NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Still on LOP's
From: George Huxtable
Date: 2002 Apr 27, 22:37 +0100
From: George Huxtable
Date: 2002 Apr 27, 22:37 +0100
Clive Sutherland appears to have difficulty accepting the concept of the true position, in considering the question of the probability of the true position lying within the cocked hat, when he says- >we can never >find the True position! Indeed I postulate that the true position is an >imaginary, zero dimensional point that can never be found. Well, satellite navigation will give a vessel's position (according to some datum, which is a matter it's best not to go into just now) to sufficient accuracy such that errors in the known true position can be neglected, in this context of measuring bearings to landmarks. If that doesn't satisfy him, perhaps he will consider taking a round of bearings of landmarks from a well-known position, such as that of Greenwich Observatory (the best-known position that I can think of). I admit that the fact that the Observatory is based on land rather than at sea is a minor complication, but the principle remains. Then Clive says- >George asks me if �I believe the true position must be inside the cocked hat�, >My question to George is �Does he think it must not?� I will answer his question, even though he has avoided answering mine. No, I don't think the true position must not be inside the cocked hat, of course. If enough measurements are made, the true position will be inside the cocked hat in roughly 1 in 4 of those measurements, and outside it in 3 in 4. Clive continued- >Some time ago I saw an analysis as described by J.E.D.Williams below in a >navigation text book and I think it was the Admiralty Manual of Navigation but >it could have been an RAF manual. I can�t be sure as I don�t have either to >hand. I think this was most likely J.E.D.Williams book "From Sails to Satellites" that I referred to and quoted from earlier. It's a fascinating work to delve into and uncover a wide range of unexpected and original insights into navigation. I am grateful to Clive for drawing attention to the correspondence about the cocked hat in the "Journal of Navigation". (no longer J.Inst of Nav, as Clive referred to it). Note that this is the UK-published journal from the Royal Institute of Navigation, and not its American namesake. Indeed, after his reminder, I found those very volumes on my own bookshelves. They make interesting reading, in that recent discussions on this list echo, with uncanny closeness, several of the arguments that arose a decade ago. They were triggered by a contribution from Williams, which corresponds closely with the reference to the same matter in his later book. For anyone that would like to follow the matter up, it can be found in the following issues of the Journal of Navigation- Vol 44 no 2 (May 1991) pages 269-271 Vol 44 no 3 (Sept 1991) page 433 Vol 45 no 1 (Jan 1992) pages 143-147 Vol 46 no 1 (Jan 1993) pages 132-137 The Journal should be available in any good library with a maritime flavour. Contained in the third of those listed issues is a contribution by P.J.D.Gething, which refers to a paper by H.E.Daniels (1951), "The theory of position finding", in Journal of the Royal Statistical Society, 13B, 186. He says " Daniels considered polygons of more than three position lines as well as triangles; his general result was that the largest closed polygon formed by n lines is a confidence region of probability given by- 1 - n/(2^(n-1)) " (where ^ means "to the power of") I haven't read Daniels' paper. George Huxtable. ------------------------------ george@huxtable.u-net.com George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. Tel. 01865 820222 or (int.) +44 1865 820222. ------------------------------