An Overbound Concept For Pseudorange Error From the LAAS Ground Facility

Abstract

The FAA’s Local Area Augmentation System (LAAS) broadcasts a parameter opr_gnd to describe the errors in the differential corrections due to the ground facility. An aircraft using LAAS computes a high probability bound on the resulting error in the position domain based on opr_gnd assuming that the errors are Gaussian distributed. This paper proposes a method for characterizing the ground error distribution and ensuring a bound is provided if the tails of the error are not Gaussian. The proposed probability density function for the ground error is synthesized from a Gaussian core and Laplacian tails. Hypothesis tests are developed for verifying error probability density and tail probability values from data. The degree to which these parameters can be verified with known confidence is derived as a function of the number of independent samples and the point on the error distribution where the tail is defined. Use of the Laplacian tail and the uncertainties in the parameters due to limited availability of data require that the estimated value of opr_gnd be inflated before broadcast to ensure the bound is achieved in the aircraft. Results show that even if thousands of independent samples are used, the inflation factors needed are significantly larger than if the tails of the error distribution are known to be Gaussian.