Quiz v v v
Assignment 1 v v v v v
Assignment 2 v v v v v v
Submission Instructions
1. All submissions should be digital and made through the StudyDesk Assignment submission link.
2. A submission checklist is included as Appendix A
3. Please ensure your name, student number (the 0061234567 number), and course code (SVY2105) appear at least once in the body of your assignment. Please also ensure that you clearly label each of your solutions with the corresponding question number (e.g. Question
1).
4. Use the following naming convention for your files:
o SVY2105_A1_[SurnameInitial]_[StudentNumber].xxx o Where [SurnameInitial] is replaced by your surname and your first initial (eg John
Smith would be SmithJ); and o [StudentNumber] is replaced by your 10 digit student number (eg 6001234567)
Academic Integrity: Academic Integrity means acting with the values of honesty, trust, fairness and respect in your studies. Your submitted work should reflect your own work and acknowledge the work of other where utilised. Academic integrity matters – producing your own work, to the best of your ability means you have demonstrated what you have learnt and that you have earned your qualifications. Please consult the Academic Integrity for Students page for more details.
Due Date: 19th April 2022
Value: 35% – 350 marks
Note: Scans of hand-written assignments will not be accepted.
Question 1 (30 marks)
An angle was measured 20 times under good environmental conditions by two different observers using a total station with a stated manufacturer accuracy of +/- 0.7”.
The angle was observed between two distant targets ( 1km) which were pointed to manually by each observer. Observer A had a pointing error of +/- 0.6” for sighting to each target and Observer B had a pointing error of 0.4”.
Observation Observer A Observer B
1 7202515.6- 7202519.7-
2 7202514.7- 7202519.3-
3 7202513.6- 7202518.6-
4 7202515.1- 7202520.2-
5 7202516.1- 7202519.4-
6 7202512.9- 7202517.3-
7 7202513.2- 7202516.9-
8 7202517.3- 7202518.9-
9 7202515.7- 7202518.4-
10 7202511.5- 7202524.7-
11 720259.8- 7202516.4-
12 7202514.6- 7202515.9-
13 7202513.8- 7202515.8-
14 7202517.3- 7202514.7-
15 7202518.4- 7202518.3-
16 7202511.6- 7202521.9-
17 7202514.9- 7202522.9-
18 7202516.4- 7202519.4-
19 7202517.1- 7202518.3-
20 7202512.9- 7202516.7-
Determine:
(a) the 95% confidence interval of the mean and variance for each observer’s angle observations . Comment on these confidence intervals and discuss whether the angles of the two observers may be considered to belong to the same population or should be considered different at a 95% confidence level. (20 marks)
(b) the predicted combined pointing and instrument error for each observer using the manufacturer’s stated accuracy and each observer’s pointing using the propagation of error rule. (5 marks)
(c) if there any outliers exist in each of the observer’s observations using the t test @ 95% confidence level (5 marks)
(Note: All results to be presented in DMS format, do not use decimal degrees)
Question 2 (60 marks)
You have been engaged by a structural engineer to monitor the diurnal (daily) movement of a new steel bridge that is under construction over a two-week period.
Your measurements from one side of the bridge to the other are presented below. Each column in the table contains hourly measurement data on day 1, 7 and 14 and the temperature at the time in degrees Celsius. The EDM accuracy of your total station is +/-( 2mm +2ppm). The coefficient of thermal expansion of steel for the structure is known to be 1.2 x 10-5 m/oC
Time Day 1 Temp C Day 7 Temp C Day 14 Temp C
1:00:00 AM 125.761 6 125.766 8 125.769 7
2:00:00 AM 125.758 6 125.763 8 125.767 7
3:00:00 AM 125.760 7 125.764 8 125.766 6
4:00:00 AM 125.758 8 125.762 7 125.764 6
5:00:00 AM 125.758 8 125.762 7 125.764 6
6:00:00 AM 125.762 6 125.761 6 125.765 5
7:00:00 AM 125.761 9 125.766 10 125.767 8
8:00:00 AM 125.765 12 125.769 11 125.774 10
9:00:00 AM 125.769 15 125.773 16 125.775 14
10:00:00 AM 125.776 17 125.776 18 125.778 17
11:00:00 AM 125.775 19 125.779 20 125.781 19
12:00:00 PM 125.776 20 125.780 20 125.782 20
1:00:00 PM 125.781 21 125.782 21 125.784 23
2:00:00 PM 125.782 22 125.786 23 125.788 24
3:00:00 PM 125.780 23 125.784 22 125.786 23
4:00:00 PM 125.770 20 125.782 23 125.786 21
5:00:00 PM 125.772 17 125.776 20 125.780 17
6:00:00 PM 125.765 16 125.774 16 125.777 16
7:00:00 PM 125.769 15 125.771 15 125.775 15
8:00:00 PM 125.768 14 125.772 14 125.776 14
9:00:00 PM 125.767 13 125.768 13 125.770 12
10:00:00 PM 125.759 10 125.768 11 125.767 10
11:00:00 PM 125.762 9 125.764 10 125.768 9
12:00:00 AM 125.761 7 125.765 9 125.767 7
Determine
(a) the mean, sample standard deviation, maximum and minimum values and the range for the raw observations for each day’s measurements (15 marks)
(b) plot the three days data over time using a line graph and comment on differences and trends (5 marks)
(c) adjust each of the raw distances for each day to compensate for hourly temperature variation using the 1:00 AM data as the baseline data point for each day (15 marks)
(d) recalculate the mean, sample standard deviation, maximum and minimum values and the range for the adjusted observations for each day and then compare the raw and adjusted data and comment on the variations (20 marks)
(e) Using the stated EDM accuracy of the instrument, determine if there are any outliers in the adjusted observations using the t test @95% confidence level (5 marks)
Question 3 (60 marks)
A Total Station has been calibrated over an EDM range with the following results:
(a) Using the least squares technique determine the prism/instrument constant and the scale factor if the correct baseline distances are known as shown in the above table (third column).
