Paired overbounding and application to GPS augmentation

The relationship between range-domain and position-domain errors remains an open issue for GPS augmentation programs, such as the Federal Aviation Administration's Local Area Augmentation System (LAAS). This paper introduces a theorem that guarantees a conservative error bound (overbound) in the position domain given similarly conservative overbounds for broadcast pseudorange statistics. This paired overbound theorem requires that a cumulative distribution function (CDF) be constructed to bound both sides of the range-domain error distribution. The paired overbound theorem holds for arbitrary error distributions, even those that are non-zero mean, asymmetric or multimodal. Two applications of the paired overbound theorem to GPS augmentation are also discussed. First, the theorem is employed to construct an inflation factor for a non-zero mean Gaussian distribution; in the context of a simulation of worst-case satellite geometries for 10 locations in the United States and Europe, the required inflation factor for broadcast sigma is only 1.18, even for biases as large as 10 cm for each satellite. Second, the theorem is applied to bound a bimodal multipath model tightly; the result shaves more than 40% off the previously established inflation factor derived through a more overly conservative analysis.