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    Re: How good is St. Hilaire?
    From: Peter Hakel
    Date: 2010 Feb 27, 10:39 -0800
    Not so long ago I did similar tests of this iterative procedure with input data for only two bodies and assuming a stationary vessel.  First, it was nice to see that the results agreed with the two direct two-body fix methods that I use.  Now in this case we have two equally good geometric solutions.  Therefore, I also tried all kinds of initial DR positions and the method always converged to one of them.  Depending on where you place your DR, the algorithm will march toward one or the other LOP intersection.  I have not studied this further, as it is a rather academic question, but it would be an interesting exercise to rigorously determine the associated "bifurcation" set of locations for this method.  I think I'll keep this problem in reserve in case some eager math student comes to me searching for a project. :-)

    Peter Hakel

    From: George Huxtable <george@hux.me.uk>
    To: NavList@fer3.com
    Sent: Sat, February 27, 2010 5:52:40 AM
    Subject: [NavList] Re: How good is St. Hilaire? was: Advancing LOPs for precision fixes

    [parts deleted by PH]

    Anyway, recently, I tried spooking that algorithm by providing it with an
    initial  DR position, that's the exact antipode of that given as a starting
    DR position in the almanac; that is, E165º, S32º, instead of W15º N32º, with
    everything else unchanged. But it wasn't spooked. It took all of 9
    iterations to work its way around the World from that absurd starting point,
    but ended up once again, back at the same best-position.

    So it seems a robust algorithm.


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