ASSIGNMENT 7 LINEAR CONDITIONAL LEAST-SQUARES ADJUSTMENT Assigned: March 15, 2023 Due: March 23, 2023 [2:59 pm] The following is an independently observed differential leveling network and its associated observations: G B F C D H E The elevation of benchmark A is to be considered fixed at 67.918 m with zero error. The weight of each observation is inversely proportional to the length of the line between each benchmark. Question 1 [80 points] Perform a weighted, linear conditional least-squares adjustment of the given differential leveling network data, including: 1. The number of observations 2. The number of independent baselines 3. The degrees of freedom 4. All necessary observation equations 5. The design matrix 6. The weight matrix 7. The misclosure vector 8. The adjusted residuals 9. The adjusted observations 10. The covariance matrix of the adjusted observations 11. The final adjusted elevations of each benchmark 12. Analysis: Do the residuals and adjusted observations make sense (sanity check)? Are the variances realistic? 1.60 Question 2 [20 points] What a priori variance was used in the adjustment? What was the estimated a posteriori variance? What is the ratio between the two and what does this tell you about the adjustment? What happens to the ratio between the two when you change the a priori variance? Why? Remember to include units! 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 Obs. 1 AB Ah (m) -2.916 Length between benchmarks (km) 1.82 2 BA 2.942 1.60 345 67 BC 2.482 1.66 CD -1.389 2.50 DE -2.578 0.75 EF 6.096 2.45 FC -2.101 0.69 8 CF 2.106 1.86 9 FB -4.566 2.27 10 FA -1.623 2.76 11 FG -1.079 0.83 12 GF 1.091 13 CH 0.435 2.42 14 HC -0.429 0.97 15 HE -4.421 1.80 16 HD -1.866 2.40