CE 506 Homework Fall 2002

• homework 1. problems from text: 3-1,3-2,3-3,3-4,3-5,3-7,3-12 do 3-7 and 3-12 by the method of "observations only". assigned thur 22-aug, due thur 29 aug. (Notes: in 3-7, even though the problems asks only for distance AC - the model includes both AB and BC. in 3-12 there is an error, angle a5 should be 50-00-20, not 40-00-20. the phrase "equal precision and uncorrelated" means equal weights, or in practice, no consideration of weights is needed) Solution
• homework 2. minimize F(x,y)=2x^2+3y^2, subject to constraint y=2x+5. do it by substitution and again by lagrange multiplier method. problems from text (do with "observation only", longhand, lagrange multiplier method): 3-8 with added weights, sigma1=5 sec, sigma2=10 sec, sigma3=15 sec, sigma4=5 sec. 3-11 with added weights, sigma1=0.003, sigma2=0.003, sigma3=0.006, sigma4=0.009, due friday, 6 sept. homework 2 solution (.pdf)
• homework 3. problems 3-9, 3-10. do them by observations only using the MATRIX approach. due friday, 13 sep. homework 3 solution (.pdf)
• homework 4. problem 4-6 done three ways: (i) indirect observations with longhand method, (ii) indirect observations by matrix method, (iii) observations only with matrix method (hint: these should all give the same result), and the following problem: fit a straight line to the following 8 data points: (x,y) = (2.0,3.0),(5.0,4.0), (9.0,6.0),(11.0,7.0),(15.0,8.0),(17.0,9.0),(18.0,10.0),(23.0,12.0). this is the standard regression model with x's constant, and the y's as observations. do it with indirect observations and matrix method. due friday, 20 sep. homework 4 solution (.pdf 1.2Mb)
• homework 5. nonlinear trilateration problem. the horizontal distance to an unknown point is observed from each of three control points. the three points are known exactly (x,y) = (30.0,150.0), (10.0,120.0), and (50.0,50.0). the corresponding observed distances are 125.0, 133.5, and 98.6, with sigmas of 0.5, 0.2, and 0.2. find the least squares estimate of the location of the unkown point by (a) indirect observations, and (b) observations only. due tuesday, 1 oct. see homework 5 solution (.pdf 2Mb) and matlab source and results (.zip)
• homework 6. (error propagation) problems from the textbook, 6-1,6-2,6-4,6-6,6-7,6-8. assigned tue., 15-oct, due tue. 22-oct. solution (.pdf)
• homework 7. (more error propagation) problems from the textbook, 6-14, 6-15, 6-16, 6-19 (uses 4-8 & 4-11), due thursday, 31-october. solution (.pdf)
• homework 8. (yet more error propagation). look again at the trilateration problem of homework 5 (indirect observation method). make the global test on the residuals at alpha=0.05. then make a 99% confidence interval for x, and for y of the unknown point. then make a 99% confidence region for the point. be sure to show where all of the numbers come from and why you are doing each step. due friday, 8 november. solution (.pdf) matlab source, listing, and ellipse plot
• homework 9. matlab program to do 2D network adjustment. see the document in homework 9 description (.pdf). program due last day of class: friday, 6-december. see the notes section of this site to download aaron braun's class example, and also some matlab code samples that you may use.
• homework 10. see the document (.pdf) for description of a circle fit problem to do by general least squares and a 2D network to be done by starnet or move3. see circle fit matlab code for correct linearization (.zip)