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Unformatted text preview: 2 w . (a) Find the initial least squares estimator of the state vector at time t = 2, in terms of the observations x 1 and x 2 . (b) If 2 w = 0, so that we have ordinary linear regression with constant coeceints and a third observation x 3 becomes available, apply the Kalman lter to show that the estimator of the state vector at time t = 3 is given by [ 3 , 3 ] = 5 6 x 3 + 1 3 x 2 1 6 x 1 , 1 2 ( x 3 x 1 ) . 3. (1 point each) Consider AR(2) process, X t = 1 X t-1 + 2 X t-2 + W t , W t N (0 , 2 ) . (a) Find a state space representation based on the state vector t = ( X t ,X t-1 ). (b) Find a state space representation based on the state vector t = ( X t , X t ), where X t is the optimal one step ahead predictor at time t ....
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This note was uploaded on 05/01/2009 for the course PSTAT 120A taught by Professor Mackgalloway during the Spring '08 term at UCSB.
- Spring '08