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    Re: That darned old cocked hat
    From: Tom Sult
    Date: 2010 Dec 10, 13:07 -0600
    Even of greater interest to me is that the fundamental way we all plot position places us on the map with a high probability of being wrong. This is starting to sound like the "uncertainty principle" of quantum physics. Just another reason to believe that the percussion of CelNav is limited by more than first meets the eye.  My original CelNav instructor was fond of saying (about fixes) "looks like we are around here someplace". 

    Thomas A. Sult, MD
    Sent from iPhone

    On Dec 10, 2010, at 12:51, George B <gbrandenburg@rcn.com> wrote:

    Dear George H and John Karl,

    I may be missing something, but I think you are both right.

    George's argument assumes a known position and then considers all possible cases of three measured LOPs. He is correct that each of eight possible outcomes that he lists (TTT, TTA. etc) are equally probable, and therefore the probability that the three measured LOPs will enclose the know position is indeed 25%.

    John Karl's argument assumes a given set of three LOPs, and then the probability that they enclose the true position is calculated. In the case where the three LOPs are chosen to intersect at a common point the probability of including the true position is clearly zero. If the three LOPs are chosen to be farther apart this probability will clearly be larger.

    Presumably if one follows the latter approach and does a three-fold, probability-weighted integration over all possible locations of the three LOPs, then one will recover the former result that the true position is enclosed 25% of the time.

    Best regards,
    George B
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