a) A survey is performed to find the position of a transponder on the seabed. Below are the collected data. The measurements were made with an instrument with a precision of 0.75m. Find the transponder position using a weighted least squares adjustment. Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 E(m) 362392.20 360514.26 360477.98 362337.53 361461.96 360156.30 361435.16 362664.41 362521.66 362155.55 361798.22 361186.68 360822.29 360245.33 360207.65 360798.87 361748.49 362077.15 362411.69 362554.54 N(m) 3106694.47 3106776.36 3104897.32 3104975.36 3107118.25 3105846.52 3104544.61 3105850.85 3106472.56 3106907.95 3107091.31 3107072.25 3106952.80 3106458.54 3105314.90 3104696.73 3104562.44 3104748.15 3105198.58 3105576.87 H(m) 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 observed slope distance (m) 2423.902 2388.955 2412.289 2410.044 2394.230 2364.210 2412.250 2407.482 2414.871 2418.920 2422.885 2375.300 2373.560 2398.369 2399.021 2402.301 2432.090 2414.001 2370.972 2365.696 Transponder 361357.852 E Provisional co-ordinates 3105850.267 N 2036.73 H b) Following the final coordinate solution you realize that the original instrument was unusable for measurements 14-20. A less precise instrument was used instead for these observations - it had a precision of 2.2m. How does this affect the coordinate position of the transponder? Find the updated transponder position and report the difference in position. For the above, we will use the following formula to fill the Design Matrix -A: Eprovisional-Eyesselt range a 2 Nprovisional - Nvesselt range 013 Dprovisional - Duessel 1 range: b = observed slope distance - computed slope distance b = Epi - Evd)2 + (Np: - Ny)2 + (Dpi - Dvi)2 W is a matrix of leading O's with on the diagonal. Part B 1) a) Given the following inverse matrix and a standard deviation of unit weight of 1.13, determine the parameters of the error ellipse. (AWA) = 0.00016159 -0.00001827] 0.00001827 0.00028020 b) The above adjustment was based on a traverse with 12 distance observations, 14 angle observations, 1 azimuth observation for a total of 27 observations. There were 9 stations having 2 unknowns for each station for a total of 18 unknowns. a. How many degrees of freedom? b. Determine the appropriate F value and the c multiplier at 95%. C. Compute the semi major and semi minor axes of the error ellipse at the above probability level. a) A survey is performed to find the position of a transponder on the seabed. Below are the collected data. The measurements were made with an instrument with a precision of 0.75m. Find the transponder position using a weighted least squares adjustment. Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 E(m) 362392.20 360514.26 360477.98 362337.53 361461.96 360156.30 361435.16 362664.41 362521.66 362155.55 361798.22 361186.68 360822.29 360245.33 360207.65 360798.87 361748.49 362077.15 362411.69 362554.54 N(m) 3106694.47 3106776.36 3104897.32 3104975.36 3107118.25 3105846.52 3104544.61 3105850.85 3106472.56 3106907.95 3107091.31 3107072.25 3106952.80 3106458.54 3105314.90 3104696.73 3104562.44 3104748.15 3105198.58 3105576.87 H(m) 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 8.10 observed slope distance (m) 2423.902 2388.955 2412.289 2410.044 2394.230 2364.210 2412.250 2407.482 2414.871 2418.920 2422.885 2375.300 2373.560 2398.369 2399.021 2402.301 2432.090 2414.001 2370.972 2365.696 Transponder 361357.852 E Provisional co-ordinates 3105850.267 N 2036.73 H b) Following the final coordinate solution you realize that the original instrument was unusable for measurements 14-20. A less precise instrument was used instead for these observations - it had a precision of 2.2m. How does this affect the coordinate position of the transponder? Find the updated transponder position and report the difference in position. For the above, we will use the following formula to fill the Design Matrix -A: Eprovisional-Eyesselt range a 2 Nprovisional - Nvesselt range 013 Dprovisional - Duessel 1 range: b = observed slope distance - computed slope distance b = Epi - Evd)2 + (Np: - Ny)2 + (Dpi - Dvi)2 W is a matrix of leading O's with on the diagonal. Part B 1) a) Given the following inverse matrix and a standard deviation of unit weight of 1.13, determine the parameters of the error ellipse. (AWA) = 0.00016159 -0.00001827] 0.00001827 0.00028020 b) The above adjustment was based on a traverse with 12 distance observations, 14 angle observations, 1 azimuth observation for a total of 27 observations. There were 9 stations having 2 unknowns for each station for a total of 18 unknowns. a. How many degrees of freedom? b. Determine the appropriate F value and the c multiplier at 95%. C. Compute the semi major and semi minor axes of the error ellipse at the above probability level
