# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Still on LOP's**

**From:**Rodney Myrvaagnes

**Date:**2002 May 3, 00:01 -0500

If that is indeed the question, most of the argument has been off the point. I thought George was maintaining that no cocked hat that could arise from 3 LOPs with whatever error distribution could enclose more than 25% of the locations that could give rise to those LOPs. Even one counterexample defeats that claim, so maybe he is claiming something else. I can give lots of counterexamples. Another one herewith: An equilateral triangle of equivalent readings, with each vertex at the .1 distance (.1 probability of the reading being at that or greater distance) produces a probability of the location falling inside of 0.9 * 0.9 * 0.9 =0.73, so 73% of locations will be inside. the triangles adjacent on each side will be inside 2 of the .9 bands, so will have a probability less than 0.9 * 0.9 * 0.1 <= .081 so less than 8% in those areas. The next triangles have 0.9 * 0.1 * 0.1 <= 0.009 or less than 1%. The probability of that set of readings actually occurring is very low, but not zero. On Thu, 2 May 2002 08:59:04 +0100, Dr. Geoffrey Kolbe wrote: > >The question (I think) we are asking is, "Given this distribution of n >cocked hats, where is the most probable position and what is the error in >its position?" This is a much more tractable problem. > >Better yet to plot means for the multiple observations on each bearing and >then use the standard deviations to say something about the errors on each >mean and so to the error on the MPP. This is the most efficient way to >proceed. > Rodney Myrvaagnes J36 Gjo/a "Curse thee, thou quadrant. No longer will I guide my earthly way by thee." Capt. Ahab