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    Re: On LOPs
    From: Jared Sherman
    Date: 2002 Apr 15, 20:36 -0400

    So far I haven't seen any justification for the "most probable" position, much 
    less for the use of an ellipse (which has 2 focii) rather than a circle (with 
    one focii, i.e. center) when using 3 or more LOPs (which would indicate a 
    need for 3 or more "focii").
    Forgive me if the plural of focus is not focii, my latin isn't rusty, it simply "isn't".
    A valid "most probable position" would have to take into account the 
    individual variations and probable errors inherent in EACH of the LOPs. 
    Graphically this could mean using a thicker pencil to draw each, i.e. if the 
    accuracy of the sextant is 0.2 minutes and the accuracy of the eye on the 
    horizon sight is another .2 minutes, draw the line to reflect the possible 
    range of positions that are derived from being off .4 minutes to each side of 
    the reading.
    Once each line is drawn, the "most probable" position them becomes that area 
    included under all three zones (the lines plus the extra width around them) 
    and if all three zone do not contain a common area, it would still be most 
    probable that the error in each site be expanded until the zones overlapped. 
    At that point a circle (yes circle) or error could be expanded out to contain 
    the probable positions, or an irregular complex shape that would be possibly 
    more accurate than the circle.
    I'd be able to do this graphically, but not statistically. I suspect the math 
    would rapidly get more complex than the "use a thicker pencil and make a 
    circle of error" approach, without giving much more useful information.

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