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    Re: least squares method for determining a fix
    From: Andr?s Ruiz
    Date: 2003 Oct 14, 12:44 +0200
    Mensaje
    Estimated Position Error

    If three or more position lines are obtained an estimate of the error in position may be calculated. In general as the number of observation increases the error in the estimated position decreased.

    The standard deviation of the estimated position, in nautical miles is:

    S = F-D*dB-E*dL*COS( BI );
    sigma = 60.0*sqrt( S/(nObs-2.0) );

    The Confidence Ellipse of axes (a,b) is:

    Prob = 0.95;
    k = sqrt(-2.0*log(1.0-Prob));  // scale factor
    theta = ATAN( 2.0*B/(A-C) )/2.0;
    a = sigma * k / sqrt( nObs/2.0 + B/SIN(2.0*theta) );
    b = sigma * k / sqrt( nObs/2.0 - B/SIN(2.0*theta) );
    More information:
    http://www.geocities.com/CapeCanaveral/Runway/3568/index.html
    http://www.geocities.com/andresruizgonzalez/
    -----Mensaje original-----
    De: Navigation Mailing List [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM] En nombre de Paul Werner
    Enviado el: martes, 14 de octubre de 2003 11:06
    Para: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM
    Asunto: Re: [NAV-L] least squares method for determining a fix

     
    ----- 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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