Protection Level Calculation Using Measurement Residuals: Theory and Results

摘要

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 in particular with error with heavy tail distributions or errors for which there is not enough data to evaluate the distribution density up to small quantiles. Because the computing power is expected to increase at the receiver level, it is worthwhile exploring new ways of computing integrity error bounds. We present a way of computing the optimal protection level when the pseudorange errors are characterized by a mixture of Gaussian modes. First, we 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 state the positioning problem using a Bayesian approach. Finally, we apply this method to protection level calculations for the Wide Area Augmentation System (WAAS) using real data from WAAS receivers. The results are very promising: Vertical Protection Levels are reduced by 50% without damaging integrity.