use matlab programming and show plots as well

6.6. Using the process of Exercise 6.5, perform the following tasks: Chapter 6. Linear Estimation a (1) Using the discrete-time model (sample time At = 0.01) simulate the process over 10 seconds with an initial condition of zero. Plot the two state variables. In a real system, this plot would be unavailable to you. However, in this simulated environment the actual state values will be useful in illustrating the performance of the estimator. (ii) Make a plot of the noise corrupted measurement, y, and compare with the uncorrupted measurement, Cx. (iii) Implement a sub-optimal state estimator using an estimator gain K = [0.000143 0.0142]*. Make plots (one for the position and one for the velocity) comparing the actual state with the state estimate. (iv) Repeat part (iii), but with the optimal estimator gain. (v) Repeat part (iv) with S, = 0.01 (vi) Repeat part (iv) with S. = 0.1 (vii) Repeat part (iv) with the following measurement equation y=[10]x + 0 and S, = 0.001. (viii) For each of the above cases, calculate the steady-state standard deviation of the error signal. Comment on any trends you observe. 6.5. Consider the following continuous-time model of a mass-spring damper: 1:2]+[] - 0 w 1 -1 y = [O 1]x + v where the first state is position and the second is velocity. Assume w(t) and v(t) are both white noise processes with zero mean and power spectral densities: S = 0.1 and S, = 0.001. (1) Determine the steady-state error covariance matrix, , of the continuous- time Kalman filter using the MATLAB function 'care'. (ii) Discretize the system using the sample and hold method (with At = 0.01). (iii) Determine the steady-state error covariance matrix of the one-step predictor, St, using the MATLAB function 'dare'. (iv) Determine the error covariance of the discrete-time optimal estimator