Lab Work Recall the normal equation (ATA)-1 AT b, and fitting a curve with a second-order polynomial 1. First work with the perfect case, "p_without_noise": 1.1. Write a function called LS_estimation.m, with 1.1.1. Input: 1.1.1.1. 1.1.1.2. A matrix b vector 1.1.2. Output: x 1.2. Construct your A matrix and b vector for this case, and show your estimated a[0], v[0], and p[0] 1.3. Plot the original data (from the .mat file) and your estimated position over time 1.3.1. The X-axis should be the time index (1-100), or time in seconds (0~9.9 seconds) 1.3.2. Y-axis should be the position 1.3.3. Use "legend" to label original data and your estimated position 2. Then work with the noisy data, "p_with_noise": 2.1. Use the same LS_estimation.m function above, show your estimated a[0], v[0] and P[0] 2.2. Plot the original data and your estimated position over time 2.2.1. The X-axis should be time index (1-100), or time in seconds (0~9.9 seconds) 2.2.2. Y-axis should be the position 2.2.3. Use "legend" to label original data and your estimated position