# NavList:

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

**Re: The Darn Old Cocked Hat - the sequel 1**

**From:**Brad Morris

**Date:**2013 Mar 13, 13:48 -0400

Hanno

Your problem statement appears to be improperly constructed.

You assume that the fix will be contained within an annulus centered about the True Location. You assume that there will be a Gaussian distribution about this annulus. Hence the reason why you have a hole at the true location.

Firstly, you should have a square window for the distribution, not Gaussian. Reason: when you have Gaussian, you know the distribution about a mean. In the case of your construction, you cannot know the mean or the distribution. John Karl, on the other hand, has a distribution about his lop, based upon his systemic errors. By what basis do you have a Gaussian distribution? Answer: none! Square (or uniform) distribution is appropriate.

For this very reason (improper construction), your answer is pre-determined. That is, the TL will differ from the fix location by the arbitrary radius to the mean distance to the annulus you select.

Instead of a cocked hat lets consider a boxed hat (azimuths 90 degrees apart) such that squareness is an indicator of symmetrical systematic error. There wouldn't be any real way to know wether the navigator is inside or outside of the box unless the systematic error was large. If the box was a perfect square 10' on a side then most navigators would expect to be inside the box near the center. If the box is small ( 0.5' on a side ) then most likely the navigator would expect to be outside the box. How about using a circle of lets say 1' in radius about the center of the box to indicate an approximate 50/50 chance of being inside the circle.

An asymmetrical rectangle would be an indication of random errors which might mean using a larger circle to represent the 50/50 inside chance.

Greg Rudzinski

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