Problem 2 Consider the following noise-corrupted state-space system: x = Ax+Bu+Gv where =G=[₁] C= [10] y=Cx+w The signal

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Problem 2 Consider The Following Noise Corrupted State Space System X Ax Bu Gv Where G C 10 Y Cx W The Signal 1 (33.1 KiB) Viewed 23 times

Problem 2 Consider the following noise-corrupted state-space system: x = Ax+Bu+Gv where =G=[₁] C= [10] y=Cx+w The signals v and w are Gaussian white noise with zero mean and with covariances given: W = [1] a) Without the aid of MATLAB, solve for all of the solutions Se of the filter algebraic Riccati equation (FARE). Show all of your algebraic steps. b) Calculate the Kalman filter with optimal observer gain matrix L and state matrix of the observer error dynamics Ae associated with each of the solutions of the FARE. Which of the solutions is valid? Justify your answer mathematically. You may use MATLAB for this part. Hint: There are four matrix solutions Se to the FARE. For this problem, each matrix Se has integer entries.