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Victor Mikailov, Karthik Nuti, Ryan Truett Texas A&M University College Station, TX 77843, US. Abstract : This report covers the theory of error estimation and propagation. Utilizing the tracking camera, the length and width of the square are measured repeatedly as it moves across the tables. These measurements are utilized in calculating the averages and uncertainties of the area, length, and width; and the uncertainty of the area can also be determined from the error propagation. In summary, this exercise cements the reminder of uncertainty with technology, like tracking cameras. Keywords: uncertainty, error 1. Introduction The goal of this lab was to measure the lengths and area of a square (in pixel 2 units) and measure the uncertainties within the measurements. Errors could happen to many things, but the two greatest factors are human and instrument error. As humans were working on this experiment, not every aspect of the data collections was controlled, so that leads to some possible error to occur. Also, the instrument only has a certain accuracy it can measure. To calculate the lengths of each side, the pixels were used a point on a graph and treated two of the pixel locations as vector and calculated the size with Equation 1 . Later, the error and uncertainty were calculated using population standard deviation ( Equation 2 ), as well as the statistical uncertainty by dividing the standard deviation by the square root of datapoints. 2. Experimental Procedure The procedure of this experiment, Error Analysis and Orientation, was broken down into multiple steps and processes. The first major process was the gathering of data. The first step was to install and open the MobaXterm application. MobaXterm must be opened under ethernet, otherwise the application will not work. Using the ethernet connection, connect to the Ubuntu desktop by running the command “ssh ubuntu@jetson” . Following that process, type in the password “ubuntu” – it will not be seen as you type. After typing in the password, to start collecting the data use python by typing in the following “python3 examples/tracking/4_track_and_print_with_camera_input.py ” . The next step is to start the air table and enable the data to be collected by spinning and moving the board around the restricted area. Only after well over three-hundred data points were collected, could MobaXterm be stopped with the command “Ctrl + C” . The next process was determining which data points were valid, usable data points. Any data point could be deemed invalid due to incomplete data for every recorded frame. Once all the data points are sorted through, there should be at least three-hundred usable data points. The data points can be treated as vectors on a graph, where vector sum would be the distance between the two points. On Google sheets, the program to do this calculation used Equation 1 - the points will be dependent on the color chosen. With the length and width calculated, the area can be calculated by multiplying the respective lengths and widths. With basic information, statistical analysis can be conducted. For this experiment, the point was to understand error, which means that the uncertainty of the data needs to be calculated. This can be achieved by first calculating the standard deviation of both the length and width of the square. The standard deviation of the area can also be calculated with the same formula used for length and width. Finally, the uncertainty of the area can be calculated using Equation 3 . 3. Results and Analysis

Figure 1: Estimated length at different times Figure 2: Estimated width at different times After sorting through the data into histograms, it’s shown that for Length, most of the data was between 214.83 pixels and 216 pixels, and much of the Width falls between 212.67 and 213 pixels. The other points for the Width essentially fall evenly through the further pixel boxes and taper out near 225.50 pixels and later. For length, the points quickly decrease in occurrence in the further points and are essentially minimal after 220.67 pixels. The Standard deviation of the length is 3.641595498 and for the width it is 5.005378949, which is significantly higher than the length. During the procedure, the edges would disappear off screen which would create moments in time where the data for certain points weren’t being recorded, creating greater uncertainty at certain times. This would cause the data being collected to have certain points being recorded while others were not, which would make some of the points to be inaccurate. 4. Conclusions In summary, the experiment used statistical analysis on data points from a program plotting the location of the corners of the square. These data points could be used to determine the area of the square. The statistical analysis would be used to determine how uncertain the experimental data points were. In this case, the data shows that there is significant uncertainty about the area – the calculated uncertainty was 85 units. This indicates that there may have been significant errors during the experiment, this could correlate to the most likely possibility of human error where the square would have been pushed out of the camera bounds and/or spun too fast. EQUATIONS √ ((y 2 -y 1 ) 2 + (x 2 – x 1 ) 2 ) Equation 1 where 𝑥 is the horizontal component of the vector y is vertical component of the vector. The equation can be used to determine the vector sum. (⅟n)( ∑ (𝒙ₐ − µ) ? 𝒏 𝒊=? Equation 2 Where n is the number of data points, x a is the specific vector point and μ is the mean. The equation is the population standard deviation. 𝜎 √(𝑛) ⁄ Equation 3 Where σ is the standard deviation . “n” is number of data points. This equation is the standard error of the mean and is used to determine the error in the data.

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