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    Re: The Darn Old Cocked Hat vs CG/MPP?
    From: Hanno Ix
    Date: 2013 Mar 21, 12:27 -0700
    Andres;

    Thanks for your detailed posting, 
    actually, for all your postings - they are always very responsive and detailed.

    Sorry, I didn't read your MPP paper with more care before 
    otherwise I would have concentrated earlier on page 5  (partial, attached).
    After thinking about the your search for the  MPP I must
    entirely agree, and I would have agreed  before had I paid that additional attention.

    The real difference between us is the method by which
    the minimum of S was found: you use classical regression to minimize S. Very well.

    I used simulation. To repeat  my approach for clarity:
    First, I assumed, according to some arbitrary rule, the TL.
    Next, I calculated a list of S's, based on simulated triplets of corners of  DOCHs.
    Then I established for each list ( i.e. each TL) a histogram -  a Rayleigh distribution, or chi2, n = 2.
    The most frequent value of S for a specific histogram was recorded.
    After many loops of above S.i = f(TL.i) appeared.
    Finally, looking up that TL.i which delivered what we both wanted, the minimum of S.i

    Perhaps there is a difference in the source of the original data.
    You claim real measured data as that source.
    I claim as sources simulated corners of the DOCH based on the assumption of a  
    normal distribution. I believe this assumption is not disputed.

    Finally, two remarks:

    It is not quite clear if you used points of the LOPs other than actual fixes. If you did
    they would not have been actual data.

    If f you were to make a histogram of your S I bet a Rayleigh / chi2 would appear.

    Regards

    h



    From: Andrés Ruiz <navigationalalgorithms---.com>
    To: hannoix---.net
    Sent: Thursday, March 21, 2013 2:58 AM
    Subject: [NavList] Re: The Darn Old Cocked Hat vs CG?



    2013/3/20 Hanno Ix <hannoix---net>

    ..
    I keep missing something here, Andres.
    I sense you are using indeed a Bayesian approach, no?

    Should it work can it be done with paper and pencil, tables and slide rulers, alone?
    Can it be done in a reasonable time, no electricity allowed?  I mean in a time that 
    is comparable to the one the classical method requires, maybe less than an hour?

    Finally: Aren't computers in CelNav a gross anachronism? There might be occasions
    when this combination is needed  - for me it is wimpy.


    Hello,
    the approach in my paper is based in the treatment of the error in the least squares method.

    I have a hand held computer, (a notebook with W7 and a tablet in android), in my sloop, and works fine for chart plotting and celnav. I do not have time to be the pilot and the navigator at the same time, but yes to use the sextant.

    If you plot the LoPs by hand,  then you can plot a CEP or a confidence ellipse based in your common sense and perception of the nearby of a danger.

    See the fix and the 95% ellipse based in 4 observations (red) and in 3 (blue), eliminating the Moon one. The distance between the two fixes is 0.70 nm.

    Regards.  
    -- 
    Andrés Ruiz
    Navigational Algorithms
    http://sites.google.com/site/navigationalalgorithms/
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