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Unformatted text preview: away from the xaxis. Let 1 be the range to s 1 , and 2 be the range to s 2 . We will Fnd our position by solving the following two equations for x and y : ( x 1x ) 2 + ( y 1y ) 2 = 2 1 , ( x 2x ) 2 + ( y 2y ) 2 = 2 2 , where ( x 1 , y 1 ) is the position of s 1 , and ( x 2 , y 2 ) is the position of s 2 . The geometry matrix for this twodimensional scenario is deFned as G , " 1 x 1 y 2 x 2 y # . 1. Show that for a person at the origin of the xyplane, G = 1 cos sin . 2. Also, show that trace n ( G T G )1 o = 2 sin 2 . 3. What value of results in the smallest 2d rms error in position? Does your answer make intuitive sense? 2...
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 Fall '08
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