ASSIGNMENT No. 8 NON-LINEAR PARAMETRIC LEAST-SQUARES ADJUSTMENT [100 points] Line Distance Observation (m) L1 1949.851 L2 1266.217 L3 3292.901 LA 1580.808 L5 2004.842 Assigned: March 22, 2022 Due: March 29, 2022 2:59 pm The following is an independently-observed station resection used to establish coordinates for station S: 15 E b A B C The coordinates of stations A, B, C, D, and E are assumed to be both fixed and errorless in a local Cartesian coordinate system. The coordinates of station S are to be determined using distances 11, 12, 13, 14, and 15 observed using an EDM instrument. The manufacturer specifications for the EDM used to perform the resection claim a standard deviation for each observation to be given by (5mm + 4ppm). The observed distances and station coordinates are summarized as follows: Question 1 Perform a weighted, non-linear parametric least-squares adjustment of the given station resection data, including: 1. All necessary observation equations 2. The weight matrix and a priori variance factor 3. The design matrix 4. The misclosure vector 5. The a priori parameter values 6. The adjusted parameters 7. The adjusted residuals 8. The adjusted observations 9. The a posteriori variance factor 10. The covariance matrix of the adjusted parameters 11. The standard deviation of the parameters 12. Analysis: Do the residuals and adjusted observations make sense (sanity check)? Are the variances realistic? How about the correlation values? What is the ratio of the a priori/a posteriori variance factors? What does this tell you about the adjustment? Station X(m) Y(m) A -2429.523 1658.688 B -2943.277 2764.172 C 1343.536 3589.309 -3529.246 3501.406 E -121.412 2724.432 Page 1 of 2 The solution for the final iteration MUST converge to less than 0.0005 m! Notes for this assignment: 1. Provide solutions to a realistic precision 2. Do not truncate values in intermediate steps 3. Provide matrix dimensions to ensure matrix operation conformability 4. Include units when necessary a. Hint: How does the weight matrix become unitless? 5. If using computer software, attach ALL necessary code 6. Clearly show all work a final solution only will not be accepted Page 2 of 2