GGE 3111 INTRODUCTION TO ADJUSTMENT CALCULUS W2017 _________________________________________________________________________________ Page 1 of 2 ASSIGNMENT No. 9 NON-LINEAR CONDITIONAL LEAST-SQUARES ADJUSTMENT Assigned: 8 March, 2017 Due: 22 March, 2017 @ 2:30 pm As part of an ongoing boundary retracement survey, you have been asked to determine the adjusted distance and azimuth observations associated with the boundary of a parcel. In order to obtain sufficient redundancy in the number of observations required to perform the necessary least-squares adjustment, you have measured the azimuths and distances depicted in the following plot of the surveyed parcel (oriented to North and NOT to scale). The subsequent distance and azimuth observations and their associated uncertainties are summarized in the table below. Assume that all observations were obtained independently. Segment Distance (m) sD (m) Azimuth sA 1 50.009 0.005 90°00'14" 11" 2 29.987 0.005 00°00'15" 8" 3 10.012 0.009 269°59'57" 8" 4 10.005 0.007 359°59'52" 10" 5 40.008 0.006 270°00'07" 6" 6 39.997 0.008 180°00'05" 7" 7 50.001 0.005 270°00'01" 5" 8 39.995 0.009 89°59'49" 10" 9 40.005 0.008 359°59'55" 9"GGE 3111 INTRODUCTION TO ADJUSTMENT CALCULUS W2017 _________________________________________________________________________________ Page 2 of 2 Question 1 [85 points] Perform a weighted, non-linear conditional least-squares adjustment of the given data, specifying: 1. The degrees of freedom 2. All necessary observation equations 3. The weight matrix and a priori variance factor 4. The "adjusted" observations 5. The residuals 6. The a posteriori variance factor 7. The covariance matrix of the adjusted observations The solution of the distances for the final iteration MUST converge to less than 0.005 m! Question 2 [15 points] Determine the final estimated area of the surveyed parcel. Notes for this assignment: 1. Provide solutions to a realistic precision 2. Do not truncate values in intermediate steps 3. Include units when necessary a. Hint: How does the weight matrix become unitless? 4. Clearly show all work – a final solution only will not be accepted 5. Analyze your results! Do the residuals and "adjusted" observations make sense (sanity check)? Are the variances realistic? What is the ratio of the a priori/a posteriori variance factors?