Compute:
(i) the most probable values (MPVs) of the prism constant and the scale factor and the expected accuracy of prism constant and scale factor (25 marks)
(ii) the residuals and the standardised residuals and the adjusted observations. Identify if there are any issues or flags with the results (10 marks) and the adjustment variance factor.
Comment on the overall adjustment outcome based on this factor and other results (5 marks).
Total 40 marks
(b) Using the data provided in (a), determine the prism constant and the scale factor using a simple linear regression technique in Excel.
Determine:
(i) the prism constant and the scale factor – include a plot of data and trend line (10 marks)
(ii) the adjusted observations (5 marks)
(iii) Compare the results obtained from the linear regression to those obtained by the least squares adjustment and comment on key differences and suggest reasons for the differences. (5 marks)
Total 20 marks
Question 4 (60 marks)
Observed elevation differences and line lengths of a level network are listed below:
Line Height difference (m) Distance (km)
A-3 -11.112 4.2
3-4 -12.368 4.0
4-B 2.148 2.2
A-4 -23.365 7.8
A-2 -6.745 2.8
2-1 -8.358 4.8
B-2 14.540 8.1
1-B -6.177 3.5
4-1 8.315 5.6
2-3 -4.347 5.2
accuracy of the level run is ± 8 mm v???? where K is the distance in kilometers.
Use the 10 steps Least Squares adjustment method to adjust the level network and to determine:
(a) the most probable values RLs for the four unknown stations 1, 2, 3, and 4, and the expected accuracy of the adjusted RLs for stations 1, 2, 3, and 4. (30 marks)
(b) the residuals and standardised residuals and the adjusted observations (10 marks)
(c) the quality of the adjustment using both F and Chi Square tests – comment on the implications of these tests and what modifications you would make to the previous calculations based on the result. (20 marks)
Question 5 (40 marks)
Use the STARNET software package to adjust the level network described in Question 4. Provide the following information with your assignment:
(a) the input file (10 marks)
(b) the output file (5 marks)
(c) a comparison of results obtained by the two methods with particular reference to the quality tests and residuals. (10 marks)
(d) The adjustment may not have passed the Chi-square test and suspect there may be a possible transcription error in the data in one of the lines. Undertake individual closes of the level loops and try to identify the error. What options are possible to improve the level adjustment? Try some adjustment options to improve the quality and describe these. (15 marks)
Question 6 (60 marks)
The angles about the horizon have been observed with different observers and have differing standard deviations.
Angle L1 = 32°25´15- ± 4.5-
Angle L2 = 61°14´38- ± 7.5-
Angle L3 = 98°09´43- ± 8.5- Angle L4 = 168°10´17- ± 6-
Angle L5 = 93°39´48- ± 6.5-
Angle L6 = 159°24´24- ± 7-
Use 10 steps least squares methods to compute the following:
(a) the most probable values (MPVs) for the six angles. (35 marks)
(b) the expected accuracy of the adjusted angles for 1, 2, 3, 4, 5, and 6. (10 marks)
(c) the residuals and standardised residuals and the adjusted observations after the adjustment. (10 marks)
(d) the quality of the adjustment. (5 marks)
Question 7 (40 marks)
The light spectrum (Measured) below was measured for a pixel in an image across five spectral bands. It is assumed that the pixel is made up of a mixture of reflectance values from three surfaces of known spectra (A, B & C).
The top left graph below shows the combined measured (Measured) spectrum value in each of the five band (400nm, 500nm,600nm, 700nm and 800nm). The remaining three graphs provide the reflectance values recorded for three surfaces, surface A, B and C in each band.
It is considered the pixel spectrum is comprised of the linear sum of the three surfaces in proportion to their area.
Total measured spectrum for a particular band (Measured) =Measured Reflectance Surface A (RA) x Proportion of Area Surface A (PA) + Measured Reflectance Surface B (RB) x Proportion of Area Surface B(PB) + Measured Reflectance Surface C (RC) x Proportion of Area Surface C (PC).
For each band this can be represented by the formula Measured = RA PA + RB PB + RC PC
Solve for the most probable values for the proportions (PA, PB, PC) using the method of least squares.
Marks will be allocated as follows:
Formulation of observation equations – 15 marks
Matrix formulation – 15 marks
Solution of equations – 10 marks
