# NavList:

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

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Re: The Darn Old Cocked Hat - the sequel 1
From: Andrew Nikitin
Date: 2013 Mar 15, 14:10 -0700

I made computer simulation of the fix taking on board "Barack Obama" aircraft carrier.

In my model:
1) There are 10000 navigators (100 would not give as clear picture).
2) All navigators are clones and use identical equipment, which enables them to perform altitude measurement with same ?=1'
3) They all shoot same 3 stars (azimuths shown on diagram with 3 short blue lines)

The gray-ish area is a distribution of fixes. Each dot is MPP obtained by
individual navigator. For example, red triangle shows 3 LOPS obtained by
navigator 5575 and red marker shows location of a symmedian (which is MPP of
choice for this navigator) of the resulting cocked hat triangle. Green triangle
shows MPP and LOPs of another, in some respect luckier, navigator 9161. Note
that true location is not inside cocked hat for navigatore 5575 and is inside
cocked hat for navigator 9161, despite 5575 having both smaller area triangle
and having closer to true MPP.

The slightly elliptical shape of distribution depends on the choice of
azimuths. Azimuths intersecting at 60° will yield perfect circle.

The second diagram shows estinmated proability distribution as a histogram of
0.25 mile distance buckets.

As Gary explained the hump in the middle is explained by the fact that this
probablity is a product of 2 functions, one grows linearly with distance (this
is area of a ring another quickly decreases with distance (could be just a
normal distribution, not sure about it. The situation is muddied by the fact that this second function depends on direction, so you need to integrate across all directions, but this does not change basic principle)

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