The Stanford – ESA Integrity Diagram: Focusing on SBAS Integrity

Article Details
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Title	The Stanford – ESA Integrity Diagram: Focusing on SBAS Integrity
Author(s)	M. Tossaint, J. Samson, F. Toran and J. Ventura-Traveset, European Space Agency, ESA; J. Sanz, M. Hernandez-Pajares and J.M. Juan, UPC, Barcelona, Spain; A. Tadjine and I. Delgado, GMV, Spain;
Year of Publication	2006

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.

The Worst Safety Index Diagram

Instead of representing each (XPE, XPL) pair for an all-in-view situation, it does that, at every second, for the sub-ensemble of satellites leading to the minimum Safety Index (XPL/XPE). The algorithm shown in Figure 1, as follows:

Figure 1: Stanford-ESA Modified Integrity Diagram Algorithm

Specifically, at each time sample, all the combinations of satellites from 4 to all-in-view are analysed. The combination of satellites leading to the minimum Safety Index (i.e. leading to the less possible comfortable Integrity margin) is selected. The Stanford-ESA Integrity diagram is then updated with the (XPE,XPL) pair corresponding to that minimum SI case. The process is repeated for every time sample. Obviously, with the Stanford-ESA Integrity diagram the obtained results for accuracy and availability do not have any meaning and the analysis of results shall only focus on Integrity. Indeed, showing that in this user domain worst-ever possible case there is no situation in which the error overcomes the protection level, is the best experimental guarantee that at user domain for a specific location and epoch over-bounding is assured.

The All Stanford ESA Diagram

In this case, instead of representing each (XPE, XPL) pair for an all-in-view situation, it does that, at every second, all the combinations of satellites from 4 to all-in-view are displayed. Moreover, the right of diagonal is modified as follows:

• If a MI happens, all the geometries on the right of diagonal are plot with the same colour, and with a common symbol (square, star, triangle,…). And the colour indicates the epoch relative to the time interval recorded in the file, in the colour bar of the plot.
• The previous rule applies only to the last 10 epochs with MIs. All the other epochs with MIs (if it happens) will be display as in the left side. Nevertheless, this situation should be extremely rare and will indicate an important anomaly from the receiver or system.

The aim of previous rules is to identify the sets of geometries associated to the same MI and, especially, to provide some information about the time correlation of such MIs. In this way, the all-geometries diagram provides a quick and clear view of the system performance for the all possible geometries (not only for all-in-view or the worst safety index). And, at the same time, the display is enhanced with time information for the unsafe geometries (i.e., with MIs), which are clustered by epochs using different symbols.

The number of geometries with MIs or with HMIs is also written in the plot, together with the number of epochs involved (notice that a given epoch can involve geometries with MIs and HMIs). Finally, at the bottom it is written the “number of epochs with XPE>XPL”, which summarizes the simple pass/fail criterion: no points on the right of diagonal (for any geometry at any epoch).

Four examples of All-Geometry diagrams are given in Figure 2. The first row shows two examples of diagram without MIs. The diagrams of second do not fulfil the integrity criteria, having geometries with MIs. In the left side diagram only two epochs are involved, labelled by yellow-squares and blue-stars. Such epochs are far in time. The first epoch (dark blue-stars) corresponds to the beginning of the file. The second one (yellow-squares) happened at the middle of data collecting period. Thence, such MIs are independent in time. The figure at bottom left shows a diagram with several geometries having MIs which involve five epochs. The MIs happen basically in three different periods of times: At the beginning of the file (dark blue-crosses), after the first quarter (light blue squares and circles) and before the third quarter of file (brown squares and triangles). HMIs happened only in two independent epochs, one of them involves only one geometry, which is in the left border of the region.

Figure 2: Four artificially generated examples of All-Stanford-ESA Integrity Diagram. The number of epochs (N) in the measurement file, the number of epochs with valid navigation solution (NV) and the number of computed geometries (NG) are shown at the top of each diagram.

The ICAO SARPS [3] requires that when performing all in view user positioning it is always verified that the protection level bounds the navigation system error all the time (i.e. points are always at the left of the diagonal of the nominal Stanford diagram). This is required, irrespectively of the alert limit, for which, instead the integrity risk is referred. Through discussions with standardisation experts the authors were informed that the main reason for such a conservative condition is to take a margin to cover the possible case that not all in view satellites are used in the position domain. When the “All Geometries Stanford–ESA Integrity diagram is considered, it could then be argued that this very conservative condition is not any more necessary, and that just showing the error does not go beyond the Alert limit without being warned by an over-bounding protection level could be sufficient. Yet, as we will show later (Section 3), EGNOS is required to meet the “out of tolerance” conservative criteria also in the case of the Stanford-ESA modified Integrity diagrams. This is consistent with EGNOS bounding design concept, in which EGNOS is required to bound always the residual error at the level of each individual PRN satellites orbit/clock and line of sight ionosphere pseudo-ranges.

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.