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    Re: Fix Maximum Probability Positions
    From: Hanno Ix
    Date: 2013 Mar 21, 14:42 -0700

    Andres and all: 

    I have to check out here for a while for travel.

    However, for my own sake and possibly of others, let me rephrase below what I have learned.
    I am sure there are disgreemnets out there, some of the very strong.

    1.   There is a single theoretical point for which a correct theoretical fix exists.

    2.   Points in its neighborhood are affected with an error caused by "noise"
         This noise is assume fixed and due to the limits of CelNav as a technology
         as a whole.
    3.   The correct point can practically be approached with an increasing number of fixes.

    4.   A circular, elliptical or other closed line around  the correct point connects
         all points with the same error - an " equal uncertainty loop".

    5.   Commonly it is assumed that these loops lie on a normal distribution.
         This normal distribution my, or my not, be cylindrical.

    6. There will always be additional noise or error due to the circumstances of the individual fix. 
        That means, even if the correct location were known  a CelNav fix will virtually never fall on it.

    7. The size of this error is extremely unlikely to be zero or "infinity", i.e very small or large.
        It is measured in distance and will always be positive.

    8. There is a certain distance from the correct point at which the fixes fall most  frequently.
    9.  A number n, say > 3, of fixes create together a polygon.  The "Center of Gravity" of that 
         polygon approaches the correct point with increasing n.

    10. The CG is the Most Probable Point (MPP) . It is the best choice when no more info is available.

    11. The CG is always within the polygon.

    12. Nevertheless, there is a probability > O that the correct point is outside the polygon.

    I reserve the right to change my views.  :)
    Thank you for your thoughts and postings.

    See you perhaps on the US carrier Barak Obama; cannot wait.



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