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 t1 + R t F T ± Σ V + FR t F T ²1 ( Y tˆ Y t ) where ˆ Y t = FG ˆ θ t1 , R t = Σ W + G Σ t1 G T and, for any t = 1 , 2 ,...,T , Σ t = R tR 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

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