Question

Question 3: Recursive Least Squares Simulate the following system: y(k)-1.5 y(k-1+0.7y(k-2)u(k1e(k) Where e(k) is a white noise with variance 4.0 and u(k) is a random binary signal with u(k) - Simulate the data set with N 400 points. a) Use the obtained data sets of (y, u) from part a) to identify the parameters using the recursive least squares algorithm. Plot the parameter estimates and the trace of the covariance matrix P. Let the forgetting factor 2 - 1.0 and 0.95. Is there a difference? b) Do the same simulation as in part a) but set u(k)- 1.0 from N-100 to N-300 and then change u(k) back into a random binary signal, u(k) - from N-301 until N-400. Set the forgetting factor to 0.95. Plot the parameter estimates and the trace of the covariance matrix P. Any comments? c) Do the same simulation as you did in part b) except this time change the parameter values at time step N-250 from a-1.5 to a1.7 and change a2-0.7 to a2 0.9 and change b 1.0 to b- 5.0. Comment on what you observe. Plot the parameter estimates and the trace of the covariance matrix

Answer 1

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