The Stanford – ESA Integrity Diagram: Focusing on SBAS Integrity

Abstract

In this article, a new concept for SBAS integrity validation is presented. The proposed concept is a modification of the well known Stanford diagram [2], where a 2D histogram shows the relationship of position errors against protection levels for a set of measurements using an all in view satellite selection. The new method consists on two diagrams: the Worst-Safety Index diagram and the “All-Geometries” diagram, known here as the Stanford-ESA and the All-Stanford-ESA, respectively. The first consist on taking, at each sample time and given location, the worst possible satellite geometrical combination (out of all possible combinations) from a SBAS integrity margin viewpoint. In the second, all possible geometries are displayed and, in case of MIs, the geometries associated to each epoch are leveled with different symbols and colors. It allows, to easily identify the different clusters and to assess the time correlation of the events. Real measurement results are presented here showing that the EGNOS integrity margins remain safe under this very exigent criterion, a certainly very positive result. It is suggested here the use the Stanford-ESA Integrity concept, for routine performance monitoring and to support and complement the safety case of the EGNOS systems with real experimental data.

Introduction

ESA detailed studies on the transfer of integrity between pseudo-range and position domains [1], have led to the introduction of a specific kind of representation technique able to provide a strong evidence of the robustness of an SBAS (Satellite Based Augmentation System) system with respect to integrity bound provision, and for all possible satellite geometrical conditions. This new representation is then exclusively focussed on Integrity (versus the Integrity, Availability, and Accuracy information of the bi-dimensional nominal Stanford Diagram). During the SBAS Interoperability Working Group meeting celebrated in Madrid (Spain) in March 2005, it was suggested to call this new Integrity representation as the “Stanford-ESA Integrity Diagram”. The Stanford-ESA modified Integrity Diagram concept is described in this Document, and a quick and simple algorithm to compute this diagram is provided in the appendix, together with a source code example of its implementation in C and in FORTRAN77. Results with real data sets from several sites in Europe are also shown here.

The Stanford-ESA Modified Integrity Diagram

The Stanford-ESA Integrity Diagram, as the name itself indicates, is a modification of the well known Integrity-Availability-Accuracy 2D histogram proposed by the WAAS laboratory of the Stanford University, commonly known as “Stanford Diagram”. The Stanford diagram has become a reference representation technique in the SBAS domain, especially to have a quick and clear view of system performances, highlighting its capability to clearly show the integrity margins offered by the SBAS system. For further details on the Stanford Diagrams, the reading of [2] is highly recommended. The Stanford-ESA Integrity Diagram concept proposes exactly the same representation technique, but introducing a modification in the data to be used as input source to build the graph, which focuses exclusively on integrity. Note that the standard Stanford Diagram uses an all-in-view approach (i.e. all GPS satellites in view) for computing the error/protection level pair to plot for each time sample. When focusing on integrity, though, the classical Stanford Diagram is not always conservative. Indeed, using all in view satellites to measure integrity over-bounding capability may lead, for instance, to a situation in which a specific integrity loss in one or more satellite or IGP may be mitigated by other “well-bounded” line of sight, so that the net effect at position domain will not be appreciated. Furthermore, there is no obligation for the users to use always all available satellites, since for instance in some cases, some satellites in view may have been discarded because of a wrong tracking. Those users may have big discrepancies in performances with respect to others. When focusing on the ability of SBAS to always maintain integrity, and to overcome the above limitations, the Stanford-ESA Integrity Diagram converts the typical Stanford Diagram into the most possible conservative analysis tool at the user domain. Two possible displays are being considered for the Stanford-ESA Integrity Diagram, booth involving the same computational load:

a) The Worst-Safety-Index diagram and

b) The All-Geometries diagram.

References

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[1] A. Tadjine. “WP 103.2: Integrity at User Level (Part II)”. Issue 1, Rev. B. Ref. GMV-EGNOSAE-TN-007/04. Dated 17/01/2005.

[2] WADGPS Laboratory (Stanford University). "WAAS Precision Approach Metrics. Accuracy, Integrity, Continuity and Availability," http://waas.stanford.edu/metrics.htm. October 1997

[3] SARPS Amendment 77, Annex 10 to the Convention on International Civil Aviation, Aeronautical Telecommunications: International Standards and Recommended Practices, Volume 1, Radio Navigation Aids, November 2002.

[4] Basic Research Utilities for SBAS. M. Hernández-Pajares, J. M Juan and J. Sanz. gAGE/UPC 2003. http://gage9.upc.es.

[5] GMS Architectural Design and Detailed Design Document, M. Hernández-Pajares, J. M. Juan and Jaume Sanz. gAGE/EEC, 2004. EUROCONTROL.

[6] Minimum Operational Performance Standards for GPS/WAAS Airborne Equipment, RTCA, Do 229C, November, 2001.