**Unformatted text preview: **ˆ θ and known covariance matrix Σ . Assume further that all the covariance matrices are positive deﬁnite. Deﬁne the estimator ˆ θ t of the latent state θ t , based on data Y 1 ,Y 2 ,...,Y t , as ˆ θ t = E ( θ t | Y 1 ,Y 2 ,...,Y t ) . Your task is to establish the following recursive formula for this estimator: ˆ θ t = G ˆ θ t-1 + R t F T ± Σ V + FR t F T ²-1 ( Y t-ˆ Y t ) where ˆ Y t = FG ˆ θ t-1 , R t = Σ W + G Σ t-1 G T and, for any t = 1 , 2 ,...,T , Σ t = R t-R t F T (Σ V + FR t F T )-1 FR t ....

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- Fall '08
- Staff
- Normal Distribution, Standard Deviation, Variance, Probability theory, Covariance matrix, Yt