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

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Re: Cocked hats, again.
From: Nicol�s de Hilster
Date: 2007 Mar 20, 17:35 +0100

```P F wrote:
>
> This shape begs the question: why would the standard deviations be so
> small compared to the shape? Remember that the standard deviations are
> derived from random error. Perhaps there is also systematic error
> present ...
The standard deviation is only predicting 68% of the error (assuming it
is Gaussian). So if the standard deviation is for instance 20 arcseconds
it only means that there is a 68% chance (or 68.27% to be more precise)
that the observation is within 20 arcseconds of the actual position. In
order to get 95% probability you need to multiply the standard deviation
by 2 (or 1.96 to be accurate, 2 will give 95.45%), so 2 x 20 arcseconds
= 40 arcseconds. With 3 times the standard deviation you will get 99.73%
probability. So with a standard deviation of 20 arcseconds your actual
observation could still be 1 arcminute off (and there even is a 0.27%
chance that it is more off than 1 arcminute).

In practical term this means that when you take 1000 observations with a
20 arcseconds standard deviation there is a fair chance that 3 of them
are off by more than 1 arcminute, while 45 of them will be over 40
arcseconds off and no less than 317 will be off by more than those 20
arcseconds.

Finally don't forget that the error works both ways of your LOP, so the
error does not always work in the same direction for every LOP, you
simply can't tell on which side the 'real' LOP should be.

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```
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