# NavList:

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

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Re: A simple three-body fix puzzle
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
>
>
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```
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