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    Re: "100 Problems in Celestial Navigation"
    From: Herbert Prinz
    Date: 2004 Apr 2, 14:55 -0500

    Joel Jacobs wrote:
    > Since you indicate an error may be the result of estimating the MPP within a
    > cocked hat, I am interested in what method you recommend to determine the
    > MPP?
    Assuming random observation error, the MPP is that point for which the sum of
    the squares of the distances from the individual LOPs is a minimum.
    1) For two LOPs, this is the point of their intersection.
    2) For three LOPs, there is a way to find this point geometrically. The
    construction is based on the fact that if a,b,c are the sides of the cocked hat
    triangle and Da, Db, Dc the distances from the MPP to the respective sides, then
    a is to Da as b is to Db and c is to Dc.
    Therefore, to construct the MPP, pick two arbitrary distances Da' and Db' that
    are in the ratio of a : b, draw parallels at these distances to a and b
    respectively (either both inside or both outside the triangle), connect their
    intersection point with C and name this line sC. Repeat the same procedure for
    b,c and A, obtaining sA. The intersecton of sC and sA is the MPP.
    3) For more than 3 LOPs, there is no geometrical way. The numeric solution is
    the one that is obtained with the algorithm published in the Nautical Almanac,
    pp. 277-283.
    Herbert Prinz

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