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    Re: least squares method for determining a fix
    From: Paul Werner
    Date: 2003 Oct 14, 11:06 +0200
     
    ----- Original Message -----
    Sent: Friday, October 10, 2003 1:39 PM
    Subject: least squares method for determining a fix

    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
       
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