An application of Gaussian Overbounding for the WAAS fault free error analysis

Timothy R. Schempp and Arthur L. Rubin

Abstract:	The Wide Area Augmentation System (WAAS) is a safety-critical, software-intensive system, augmenting the satellite-based Global Positioning System (GPS). The system provides airborne users with positions of adequate accuracy, availability, continuity, and integrity to support different phases of flight. WAAS has a top-level safety requirement to protect users against Hazardously Misleading Information (HMI) with seven 9’s of integrity (10-7 probability of HMI). An integral part of the proof that WAAS meets this strict safety requirement lies in the “Fault Free” HMI Analysis. The fault free HMI analysis consists of a rigorous examination of error distributions collected under fault- free conditions. Fault-free is interpreted to mean that each component of the system (hardware and software) is functioning as intended. WAAS has conducted extensive analysis to ensure that integrity is maintained under hardware and software failure conditions as well. The faulted case will be the topic of future papers. A WAAS user computes position solutions and error bounds based on a Gaussian model of the error distributions. A user combines the range estimates from all satellites in view and computes a least squares position estimate. The error in the position estimate is a linear combination of the individual error sources. The user computes the overall integrity bound by combining the error bounds for each error source assuming independent Gaussian distributions. Theoretical analysis often relies on distributions having nice properties so that zero mean Gaussian curves can be used as the model. Real life distributions rarely have these nice qualities making it difficult to do theoretical work with empirical distributions. The Gaussian Overbounding technique used on WAAS provides a rigorous framework for dealing with non-zero mean distributions collected from empirical data. This analysis lays out a theoretical approach for showing that a user’s position error is always bounded by the user’s protection limit for every possible user/satellite geometry. The approach adds three important concepts to the existing body of knowledge. First, a method to rigorously handle non-zero mean distributions is presented. Second, the approach is generalized so that it may be applied to any combination of error sources a user may be using. Third, the desired probability of failing to bound the error can be arbitrarily set. WAAS uses a fault tree to allocate the top-level safety requirement among every conceivable error source. The fault tree allocation to this particular analysis is 3.33x10-10. As the reader will see, in the fault free case, WAAS has a great deal of margin. The theoretical analysis is applied to error distributions derived from 30 days of WAAS data collected from 25 reference stations.
Published in:	Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002) September 24 - 27, 2002 Oregon Convention Center Portland, OR
Pages:	766 - 772
Cite this article:	Schempp, Timothy R., Rubin, Arthur L., "An application of Gaussian Overbounding for the WAAS fault free error analysis," Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 766-772.
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