Problem 4.(10 points) Consider the nonlinear discrete time system 21(k) + Tu1(k) cos(13(k)) x(k+1) = 22(k) + Tu (k) sin(

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Problem 4 10 Points Consider The Nonlinear Discrete Time System 21 K Tu1 K Cos 13 K X K 1 22 K Tu K Sin 1 (54 KiB) Viewed 47 times

Problem 4.(10 points) Consider the nonlinear discrete time system 21(k) + Tu1(k) cos(13(k)) x(k+1) = 22(k) + Tu (k) sin(13(k)) y(k) = 11(k) +v(k) z3(k) + Tuz(k) where v(k) is Gaussian white noise with zero mean and variance 0.5. Suppose the estimate f(1) = (1, 1,0]", the input u (1) = 1, u2(1) = 0, and the time step T = 1. Also suppose that the covariance estimate P(1) is the 3 x 3 identity matrix. Using the extended Kalman filter formulation compute the time update estimate and covariance 7(2) and M (2) • given the measurement y(2) = 1.8, compute (2) and P(2). =