Q1. Using the provided quiescent gyro data file (hwk8_Prob1_data.mat), plot the x-axis data in deg/s vs time in Figure 1 (be sure to add a title, axis labels, and units)

a. Compute the mean and standard deviation.

b. Plot the histogram (in Figure 2) of this data and using ONLY the histogram data again compute the mean and standard deviation.

c. Plot the autocorrelation function of the x-gyro signal in Figure 3 for τ = 0 to 1sec

d. Compute the standard deviation using only the computed autocorrelation fn.

e. Compute the average power in the signal.

f. Plot the one sided power spectral density of the signal.

Q2. Self-alignment: Given the accel data (in m/s²) and gyro data (in rad/s) of an IMU at rest (load file "hwk8_Prob2_data.mat") on earth's surface at a latitude of L_t = 34.6155794^o, longitude of λ_t = -112.4504^o, and height of h_t = 1578 m determine the orientation of the body wrt the n-frame.  Assume that the IMU is perfectly aligned with the b-frame and local gravity is g = 9.79213m/s².

a. Use the scalar method: Develop a MATLAB fn [roll, pitch, yaw, C_n__b] = coarse_alignment_scalar(gyro, accel)

which accepts the means of the (assumed stationary) gyro and accel data and determines angles (in rad) and C_n__b. Compute the following:

i. Roll =

ii. Pitch =

iii. Yaw =

iv.  C_bⁿ

b. Use the vector method: Develop a MATLAB fn [C_n__b] = coarse_alignment_vector(gyro, accel, Lb, g)

which accepts the means of the (assumed stationary) gyro and accel data, Latitude (in rad), and local g (in m/s2)to determine C_n__b.  Compute the following: C_bⁿ.

Attachment:- Assignment Files.rar