NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Least squares method for determining a fix
From: Federico Rossi
Date: 2003 Oct 10, 13:39 +0200
From: Federico Rossi
Date: 2003 Oct 10, 13:39 +0200
Hi,
does anybody know the formulas to
calculate the error ellipse around the fix obtained with the least squares
method?
I've got some formulas that I
found on a Spanish site, but they don't explain what is sigma (I
suppose a variance) and most of all how to compute it.
The formulas are (a probability of
0.95 is generally considered):
k=sqrt(-2*log(1-probability)
theta=arctan(2*B/(A-C)
a=sigma*k/sqrt(nObs/2+B/sin(theta))
b=sigma*k/sqrt(nObs/2-B/sin(theta))
where: a and b are
the axis of the ellipse
nObs is the number of sights
A, B and C are parameters calculated with the
least squares method as found in the Nautical Almanac
These formulas only give a and b,
what about the orientation of the two axis?
Thanks.
Federico