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hw7 - EE 378 Statistical Signal Processing Homework Set#7...

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EE 378 Handout #14 Statistical Signal Processing Wednesday, May 23, 2007 Homework Set #7 Due: Wednesday, May 30, 2007. Consider the following problem setting, X k = f k ( X k - 1 ) + W k Z k = X 2 k 20 + V k where, f k ( X k - 1 ) = X k - 1 2 + 25 X k - 1 1 + X 2 k - 1 + 8 cos(1 . 2 k ) . { W k } and { V k } are independent Gaussian white noise processes of respective variances 10 and 1, independent of the initial state X 0 ∼ N (0 , 1). In practice, we would of course only have samples of the observation process, { Z k } , and we would have to estimate the underlying state process, X k , on the basis of Z k . In this exercise, however, we will generate samples of Z k by first generating samples of X k . We will then use samples of this observation process, { Z k } , and filtering techniques discussed in class, to estimate the underlying state process, { X k } . Generate a sample path of the state process, { X k } 500 k =1 , and the corresponding obser- vation process, { Z k } , using the dynamics given above. 1. Use the Extended Kalman Filter (EKF) formulation discussed in class to estimate

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