NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: A simple three-body fix puzzle
From: Tom Sult
Date: 2010 Dec 10, 21:08 -0600
From: Tom Sult
Date: 2010 Dec 10, 21:08 -0600
Glad to hear it but I must say I am still confused by the assertion that the probability of being at the center of a perfect crossing 3 body fix is "0" Thomas A. Sult, MD 3rd Opinion 1415 First First St. South #5 Willmar, MN 56201 320 235 2101 Office www.3rdOpinion.us tsult@mac.com On Dec 10, 2010, at 4:27 PM, Frank Reed wrote: > Tom, you wrote: > "It seems to me the point of this is that the best probability of > location is a "donut" that roughly follows the lop's around the hat. > We have learned that we have perhaps a 25% +/- the details chance of > being close to any "center" of the hat. And we can calculate the > probability distribution of our location along any one of our LOP's. > If the gausien distribution is centered on the LOP then we have a > "fuzzy donut" probability and not a Position. " > > No, no donuts. This is one of the things that can go wrong when > people have this discussion. The point with highest probability is > at the fix, inside the triangle formed by the crossing LOPs. The > ellipse of non-negligible probability, however, extends well outside > the triangle. Picture a low, broad "hill" of probability with a > "bell curve" cross-section. There is a 75% chance of being outside > the triangle. But this doesn't mean that there is a "hole" in the > donut. The location of maximum probability is right where we have > been discussing: at the "symmedian" point. But the triangle is NOT > an approximation to the error. The probability steadily decreases as > you move away from the fix, and this applies to any number of lines > of position (greater than one). EVERY fix yields an error ellipse > (or better yet, a family of concentric error ellipses, each > reprsenting a lower probability than the one before it). That's the > final product. The center of that error ellipse, which is the high > point on a low, flat hill, is located at that point inside the > triangle, but the sides of the hill decline away much more gradually > than most people expect. > > -FER > > > ---------------------------------------------------------------- > NavList message boards and member settings: www.fer3.com/NavList > Members may optionally receive posts by email. > To cancel email delivery, send a message to NoMail[at]fer3.com > ---------------------------------------------------------------- >