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    Re: Running fix Monte Carlo analysis
    From: Paul Hirose
    Date: 2013 Oct 28, 20:44 -0700

    I wrote:
    > But what about accuracy? Unable to answer the question
    > on a theoretical basis, I decided to program a Monte Carlo simulation.
    That program has been improved and put online as a Windows executable
    with documentation. It's been said the ultimate documentation is source
    code, and that's there too (C# language).
    Someone reminded me this topic was discussed in December 2009. I had no
    recollection. Based on reviewing messages in the archives, it's likely I
    put a kill filter on the thread because it seemed to be going nowhere.
    In January 2010 Dave Walden gave results of his Monte Carlo analysis.
    There was disappointingly little response. Apparently people found an
    argument about the running fix more interesting than a scientific
    He wrote, "First, a plot of average distance from true postion to Rfix
    or EP in nautical miles. This shows a number of things. When the
    crossing angle between the two LOP's is small, the traditional running
    fix can produce large errors. Not surprinsing. In fact, well known and
    expected. (And reassuring to find in the result!) When the crossing
    angle between the two LOP's is small, the EP does well. Not surprising
    after a little thought. The EP is "anchored" by the DR and doesn't get
    too far away. At 90 degrees, the two methods give the same result.
    Again, expected and reassuring to see. Interestingly, for crossing
    angles between about 25 degrees and 90 degrees, the traditional running
    fix method gives better results."
    The summary on my Web page says, "a large systematic error (relative to
    the random error) favors the running fix, the more so as the angle
    between LOPs decreases. On the other hand, if the error is entirely
    random, the estimated fix is more accurate than the running fix when
    there is a large angle between the LOPs, and equally accurate at small
    There appears to be little in common between those paragraphs. However,
    the simulations are quite different in the magnitude of the errors,
    their distribution (rectangular vs. Gaussian), presence or absence of a
    systematic error superimposed on the random error, and dependence
    between the separate iterations. Regarding that last, one run of my
    program is a single voyage, the vessel proceeding from one running (or
    estimated) fix to the next, for as many hundreds or thousands of fixes
    as the user desires.
    That is significant when analyzing the performance of the estimated fix,
    which is more sensitive to systematic error. It might be argued that the
    systematic error I used is excessive, since a navigator would surely
    notice and remove such error in a long voyage. But with the program
    available now, any interested reader (with Windows) can experiment with
    his own settings.
    I filter out messages with attachments or HTML.

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