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    Re: Running Fix vs Estimated Position -- Monte Carlo assessment
    From: George Huxtable
    Date: 2010 Jan 17, 11:48 -0000

    I've been trying to follow the dialogue under this threadname between Dave
    Walden and Joe Schultz. This started with a posting on Jan 11 by Dave
    Walden. Within the text he referred to 3 attachments, but only one
    attachment arrived, headed jkarl.jpg. What am I missing?
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    Sent: Monday, January 11, 2010 5:30 PM
    Subject: [NavList] Running Fix vs Estimated Position -- Monte Carlo
    Running Fix vs Estimated Position -- Monte Carlo assessment
    The question of the relative merits of a traditional running fix vs an
    estimated postion based on minimizing the distance from the DR position to a
    point on a second LOP has been discussed recently.  Three attachents are
    given which summarize a Monte Carlo simulation that was carried out in an
    attempt to provide some quantitative results to further the discussion.
    A quote from the renowned naturalist Louis Agassiz: "Go to nature; take the
    facts into your own hands; look, and see for yourself."
    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.
    Next, is a scatter plot showing error in nautical miles as a function of
    crossing angle between LOP's.  As expected from the above, when the angle is
    near 90 (or equivalently, 270), the error is lower.  At 0 (or 180) the
    errors in Rfix are large.  (In fact there were Rfix values off scale at very
    small crossing angles, but the scale was chosen so as to provide a
    'reasonable' view over the range of anagles.)
    Last, a view of the spread sheet that was used to produce the data above.
    The Rfix and EP are both plotted.  A visual basic macro was written to copy
    the inputs and results of this sheet to a table on another sheet.  The excel
    rand() function was used to provide variation and 1000 runs were made. The
    input values for the above results were:
    Latitude:  2 degrees North  (but not expected to affect the conclusions)
    Longitude: 2 degrees East   (but not expected to affect the conclusions)
    ships course: 45 degrees  (but not expected to affect the conclusions)
    error in estimated ship course:  +/- 5 degrees, uniformly distributed
    Ships speed: 6 knots
    error in estimated ship speed:  +/- 2 knot, uniformly distributed randomly
    time interval: 1 hour
    Azimuth of LOP 1: 0-360 degrees, uniformly distributed randomly
    Azimuth of LOP 2: 0-360 degrees, uniformly distributed randomly (independant
    of LOP1)
    Error in initial DR postion: +/- 3 nautical miles along LOP1, uniformly
    distributed randomly
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