Geomatics_Lab4_EliasZamora

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❶ Lab Teaching Assistant Aser Eissa (eissaa@purdue.edu) Assignment date: 01/31/2024 Submission date: 02/11/2024 Purdue University Lyles School of Civil Engineering CE 203 – Principles and Practice of Geomatics Propagation of Errors/Uncertainty Elias Zamora (zamora14@purdue.edu) Fall 2024
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1. The propagation of error/uncertainty formula for a non-linear model is more general and the variables for the 7th equation, as it involves using a matrix to get the same result. There are two ways to go about using the 9th equation, and either will work for a non-linear, or a linear equation. 2. The variance for a derived variable T is given by: a. a 2 𝜎 x 2 + b 2 𝜎 y 2 - c 2 𝜎 2 z 3. The standard deviation for n independent measurements will be equal to 1/n. The standard deviation for these measurements will be equal to 0 if all of the values are equal to each other, since the average is equal to all of the other measurements (there is no deviation from the mean). 4. The standard deviation of the radial distance from the nadir point to the top of the building is plus or minus 3 micrometers. 5. The standard deviation for this relief displacement is 3.5 micrometers. This is higher than problem 4, since x 1 is closer to x 2 . 6. The image scale for the images based on the coordinates and their standard deviation is between (1.04 to .94), going off of the first pair, (0.98 to 1.003) for pair two, and (.9993 to .9998). These numbers are measured in (micrometers, millimeters). I would infer that the scale gets more accurate the larger numbers we get in pairs. The most accurate deviation is the lowest spread between the distances, which the 3rd pair shows. 7. The object distance between these two points is 4840 feet, with a standard deviation that is very minimal in feet. 8. Using the scale of the image is 56.92 meters tall, with the standard deviation of plus or minus 30 millimeters. 9. With a standard deviation of 0.7713, my assessment of these measurements is that there is gross errors in two calculations (284 and 281), and possibly some random errors. A UAV experiences mass amounts of wind at heights that are 30+ ASL. A 10-20 knot gust of wind could have tipped the lens slightly to cause a deviation in the calculations. Given the information, we can find that the distance between the pillars is around 283 and a standard deviation of 0.77, but with no errors I believe that this number will be around 282 with a standard deviation of 0.2. 7
10. The standard deviation: a. sigma (H-h) = ((H - h) / B) * ((H - h) / C)* sqrt(2) sigma x 11. Standard deviation for ground coordinates, given that the only source of error is the UAV’s own errors, are as follows: a. Sigma i = ((H - h) / C) * sigma H-h . 12. If you were to fly from 50m high: a. You would have results quicker, that would have more parallax –very high parallax for tall buildings since a 3-story building can be 10 meters– but with higher parallax, comes higher quality of the top and bottom of the building since you are closer to it. You would be able to calculate the heights and positions easily, but that can be seen as a con. If you were to fly from 100m high: a. At 100m, there is much less parallax, but also more flight time since you need to reach the altitude for Navigation mode. From this height, you could see more of the site, meaning less flyovers and less pictures. You will also have less parallax near the center of the image, but you would have less accurate results when finding the parallax. 13. The standard deviation in the flying height of 6851.05 is plus or minus 8 inches. 14. 64000000 square inches plus or minus 0.0001 inches. 8
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