Protection Level Calculation Using Measurement Residuals: Theory and Results

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. INTRODUCTION In the next ten years the number of pseudorange sources for satellite navigation and their quality is expected to increase dramatically: The United States is going to add two new civil frequencies (L5 and L2C) in the modernized GPS, and Europe is planning to launch Galileo which should be fully operative before 2015, also with multiple frequencies. By combining two frequencies, users will be able to remove the ionospheric delay which is currently the largest error, thus reducing nominal error bounds by more than 50%. In particular, safety-of-life applications using augmentation systems will be greatly enhanced. However, it will remain a challenge to provide small hard error bounds Protection Levels – to meet stringent navigation requirements. Airborne multipath, ephemeris error, loss of signal due to scintillation (in equatorial regions), are still a challenge in the path to provide Cat III GNSS augmentation systems. For example, even with dual frequency, it is not obvious that the Wide Area Augmentation System (WAAS) with GPS alone would meet 100% APV II (20 meters vertical) availability over the United States [1]. There are many ways to improve the performance of an SBAS without changing the message standards [2]: by adding satellites, by adding reference stations, by improving the algorithms at the master station (specially the clock and ephemeris algorithms). It is worthwhile however, now that the new L5 MOPS is being developed, to explore possible modifications to the message content to improve performance. The current methodologies to provide integrity to augmentation system users are based on Gaussian overbounding techniques. For every source of error, the user receives a standard deviation that corresponds to the Gaussian overbound of the error. For this reason, every source of pseudorange error needs to be overbound, in a certain sense, by a gaussian distribution up to very small quantiles on the order of the probability of hazardously misdetection (10) [3] This is a very difficult task: for example, it is not possible to have experimental stationary distributions for the errors because the conditions and environment are always changing. Also, the errors are all mixed together so it is hard to isolate them. As a result, it is necessary to increase the Gaussian overbound to be sure to cover the tails of the individual error distributions. However, by doing so, we ignore the fact that the core of the distribution is usually much tighter than the overbound (by a large factor), thus giving up performance [4], [5]. In this paper, we present an estimation technique where errors are characterized by Gaussian mixtures. By using a bayesian approach, this technique optimally takes advantage of the tight core of the error distributions while