1. Work through, code up and show the results of example 6.1 from the textbook. Show, discuss, and comment on all intermediate steps. Explicitly name the update, propagation, update, and reset step. Note: Only the filter part is needed, you can ignore the smoother part. The details and individual parts of the problem are the following: (a) Simulate the true attitude of your spacecraft. You may assume a torque free attitude mo- tion with the intial truth angular velocity of @true = 0.1 [sin(0.01t), sin(0.0085t), cos(0.0085t)]T. At t=0, the orientation is represented via the following quaternion 9true = 2. [1,0,0,1]7 (b) Simulate the gyro measurements with one measurement per second. Use the fol- lowing values: Initial gyro bias of 0.1 deg/h in all three axis, scale factors of s = 1500ppm, s2=1000ppm, s3 = 1500ppm gyro misalignments of ku = 1000ppm, ku2 = 1500ppm, ku2=2000ppm, k = 500ppm, k = 1000ppm, k3 = 1500ppm. The noise in the gyro can be modeled by the following values: = 10-10-10 rad rad 10.107, = = L = 0. Os OU $3/2,0y=