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Tutorial 1.pdf

Class Tutorial Ques�ons Unit 01 - Introduc�on 1. A baseline was measured with a tape and with a total sta�on equipment. Each measuring procedure was repeated five �mes and summarized as follows: − mean distance (tape) = 200.15m, tape SD = ±0.03m − mean distance (total sta�on) = 200.183m, and total sta�on SD = ±0.008m a) Which of the measurement sets is more precise? Why? b) Is it possible to determine which of two instruments measures more accurately based only on the data given above? Why? c) The total sta�on measurements are 20mm off and are later found to be too high because of prism constant error. A�er correc�ng these measurements for prism constant, the new computed mean value is 200.163m, and standard devia�on of measurements is now ±0.008m. i. Comparing new results in (c) with old ones above, explain (using your deduc�on from the results only) if systema�c error affects accuracy. ii. Comparing new results in (c) with old ones above, explain (using your deduc�on from the results only) if systema�c error affects precision. 2. To determine the length of one baseline, it is measured 10 �mes (providing 10 baseline measurements). Answer the following ques�ons based on this problem. a) How many observables are in this problem? Explain the reason for your answer. b) Explain (providing clear reason) if there is a need for adjustment in this problem. 3. If two survey observables are measured independent of each other, which of the following will be false concerning their measurements? a) The off-diagonal elements of the covariance matrix of the measurements will be zero. b) The correla�on coefficients of any pair of observa�ons will be close to one. c) The measurements are not related to each other. d) The cofactor matrix of the measurements will be diagonal 4. Which of the following is false about accuracy of observa�ons? a) It is a measure of how close the observa�ons are to the true value. b) It is equivalent to the standard devia�on of the observa�ons assuming all possible systema�c errors in observa�ons have not been removed yet. c) It is a measure of the amount of systema�c and random errors present in the observa�ons. d) It is equivalent to precision if all possible systema�c errors in the observa�ons had been removed. Unit 02 – Analysis and Error Propaga�on of Survey Observa�ons 5. Two angles A and B of a triangle were measured as 75° 40ʹ 35ʺ ±3ʺ and 44° 50ʹ 20ʺ ±3ʺ, respec�vely, with a correla�on between the measurements as 0.6. a) Determine the third angle C and its standard devia�on (to 1 decimal second). b) If it is later detected that each angle measurement in (a) has a systema�c error of −40ʺ, use systema�c error propaga�on approach to determine the propagated systema�c error in the derived angle C, and correct all the angles for the corresponding systema�c errors. 6. Given two independent distance measurements having standard devia�ons σ1 = 0.20m and σ2 = 0.15m, respec�vely, a) Calculate the standard devia�ons of the sum and difference of the two measurements. b) Calculate the correla�on between the sum and the difference. 7. To determine the eleva�on difference between two points, the slope distance and the ver�cal angle between the two points were measured. If these measurements were later found to be larger than expected, what procedure should be followed to take care of their effects on the already calculated eleva�on difference? a) perform variance-covariance propaga�on b) perform systema�c error propaga�on c) perform Taylor’ series expansion d) ignore the effects 8. A distance measuring equipment with a specified standard devia�on of 3mm + 2ppm was used to measure 1km. If 3mm and 2ppm are considered as two independent random errors, what is the propagated error for the distance? a) 3.0mm b) 3.6mm c) 4.0mm d) 5.0mm Unit04 - Adjustment Methods and Concepts 9. A horizontal triangular survey network (A–B–C) in (see figure) was measured for the purpose of determining the coordinates of a point C(xC, yC). The network measurements include two distances; two angles; a bearing measured in a previous survey; the coordinates (and their standard devia�ons) of point B being determined from the previous GPS survey; and point A being fixed and errorless. Answer the following, giving your reasons. a) What is the number of datum defect(s)? b) List the free coordinates in the network c) List the weighted constraint coordinate(s) in the network. d) Give the absolutely constrained point in the network. e) Is the network over constrained? Why? 10. The main purpose of Least Squares method is to a) Minimize systema�c error b) Remove systema�c error c) Remove random error d) Minimize random error 11. What type of error is most likely represented by the observa�on residuals in Least Squares adjustment? a) Blunders b) Systema�c error c) Random error d) Both random and systema�c errors

