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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Avoiding the symmedian (and other) points
From: Bill Lionheart
Date: 2018 Nov 7, 06:05 +0000
From: Bill Lionheart
Date: 2018 Nov 7, 06:05 +0000
> A serious problem with the history of the computation of error ellipses was a choice made by the editors at the Nautical Almanac office years ago. Around the same time that the least squares solution started to be published regularly in the Nautical Almanac itself (after 1989), a volume was published covering a variety of calculation methods including the calculation of error ellipses. Unfortunately they chose to calculate the standard deviation of the observations from the observed sights themselves. This is an option but it meant that error ellipses were undefined for a pair of lines of position, and it implied certain other oddities. For example, a larger triangle for three crossing lines automatically yielded a larger error ellipse. This apparently satisfied the preconceived notions of navigation lore, but it was a poor choice in mathematical terms. The standard deviation of observations should be estimated a priori. Then two sights have an error ellipse that means somethings. And also three sights have an error ellipse that does not misleadingly shrink when the lines of position cross in a tiny triangle. > That is an interesting point Frank and gets to the origin of the confusion. Was there a specific methodology published (eg in the Nautical Almanac) for estimating the standard deviation of the sights from the residual error? Bill
