# NavList:

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

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Re: Still on LOP's
From: Rodney Myrvaagnes
Date: 2002 Apr 23, 17:13 -0500

```On Mon, 22 Apr 2002 19:06:42 +0100, Dr. Geoffrey Kolbe wrote:

>
>My "proof", as you were kind enough to call it, has nothing to say
>regarding the size of the 'hat. All that is demonstrated is that the 'hat
>will enclose the actual position 25% of the time.
>
Help me understand what you are saying here, speaking of normal
distributions.

Let us consider a location we are trying to determine, with three
visible landmarks equidistant at 120 degrees apart, so our bearings
have similar error distribution.

Among the possible triangles we could get are equilateral triangles
tangent (within a distance as small as we want to wait for) to 1-sigma,
2-sigma, 3-sigma, and 4-sigma contours.

Any one of these equilateral triangles will recur at locations not
exactly on the center of our space if enough bearings are taken. They
will (I suppose?) also have a normal distribution. Your statement is:

1) that in a long enough run of observations, 25% of triangles of a
given size will contain the true location.

OR

2) that in a long enough run of observations, not more than 25% of
triangles of a given size will contain the true location.

If 2 is the assertion, there must be some size of triangle that
maximizes the function P(inside) or approaches most closely to 25%. I
would be much happier with an analytic answer to this one, since I have
not seen anything yet that doesn't appear to assume a flat, rather than
normal, distribution. If I have missed something that does take care of
this, perhaps someone will send it to me off list.

Thanks,

Rodney Myrvaagnes                                  J36 Gjo/a

"Curse thee, thou quadrant. No longer will I guide my earthly way by thee."  Capt. Ahab

```
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