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least squares method for determining a fix

From: Federico Rossi (no email)
Date: Fri Oct 10 2003 - 07:39:00 EDT

  • Next message: José Otavio O. de Almeida: "RES: Lights etc."

    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

  • Next message: José Otavio O. de Almeida: "RES: Lights etc."



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