Treatment of Biased Error Distributions in SBAS

Todd Walter, Juan Blanch, Jason Rife

Stanford University, Stanford, CA 94305-4035.

DOI:                 

Abstract

The original protection level equations for SBAS assumed that all actual error distributions could be easily overbounded by zero-mean gaussian distributions. However, several error sources have since been found that could lead to significant biases for specific users. The expectation is that over long periods of time and all users, the aggregate errors should have a very small mean. However, certain users, at specific times or locations, may have significant biases in their measured pseudoranges. One source of bias is signal deformations. Originally thought of as a failure mode, it is now recognized that geostationary satellites have a noticeably different signal than the GPS satellites (primarily due to their bandwidth limit). Recent results also show that the GPS satellites have measurable differences from satellite to satellite as well. The magnitude and sign of the biases depend on the user equipment and have been shown to have significant unit-to-unit variation. A biased distribution may be overbounded by a zero mean gaussian, provided the sigma value has been sufficiently increased. As the bias becomes larger, this inflation leads to a greater loss of availability than if the protection level equations had explicitly accounted for it. It is therefore important to find the smallest possible inflation to adequately bound the bias. This paper makes use of new overbounding methods to relate the required inflation to the bound.

Keywords

SBAS, bias, overbound, integrity, CDF

Conflicts of Interest

The authors declare no conflicts of interest.

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