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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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From: Gary LaPook
Date: 2015 Feb 4, 17:21 -0800
We have discussed MANY TIMES finding the position both inside and outside of the "cocked hat." My advice----take only two shots then no "cocked hat," no quadrilateral, NO PROBLEM.

gl

To: garylapook@pacbell.net
Sent: Wednesday, February 4, 2015 4:36 PM
Subject: [NavList] Re: Irregular Quadrilateral Center

Frank Wrote:
That doesn't work. Consider the case of a long, narrow triangle from three LOPs. The best estimate of the position is actually very close to the short side of the triangle rather than out in the middle of the triangle, which is where the center of mass (balance point) would be located. The shape of the figure (triangle, quadrilateral, complicated polygon) is seriously misleading. It provides neither an estimate of the correct fix, nor a proper estimation of the size and shape of the error ellipse!

I think it would depend upon the bands of error of the individual lines.  If the lines were from different navigational aids, e.g. an NDB line, a VOR line, crossing a railway line, and a sun line, three of which had been transferred up along track, the bands of error would be different for each line.  I suppose statistically, if you could superimpose the four Gaussian distributions, the most probable position would be the peak of the total sum.  Of course the true position doesn’t even have to lie inside the cocked hat.  It’s fairly easy to show that for three relative bearings on the same side of the aircraft say 030, 090, and 150 for an aircraft with 5degrees compass error, say compass heading = 005 actual heading 360, the aircraft’s true position lies outside the cocked hat.  Therefore, the moral is take position lines, not just with a good cut, but also from both sides of the aircraft.  I’ll let you think about it for a day and provide a drawn answer tomorrow evening if no one’s beaten me to it.  Dave

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