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: Hanno Ix
Date: 2013 Mar 13, 15:19 -0700
From: Hanno Ix
Date: 2013 Mar 13, 15:19 -0700
Greg:
I do assume a Gaussian curve in the measurement of one single coordinate, an angle.
This is justified by any engineer's experience making measurements.
In CelNav, that will happen in two coordinates.
For my San Diego Convention this means (hope you had a chance to read it):
The pdf of the results of those 3000 fixes will be on a Gaussian surface with the center
as the most likely location which, btw, is not necessarely the True Location TL.
This is not a definition or
assumption but a consequence of above experience.
As surprising as it may sound, in my dicussion I am not - NOT - interested in *location*
which is defined in two dimensions. Rather I am interested in a *length* called distance Fix-TL
which has
only one dimension. Azimuths are disregarded. Again there is no arbitrary radius
either, there is a distribution resulting from the application of the above experience.
I claim that the probability of this *distance* is described by the Rayleigh Distribution.
In my memo, that is the curve that FER will get when he makes a histogram of the
distances Fix-TL ( or "errors").
Everything else I claim is a consequence of this claim. I cannot proceed
with discussing consequences before the Rayleigh theorem, if you will, has been verified.
Thank you so much
h
From: Brad Morris <bradley.r.morris@gmail.com>
To: hannoix@att.net
Sent: Wednesday, March 13, 2013 9:51 AM
Subject: [NavList] Re: The Darn Old Cocked Hat - the sequel 1
Subject: [NavList] Re: The Darn Old Cocked Hat - the sequel 1
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.
On Mar 13, 2013 1:27 PM, "Greg Rudzinski" <gregrudzinski---com> wrote:
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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