NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: On LOPs
From: Herbert Prinz
Date: 2002 Apr 16, 18:02 +0000
From: Herbert Prinz
Date: 2002 Apr 16, 18:02 +0000
Steven, Thank you for the clarification. I was already getting worried that I would have to dig out my old statistics book from the basement. It is buried there for a reason, together with other dreadful books. I would like to ask you a favour. The images in pp1.gif and pp2.gif in your message from 04/16 show beautifully the spatial relation of confidence ellipse and cocked hat. I assume that you are showing 95% ellipses. With this assumption, it looks very reasonable that the confidence level of the entire hat should be 25%. It also gives an idea of the variation of probability density within the hat. Could you redraw these two images again, this time with a 25% confidence ellipse, and post it? Thank you in advance. Herbert Steven Tripp wrote: > On 4/16/02 11:39 AM, "Herbert Prinz"wrote: > > > Steven, > > > > Could you please explain to us why the size of the confidence ellipse would > > depend in part on the angles that the three LOPs cross at? > > I was wrong. > > After playing with my program a little I see that the size can actually get > smaller with acute angles, provided that the intercepts (in the navigation > sense) are similar. It can also get larger if the intercepts are (somewhat) > different. > > Here are three examples. > > 1. azimuths: 0, 60,120, intercepts: -2, 5, -1 > 2. azimuths: 0, 110,120 ints: same > 3. azimuths: 110, 60, 120 ints: same > > Note that two lines are the same in all plots. > > In #2 the error in the NE-SW direction increases, but is a little less in > the NW-SE direction. > > In #3 error is reduced in all directions. > > Steve Tripp > > ------------------------------------------------------------------------ > Name: pp2.gif > pp2.gif Type: GIF Image (image/gif) > Encoding: base64 > > Name: pp1.gif > pp1.gif Type: GIF Image (image/gif) > Encoding: base64 > > Name: pp3.gif > pp3.gif Type: GIF Image (image/gif) > Encoding: base64