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    Re: Almanac for Computers
    From: John H Henderson
    Date: 1996 Aug 28, 12:03 EDT

    >                  Computing Position w/o a DR Position
    > In principle, taking a sight reduces the possible positions you
    > might be at in 3-dimensional space to a single plane in space.
    Taking one sight put you on a cone in space (which, when it intersects
    the surface of the earth, gives you a circle.)
    > Taking two separate sights reduces it still further to the
    > intersection of two planes, which is, of course, a line. You
    > know, a priori, that your position is also on the surface of the
    > earth.  So the intersection of that line with the surface of the
    > earth yields exactly two points at which you might be.  Usually
    > one of them is ridiculous, and so you choose the nonridiculous one.
    Two sights give you two intersecting cones, which give you
    two lines at their intersection, and thus two points at the surface
    of the earth, one of which you can rule out as unreasonable.
    > The equations for the two planes are:
    >   x_1 * x  +  y_1 * y  +  z_1 * z   =   sin(theta_1)
    > and...
    I could understand this plane approach if the planes were tangent to the
    cones at your location, but there is no information from the other
    sight in each equation, so I don't know how these equations express
    the one correct plane.  Also, these planes are not tangent to the
    "sight cone" since they do not pass through the center of the earth.
    (Unless theta=0: set x=y=z=0). (Although any two planes that pass through
    the observer's location would work.)
    I just need help understanding how this expression for these planes
    is derived.
    John H. Henderson - Department of Electrical Engineering - Auburn University
                 "That's not flying...  "  that's falling with style!"
                                                      -- Woody in "Toy Story"
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