NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Tom Sult
Date: 2010 Dec 10, 13:07 -0600
Thomas A. Sult, MD
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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