A Comparison of LAAS Error Bounding Concepts

The FAA's Local Area Augmentation System (LAAS) broadcasts a parameter spr_gnd to describe the errors in the differential corrections due to the ground facility. An aircraft using LAAS computes an upper bound with high probability on the resulting error in the position domain based on spr_gnd assuming that the errors are Gaussian distributed. This paper compares five bounding methods in terms of assumptions and resulting performance. Assumptions regarding the tails of the error distribution range from a Gaussian model to an exponential model. Performance is compared in terms of the factor by which the estimated value of spr_gnd must be inflated before broadcast to ensure the bound is provided with known confidence. For fixed, desired confidence the inflation factor varies with the number of independent samples used to estimate spr_gnd. Results show that using the same number of samples, methods assuming Gaussian tails give significantly smaller inflation factors than does the exponential tail method. Between these two extremes, is a more recently conceived method that assumes the error distribution is a mixture of Gaussian distributions with different standard deviations. The Gaussian mixture method gives inflation factors that are smaller than for the exponential tail method and may most closely correspond to the manner in which errors are present in real data. The contents of this material reflect the views of the author. Neither the Federal Aviation Administration nor the Department of Transportation makes any warranty or guarantee, or promise, expressed or implied concerning the content or accuracy of the views expressed herein.