Homework10_Sol-1

3 nonlinear least squares 25 solve the incomplete

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Unformatted text preview: ferentiation. 3) Nonlinear Least Squares (25%) Solve the incomplete traverse lab measurements given below with nonlinear least squares techniques. The coordinates sought are Bx, By, Cx, and Cy. Known Points: A = [1000, 1000] ft Azmk=[1500,1000] ft Side AB BC AC CA Length, ft 91.84 86.94 101.34 101.27 Angle Angle zmkAB HA (deg) 135.14 81.68 AzmkAC Solution 1.) Estimate coordinates Bx, By, Cx, and Cy.. Bx=1000+sin(90+135.14)*91.84 = 934.9008 By=1000+cos(90+135.14)*91.84 = 935.2182 Cx=1000+sin(90+81.68)*101.34 = 1014.6641 Cy=1000+cos(90+81.68)*101.34 = 899.7266 Calculate Lengths and Azimuths using estimated coordinates L0AB=91.84 ft; L0AC=101.34 ft; L0BC=87.3031 ft Az0AB = 225.14 deg; Az0AC = 171.68 deg; AZ0BC = 113.992 2 2.) Setup linearized equations in Matrix Form. M x =B [ [ The linearized equations are Azimuth X XA YA YB X X Y Y X X dX A A 2 B dYA B 2 A dX B B 2 A dYB Az AB tan 1 B vz AB 2 AB o AB o AB o AB o YB YA Distance XA XB YA YB XB XA YB YA dX A dYA dX B dYB AB o AB o AB o AB o Row 1 - Measurement of distance AB Row 2 - Measurement of distance BC Row 3 - Measurement of distance AC Row 4 - Measurement of Azimuth AB Row 5 - Measurement of Azimuth BC 3 AB - AB0 Row 6 - Measurement of Azimuth AC The matrix setup takes the form: [ [ 3.) Solve and iterate. Solution With these the corrected coordinates are: Bx=934.9008 + dX...
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