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Consider the following state space model (signal and observation model). Y t = H t X t + W t , W t ∼ N (0, R) (1) X t = F t X t−1 + U t , U t ∼ N (0, Q) (2)
1. First, assume a scalar unknown parameter θ (a) Min classical MSE estimator: ˆ θ(X) = arg minˆθ E X [(θ − ˆ θ(X)) 2 2 ] (b) Often the resulting estimator is not realizable, i.e. it depends on θ.
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