Non-Gaussian Error Modeling for GBAS Integrity Assessment

Abstract

Four basic error sources exist for residual pseudo-range errors in a single frequency differential GPS system for ground based augmentation (GBAS): signal multipath, increased receiver noise (carrier-to-noise density ratios ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> )) due to interference, residual differential troposphere error, and the error induced by ionosphere gradients. Without restricting ourselves to classical Gaussian overbounding, we combine their probability density functions (pdfs) to a total pseudo-range error distribution. This distribution is propagated through the GBAS Hatch filter and then mapped into the position domain using a worst case (selected by maximum vertical dilution of precision (VDOP)) of a full 31 satellite constellation with the two most critical satellites failed observed at Braunschweig Airport, Germany. Our calculations yield a significant reduction amounting to 46% of the position domain error at the 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> integrity risk level when compared with the classical Gaussian overbounding approach.