Proving the Integrity of the Weighted Sum Squated Error (WSSE) Loran Cycle Confidence Algorithm

Sherman C. Lo, Benjamin B. Peterson, and Per K. Enge

Abstract:	For Loran to provide redundancy to GPS for aviation, Loran must meet aviation integrity requirements. The integrity under nominal conditions derives from being able to bound the horizontal position error via the horizontal protection level (HPL). This is accomplished by guaranteeing that the correct Loran cycles are being tracked, adequate and complete error bound models are used for the HPL, and HPL calculations are performed correctly. The means of providing a guarantee on cycle selection is through a calculation of its confidence (“cycle confidence”). The cycle confidence algorithm needs to be conservative since it ensures that the measurements used by the navigation solution and the HPL is free of cycle error. When available, the algorithm uses redundant measurements in a manner similar to GPS receiver autonomous integrity measurement (RAIM) algorithms where testing using ÷2 distributions are conducted. This paper will examine the use of redundant measurements in the form of the weighted sum squared error (WSSE) and determine when the ÷2 assumption is valid. It will apply those results to the Loran cycle confidence algorithm and use them to help develop the demonstration of integrity.
Published in:	Proceedings of the 2007 National Technical Meeting of The Institute of Navigation January 22 - 24, 2007 The Catamaran Resort Hotel San Diego, CA
Pages:	187 - 200
Cite this article:	Lo, Sherman C., Peterson, Benjamin B., Enge, Per K., "Proving the Integrity of the Weighted Sum Squated Error (WSSE) Loran Cycle Confidence Algorithm," Proceedings of the 2007 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2007, pp. 187-200.
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