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

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

Peer Reviewed

Abstract: For Loran to provide redundancy to GPS for aviation, Loran must meet aviation integrity requirements. Under nominal conditions, integrity derives from being able to bound the horizontal position error using the horizontal protection level (HPL). This is accomplished by guaranteeing that the correct Loran cycles are tracked, sufficient error bound models are used, and HPL calculations are correctly performed. Cycle selection integrity is provided by the cycle confidence calculation. The cycle confidence algorithm needs to be conservative in estimating cycle error probability. When available, the algorithm uses redundant measurements in a manner similar to GPS RAIM algorithms where testing using chi squared (w2) distributions is conducted. This paper examines the use of redundant measurements in the form of the weighted sum squared error (WSSE) and determines when the w2 assumption is valid. It applies those results to the Loran cycle confidence algorithm and uses them to help demonstrate its integrity.
Published in: NAVIGATION: Journal of the Institute of Navigation, Volume 54, Number 4
Pages: 277 - 291
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