NavList:

There has been a lot of discussion about the Ellipse of Confidence, how one might compute it theoretically, and a little discussion about how useful it is to the practical navigator.

Continuing a little further down the validity of such discussions in the real world, I would note that all this discussion assumes the Marc St Hilaire method is assumed, where the navigator starts from an assumed position to produce lines (Lines of Position) along which the measured altitude of the celestial body would be equal. Where those lines intersect is the true position, within a margin of error given by the Ellipse of Confidence.

Where those Lines of Position are in fact circles of position centred on the geographical positions of the celestial bodies, it will not matter where the assumed position is relative the true position - the true position will be given with one iteration of sight reduction. However, the usual assumption when using the Marc St Hilaire method is that the Lines of Position are well approximated by straight lines, not arcs of a circle. The question then arises: how far does the assumed position have to be from the true position before the error due this approximation starts to become equivalent to the 'average' radius of the Ellipse of Confidence?

Geoffrey Kolbe