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    Re: Still on LOP's
    From: Arthur Pearson
    Date: 2002 Apr 22, 22:18 -0400

    I am unable to refute the various arguments for the 25% (or less)
    probability of the cocked hat containing the MPP. However, this note
    from Chuck resolves a great deal of my puzzlement over how to improve on
    the practice of placing my assumed position at sea within a reasonably
    sized cocked hat from a reliable set of sites. It makes sense to me that
    while the probability of being within the hat may only be 25%, that 25%
    probability is better than I can do by placing the MPP in any of the
    regions outside the hat.
    
    The only additional observation I would make is that I don't believe
    that for a typical set of star sights taken at sea the error around each
    of the sites will be random and independent error.  The horizon is
    bright on one side, dim on the other, cloud cover intervenes
    intermittently, and posture and stance vary for the different sites.  I
    frequently feel I know which sites I nailed, and which I bobbled, and
    those judgments factor into my determination of where I place the MPP.
    
    
    -----Original Message-----
    From: Navigation Mailing List
    [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM] On Behalf Of Chuck Taylor
    Sent: Monday, April 22, 2002 3:46 AM
    To: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM
    Subject: Re: Still on LOP's
    
    Trevor wrote:
    
    > But, unless I am mistaking something (which is by no means
    > impossible!), the probability that the cocked hat lies over the true
    > position is numerically equal to the probability that that true
    position
    > lies within the cocked hat.
    
    From the point of view of probability theory, it is precisely the
    probability
    that the cocked hat lies over the true position that we are talking
    about. All
    the uncertainty lies in the measurements and plots of the bearings and
    hence in
    the resulting cocked hat.  There is no uncertainty in the true position,
    only in
    our knowledge of the true position, as represented by the cocked hat.
    
    Trevor then went on to mention "the best estimate of the MPP".  Even if
    we grant
    that the probability is 0.25 that the cocked hat lies over the true
    position, I
    would argue that the Most Probable Position (MPP) is still the center of
    the
    cocked hat.  Notice that the various possible cocked hats in Geoffrey's
    diagram
    lie symmetrically about the true position. Even if you believe (with
    probability
    0.75) that your particular cocked hat does not contain the true
    position, you
    have no idea in which direction the true position lies relative to your
    cocked
    hat, so you can do no better than select the center of your cocked hat
    as the
    best estimate of your position given available information.  Can anyone
    refute
    that argument?
    
    Chuck Taylor
    Everett, WA, USA
    
    
    

       
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