NavList:

I agree you must make practical assumptions. And the practical assumption that the position is inside the cocked hat is commonly held - but it is not correct. In fact, where the size of the cocked hat is only determined by random errors, the chances of the actual position being inside the cocked hat is just one in four. So, the practical assumption you should made is that the actual position is NOT inside the cocked hat.

See the previous discussion under the subject of "Cocked Hats" back in December last, and in particular my posting (NavList 1908) on the 16th of December for more detail.

Geoffrey Kolbe



At 11:40 02/03/2007, you wrote:

Well, maybe it wouldn't be, in fact it might be many  thousands of miles away but that is very unlikely (though with a probability greater than zero.)

But, the basic assumption in plotting the fix, after you have eliminated the systematic or constant error leaving only random errors, is that you are most likely located at the point where you are equal distant from the position lines and this is generally taken to be in the center of the triangle. "If a fix is obtained from three or more lines of position, and the error of each line is normal and equal to that of the others, the most probable position is the center of the figure. By  'center' is meant that point within the figure which is equidistant from the sides."  Bowditch, volume 2, chapter III article 308, 1977 ed.; and see volume 1, chapter XVII, article 1708 , 1977 ed. Although it is "possible" to be way outside of the triangle you must make some practical assumptions otherwise everything becomes Jell-O.

What is your argument that after eliminating the systematic error that the fix is more likely to be outside the triangle than inside?

Gary LaPook

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