Geomatics_Lab6_EliasZamora.docx

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❶ Lab Teaching Assistant Aser Eissa (eissaa@purdue.edu) Assignment date: 02/14/2024 Submission date: 02/25/2024 Purdue University Lyles School of Civil Engineering CE 203 – Principles and Practice of Geomatics Bundle Adjustment With Self Calibration (zamora14@purdue.edu)

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1. a. These are the plots relating the data correlation. It seems that the data has a correlation and contains groups of precise measurements in not-so accurate areas of the trendline. It looks very symmetrical near the bottom, and there is one group of iterations at the top. This is a negative trendline. b. The results for solving for distortions parameters (K1, K2, K3, P1, P2, P3) are as follows: -3.95393331e-002, -1.14165240e-003, -1.35612348e-004, -1.46951154e-004, 1.13783738e-004, 8.97421235e-004. The principal point coordinates are as follows, (-0.0810671, .0879017, 2.69723297). Using these values and the residuals, we can graph these 3 plots: 7

c. Much like the graphs given by the BASC Software, we can see a correlation between the residual points and radial distance. The magnitude of the residual gives a very interesting curve that I can only describe as a triangle-like shape, almost like there’s two boundary lines making the chart. 1b. The next parts are without the distortion parameters a. When we remove the distortion parameter, the matrix for distortion simply has very small numbers. With no solutions for our unknowns, the IOP has zero’s for every unknown K and P value. The IOP Covariance matrix is only a 3x3 matrix as well. The principle point coordinates are also different, being (-0.003494062, -0.21457666, 2.08324322). The graphs for this can be seen here: b. The Magnitude vs Radial Distance looks very similar to Test 1’s. The first two graphs changed a lot, and there seems to be positive or negative correlation for the X-residual to the Radial Distance. 9

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1c. The next parts with including a Gross Error a. For Run 3, the data was reverted back to the conditions in Run 1. We will consider the distortion again, but we will introduce an error of 0.5 in the x-coordinate for a point. The principle point coordinates are (-0.021580219, -0.07.09911876, 2.62996716). The Distortion Parameters are (K1, K2, K3, P1, P2, P3) equal to: (-0.0544906, 0.00717276, -0.000904058, 0.00137212, 0.003038649, 0.0466495). Here are the graph results for this: 10

c. There seems to be a lot of problems with this graph after the gross error was introduced into the mix. The graphs don’t look right at all, and while the trendline for the magnitude res vs the radial distance may be the same, the graphed points look very bizarre, with all of the points being concentrated near the origin. It’s safe to assume that having a gross error in the BASC software is not good for the program and will terribly mess up your results when calculating. 2. I will use tables to provide the sigma values for each iteration: Run 1 .sigma Values Iteration Sigma 1 8.2669646238e-001 2 2.1763342768e-001 3 5.1239463753e-002 4 2.0149081678e-002 5 1.8888810028e-002 6 1.8886058996e-002 7 1.8886005122e-002 8 1.8886003370e-002 Run 2 .sigma Values Iteration Sigma 1 8.2669646238e-001 2 1.9167534357e-001 3 8.3282570838e-002 4 1.6064765434e-002 5 9.9005904488e-003 6 5.4185811057e-003 7 3.9824426357e-003 8 2.6869585397e-003 11

Run 3 .sigma Values Iteration Sigma 1 8.2792740708e-001 2 1.9889871394e-001 3 8.9290830779e-002 4 2.7585811389e-002 5 2.5028378360e-002 6 2.2286723834e-002 7 2.1852136140e-002 8 2.1844466698e-002 a. The results in these tables are all different, but they start with a very similar first value. After the iterations go on, they get more and more distant from each other as the iterations define them in their own terms as the tests go on. 3. Here are the results for the EOP’s for one Iteration (Some of the runs have over 100+ iterations of the samples): 12

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4. The different residual plots have no resemblance to one another in each of the three runs. Every change that was made had a large impact and gave us entirely different results. This is evident in the graphs that are shown in this lab report. 5. The main problems that I encountered during this lab was how to start and execute the program BASC. The first Run I executed was actually run 2, where we don’t consider the distortion parameters. The matrix had values of 1.0e-15 in them, which is a very small number, meaning we weren’t considering the distortion parameters. I kept the solutions for this run–Since it is actually Run 2– and re-ran it with 1’s in the matrix value locations in every row, except the first–We don’t need K0. 13

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