# NavList:

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

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Re: On LOPs
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

```
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