辅导 LSGI2341A Survey Adjustment辅导 Matlab语言

LSGI2341A

Survey Adjustment

Practical Assignment 1: Level Network Adjustment

Date given: Thursday 6 February 2025

Date due:        Friday 7 March 2025 (5 pm)

PREAMBLE

This assignment consists of two parts. Your task is to adjust a level network using different computational tools.

LEARNING OUTCOMES

Upon successful completion of this assignment, you will:

1.   be familiar with writing height difference observation equations;

2.   be able to form. the system of level network observation equations in matrix form;

3.   be able to solve a level network by least-squares using a hand-held calculator/Excel;

4.   be able to solve a least-squares problem using MATLAB M-files;

5.   be able to analyse the results of a least-squares level network adjustment.

LEVEL NETWORK ADJUSTMENT

A small level network is illustrated in Figure 1.  The accompanying survey data are listed in Table 1. All observed height differences have been corrected for systematic error effects and can be considered uncorrelated. The height of the known station (benchmark)  1 is 257.891 m.

Figure 1.  Level Network Configuration.

Table 1.  Level Network Observation Data.

The standard deviation for each observation, in millimetres, is given by the formula

where L is the leg length in kilometres.

PART 1 — PARAMETRIC MODEL ADJUSTMENT BY CALCULATOR/EXCEL

Adjust the level network by the parametric method using your hand-held calculator. If you do not have access to a calculator that is capable of matrix multiplication and/or inversion, you can use Microsoft Excel instead (use the MMULT and MINVERSE functions). The following steps should be followed in order to accomplish this goal:

1.   Choose appropriate approximate values for the heights of the unknown stations.

2.   Write out the system of observation equations in matrix form. (r^ = A + w). Explicitly indicate all matrix elements and dimensions.

3.    Write out the covariance matrix of the observations Cl and weight matrix P. Indicate all matrix elements and dimensions.

Using the matrix formulae presented in the lectures, solve for the estimated parameters, residuals and adjusted observations. Also calculate the estimated (a posteriori) variance factor and the covariance matrix of parameters.

PART 2 — PARAMETRIC MODEL ADJUSTMENT BY MATLAB

Compose a set of M-files to perform the parametric adjustment of the level network using MATLAB. All data given in Table 1 must be read in by your M-file from a text file (i.e., no hard-coding). Solve for the estimated parameters, residuals and adjusted observations and their respective covariance matrices as well as the estimated variance factor. Also calculate the correlation coefficient matrix for each covariance matrix.

ANALYSIS AND QUESTIONS

1.  Using the covariance matrix of parameters, neatly plot the point error bars onto the network map shown in Figure 1 (by hand or digitally; see lecture 8, slide 9, for an example of point error bars; variable c mentioned on this slide can be set equal to  1). Explain the nature and cause of any trends that may be visible.

2.  Analyse the  correlation matrix of parameters. Explain what causes some pairs of parameters in this network to be strongly correlated and others to be weakly correlated.

3.   Which of the residuals are most correlated and how can this be seen from the correlation matrix of residuals? Explain why these residuals are most correlated by analysing the network geometry.

4.  What are the main weaknesses in the network and how could the network be improved?

Give specific suggestions.

SUBMISSION

Before the due date and time you must submit two files by groups:

1)  A report in pdf format containing:

o Results from Part 1 (maybe handwritten and scanned)

o Results from Part 2 presented in tabular form. as demonstrated on the last page

o Your MATLAB code

o Answers to the questions

2)  A zip-file containing:

o  All M-files and input files used to complete part 2, and the Excel file used to complete part 1 (if applicable)

ASSESSMENT CRITERIA

Your submission for this assignment will be marked based on the criteria shown in Table

2. A complete rubric is available on Blackboard.

Table 2. Assessment criteria

Note that the quality of your MATLAB code constitutes only 20% of the final mark. The most important part of the assignment is to obtain and report complete and correct results, and to show your understanding of the topic through your answers to the questions. If you find coding challenging, it is better to keep your code simple than to try (unsuccessfully) to write  sophisticated code. Also, do not hesitate to ask your lab instructor for advice during the computer laboratories, as this will greatly help you learn!

CHECKLIST

The following is a checklist of items that need to be included in your report. If some results are not included in the report, your results will be marked as incomplete according to the rubric. All the items below must be included in the pdf-report, and not just in the zip- file.

PLAGIARISM AND COLLUSION

Note that all work submitted must be your own. Copying (parts of) the report and/or M-file code from another student is unacceptable and will be dealt with under plagiarism and collusion regulations.

REQUIRED FORMAT FOR ADJUSTMENT OUTPUT

Your results must be neatly tabulated in a legible format, comparable to the example below. Note the use of no more than four decimals for quantities expressed in metres (do not show results to the nearest nanometre!). Also note the use of scientific notation in the covariance matrices. If your results are not clearly legible, your assignments may not be marked. The indicated precision was obtained using format short. Note the use of meaningful variable names throughout.