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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Position Lines and a Systematic Error
From: Trevor Kenchington
Date: 2003 May 30, 22:13 -0300
From: Trevor Kenchington
Date: 2003 May 30, 22:13 -0300
Jared Sherman wrote: > A circle of error may still be needed to accomodate other factors, but at least the inherent error RANGE in each sighting is immediately visible when a simple wide stroke is drawn. I applaud Jared's intent. (I get to waste far too much energy arguing with scientific colleagues who present their point estimates and grossly misrepresent the massive uncertainties surrounding them. It makes me sensitive to questions of precision of measurements.) One caution though: Drawing two "fat" LOPs will result in a parallelogram of overlap which would then seem to represent the area within which the true position most probably lies. That would, however, be unduly pessimistic. If the errors in the LOPs are largely random (rather than systematic), then it is most unlikely that both of a pair of LOPs will have high errors. If there is a 95% chance that each LOP passes within 4 miles of the true position, then there is a 5% chance that one LOP is 4 miles or more from that position. But there is only a 5%x5% = 0.25% that both LOPs are so far off the mark. In more practical terms, the contour surrounding the probable area in which the true position lies will be an ellipse drawn inside the parallelogram formed by the margins of Jared's two thick lines. The likelihood that the true position lies in one of the corners of the parallelogram is very low. Of course, in an ideal representation, Jared's lines would be drawn with soem computer graphics set up that could make the centre of each line near-black while it faded away to a very pale grey on either side. At least, I suspect that the random errors have a somewhat "bell-shaped" distribution, such that most LOPs are not so far from the true position even though a few are a long way off. Such complex plotting is not, of course, either needed or practical. Trevor Kenchington -- Trevor J. Kenchington PhD Gadus@iStar.ca Gadus Associates, Office(902) 889-9250 R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251 Nova Scotia B0J 2L0, CANADA Home (902) 889-3555 Science Serving the Fisheries http://home.istar.ca/~gadus