Class Tutorial Ques�ons Unit 01 - Introduc�on 1. A baseline was measured with a tape and with a total sta�on equipment. Each measuring procedure was repeated five �mes and summarized as follows: − mean distance (tape) = 200.15m, tape SD = ±0.03m − mean distance (total sta�on) = 200.183m, and total sta�on SD = ±0.008m a) Which of the measurement sets is more precise? Why? b) Is it possible to determine which of two instruments measures more accurately based only on the data given above? Why? c) The total sta�on measurements are 20mm off and are later found to be too high because of prism constant error. A�er correc�ng these measurements for prism constant, the new computed mean value is 200.163m, and standard devia�on of measurements is now ±0.008m. i. Comparing new results in (c) with old ones above, explain (using your deduc�on from the results only) if systema�c error affects accuracy. ii. Comparing new results in (c) with old ones above, explain (using your deduc�on from the results only) if systema�c error affects precision. 2. To determine the length of one baseline, it is measured 10 �mes (providing 10 baseline measurements). Answer the following ques�ons based on this problem. a) How many observables are in this problem? Explain the reason for your answer. b) Explain (providing clear reason) if there is a need for adjustment in this problem. 3. If two survey observables are measured independent of each other, which of the following will be false concerning their measurements? a) The off-diagonal elements of the covariance matrix of the measurements will be zero. b) The correla�on coefficients of any pair of observa�ons will be close to one. c) The measurements are not related to each other. d) The cofactor matrix of the measurements will be diagonal 4. Which of the following is false about accuracy of observa�ons? a) It is a measure of how close the observa�ons are to the true value. b) It is equivalent to the standard devia�on of the observa�ons assuming all possible systema�c errors in observa�ons have not been removed yet. c) It is a measure of the amount of systema�c and random errors present in the observa�ons. d) It is equivalent to precision if all possible systema�c errors in the observa�ons had been removed. Unit 02 – Analysis and Error Propaga�on of Survey Observa�ons 5. Two angles A and B of a triangle were measured as 75° 40ʹ 35ʺ ±3ʺ and 44° 50ʹ 20ʺ ±3ʺ, respec�vely, with a correla�on between the measurements as 0.6. a) Determine the third angle C and its standard devia�on (to 1 decimal second). b) If it is later detected that each angle measurement in (a) has a systema�c error of −40ʺ, use systema�c error propaga�on approach to determine the propagated systema�c error in the derived angle C, and correct all the angles for the corresponding systema�c errors. 6. Given two independent distance measurements having standard devia�ons σ1 = 0.20m and σ2 = 0.15m, respec�vely, a) Calculate the standard devia�ons of the sum and difference of the two measurements. b) Calculate the correla�on between the sum and the difference. 7. To determine the eleva�on difference between two points, the slope distance and the ver�cal angle between the two points were measured. If these measurements were later found to be larger than expected, what procedure should be followed to take care of their effects on the already calculated eleva�on difference? a) perform variance-covariance propaga�on b) perform systema�c error propaga�on c) perform Taylor’ series expansion d) ignore the effects 8. A distance measuring equipment with a specified standard devia�on of 3mm + 2ppm was used to measure 1km. If 3mm and 2ppm are considered as two independent random errors, what is the propagated error for the distance? a) 3.0mm b) 3.6mm c) 4.0mm d) 5.0mm Unit04 - Adjustment Methods and Concepts 9. A horizontal triangular survey network (A–B–C) in (see figure) was measured for the purpose of determining the coordinates of a point C(xC, yC). The network measurements include two distances; two angles; a bearing measured in a previous survey; the coordinates (and their standard devia�ons) of point B being determined from the previous GPS survey; and point A being fixed and errorless. Answer the following, giving your reasons. a) What is the number of datum defect(s)? b) List the free coordinates in the network c) List the weighted constraint coordinate(s) in the network. d) Give the absolutely constrained point in the network. e) Is the network over constrained? Why? 10. The main purpose of Least Squares method is to a) Minimize systema�c error b) Remove systema�c error c) Remove random error d) Minimize random error 11. What type of error is most likely represented by the observa�on residuals in Least Squares adjustment? a) Blunders b) Systema�c error c) Random error d) Both random and systema�c errors

May 16, 2022

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