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    Re: Two-body fix caveat
    From: Peter Hakel
    Date: 2009 Nov 4, 09:21 -0800

    The Van Allen's method works fine for me even in this singular case, see the attached screenshot of the lops.xls spreadsheet.

    At the core of this method is a solution of a quadratic equation whose discriminant D, as always, defines three cases:

    D>0, two distinct solutions (LOPs intersect, the usual CelNav case)

    D=0, one solution (LOPs touch, like in this artificial test case)

    D<0, no solution

    I was concerned about round-off errors for the D=0 case when I was writing that spreadsheet.  If D comes out ever so slightly negative instead of zero, then SQRT(D) has a problem.  So far, however, Excel numerics has passed all such tests OK, including this one.

    Peter Hakel

    From: Andres Ruiz <aruiz@orona.es>
    To: navlist@fer3.com
    Sent: Wed, November 4, 2009 2:12:28 AM
    Subject: [NavList 10426] Re: Two-body fix caveat

    Solving this singular case with Van Allen’s method: no solution. Vector Solution works fine.


    An analytical solution of the two star sight problem of celestial navigation

    James A. Van Allen. NAVIGATION Vol. 28, No. 1, 1981

    iter  Err   Be    Le    B1    L1    B2    L2    GHA1f dec1f GHA2f dec2f

    0     NaN   NaN   NaN   NaN   NaN   NaN   NaN    10.000000   0.000010    0.000000    -0.000010

    I1: NaN     NaN

    I2: NaN     NaN



    Vector Solution for the Intersection of two Circles of Equal Altitude

    THE JOURNAL OF NAVIGATION (2008), 61, 355-365. The Royal Institute of Navigation

    Andrés Ruiz González - Navigational Algorithms - http://sites.google.com/site/navigationalalgorithms/

    iter  Err   Be    Le    B1    L1    B2    L2    GHA1f dec1f GHA2f dec2f

    0     134.146176409012696     0.000058    -20.000000  0.000058    -20.000000  0.000001    -20.000000   10.000000   0.000010    0.000000    -0.000010

    I1: 0.00000 -20.000000

    I2: 0.00000 -20.000000






    Andrés Ruiz

    Navigational Algorithms




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