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    Re: The Darn Old Cocked Hat vs CG?
    From: Hanno Ix
    Date: 2013 Mar 19, 16:17 -0700
    Andres:

    Thanks so much. 

    Your answer is elliptical. 
    I keep missing something here, Andres.
    I sense you are using indeed a Bayesian approach, no?
    If so, can it really  improve on the "classical" approach"?
    I am sure, you have heard all the arguments against it.
    One is that a preconceived model is simply getting massaged until it fits.

    My doubt is based on a negative experience. I worked for a Co that
    wanted to find living pathogens in drinking water. They hired a, suffice it to say, 
    celebrated Professor from Cambridge, GB - you may know him;  
    he specializes in Bayesian Statistics. He was asked to do the signal analysis.
    Eventually, he came close to "frequentist" results but certainly did not exceed them.
    He left, mumbling about a Curse of Dimensionality and Combinatorial Explosion.
    Ok, CelNav  might be in a more favorite situation. 

    Bayes or not Bayes, you are in a good place to to explain the MPP approach. 
    May I challenge you to demonstrate its superiority over classical approaches based 
    on the same data? If you don't find one, please construe a case.
    If you know one from literature, please let us know the citation.
    If you find the time it would help so much.

    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.

    Regards

    h







    From: Andrés Ruiz <navigationalalgorithms@gmail.com>
    To: hannoix@att.net
    Sent: Tuesday, March 19, 2013 11:01 AM
    Subject: [NavList] Re: The Darn Old Cocked Hat vs CG?


    Hello Hanno,
    You wrote: Is there an counter example, one in which my choice of the TL would be far outside that ellipse?
    ...
    No the fix is the MPP, most probable position, and the ellipse of confidence is centered on it. Why?, because is based in real observations, no random data. With an associated probability to be inside proportional to the area of the ellipse and inversely to the number of observations.

    In your random model the high prob is near the true position, but a priori is not known.
    And I insist each theoretical model must be validated against real data.

    Regards

    2013/3/19 Hanno Ix <hannoix---net>

    Andres:

    My rough-and-ready approach predicts the TL 2/3 down the median
    as seen from the vertex (iow: at the CG) which it is - or at least rather close.
    In your diagram, it certainly is within the 99% ellipse.

    Could this be just a random coincidence? 
    Is there an counter example, one in which my choice of the TL would be far outside that ellipse?
    If it is not by coincidence then the probability of its being within the Doch must be bigh.

    Regards

    h


    From: Andrés Ruiz <navigationalalgorithms---com>
    To: hannoix---net
    Sent: Tuesday, March 19, 2013 6:59 AM
    Subject: [NavList] Re: Cocked hat vs Confidence ellipse


    An example for 4 LoPs: see the attached animation for the ellipse of conficence of 25% 50% 75% 95% and 99% prob.

    Error:
    S = 0.0011
    sigma = 1.3999
    sigmaB = 1.0029
    sigmaL = 1.0499

    Ellipse:
    Prob = 0.01 0.25 0.5 0.75 0.95
    k = 0.1418 0.7585 1.1774 1.6651 2.4477
    theta = 40.0289 40.0289 40.0289 40.0289 40.0289
    a = 0.1637 0.876 1.3598 1.9231 2.8269
    b = 0.1248 0.6675 1.036 1.4652 2.1539

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







    --
    Andrés Ruiz
    Navigational Algorithms
    http://sites.google.com/site/navigationalalgorithms/
    : http://fer3.com/arc/m2.aspx?i=122958


       
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