heavy tail distributions or errors for which there is not enough data to evaluate the distribution density up to small quantiles. Also, in the certification process, it is very difficult to agree on a given distribution when the statistics are gathered from a multitude of situations (like elevation angle in the case of multipath). With the development of new optimization methods and the increasing computing power, it is worthwhile exploring new ways of computing integrity error bounds. In this paper we present a way of computing the optimal protection level when the pseudorange errors are characterized by a mixture of Gaussian modes. First, we will show that this error characterization adds a new flexibility and helps account for heavy tails without losing the benefit of tight core distributions. Then, we will state the positioning problem using a Bayesian approach. Finally, we will apply this method to