A Novel Integrity Concept for GBAS Precision Approaches Induced by Error Propagation with Non-Gaussian Distributions

In a differential GPS system such as the ground based augmentation system (GBAS) for precision approaches of aircraft, GPS reference stations with known locations are utilized to determine and remove most of the ranging uncertainties of the GNSS system in use. Corrections are broadcast to the aircraft and all but residual errors are eliminated. These residual pseudorange errors are due to the position difference between the aircraft and the reference station and lead to a position uncertainty of the aircraft. To qualify for category I precision guidance, the system has to guarantee that undetected pseudorange errors do not cause horizontal and vertical position errors larger than the horizontal and vertical alert limits with a probability smaller than $2\times 10^{-7}$ per approach. There are four fundamental sources of residual pseudorange error for a single frequency GBAS system: signal multipath, receiver noise $N_0$, residual troposphere error due to the differential applied troposphere model and the error induced by ionosphere gradients. In this work we combined different theoretical probability density functions (PDF) for each individual error to a combined pseudorange error distribution. This distribution was propagated through the GBAS Hatch filter and then mapped into the position domain using a one day constellation change observed at Oberpfaffenhofen, Germany (ICAO Identifier EDMO). Where possible, the propagation process was carried out through analytical convolution. When no analytical solution existed, we either performed a numerical solution of the convolution integrals (if the PDF was available in an analytical form) or used numerical convolution for discrete timeseries. The PDF propagation though the Hatch filter was simulated using a pseudo random generator based on the pseudorange error PDF. Our calculations using the unapproximated PDFs yielded a significant reduction of the position domain error at the $2\times 10^{-7}$ integrity risk level when compared to classical methods like Gaussian or Gaussian Mixture overbounding. Indeed, the results suggest a new integrity concept that could be beneficial in obtaining CAT-III performance. The concept employs alert limits and protection levels in the along-track, cross-track and vertical direction rather than the traditional dual split in horizontal and vertical components only. This new concept does not need inflation factors and promises real-time performance through look-up tables. With assumed realistic minimum detectable errors (MDE) for GBAS monitoring algorithms, the position domain error bounds can be reduced even further and decrease close to the projected CAT-III alert limits. This is especially true since the projected ionosphere threat space for Europe does not contain the extreme gradients that have been observed over the continental US