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On the approximation of optimal realizable linear filters using a Karhunen-Loeve expansion (Corresp.)

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2 Author(s)

The Karhunen-Loève expansion of a random process is used to derive the impulse response of the optimal realizable linear estimator for the process. The expansion is truncated to yield an approximate state-variable model of the process in terms of the first N eigenvalues and eigenfunctions. The Kalman-Bucy filter for this model provides an approximate realizable linear estimator which approaches the optimal one as N \rightarrow \infty . A bound on the truncation error is obtained.

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Information Theory, IEEE Transactions on  (Volume:19 ,  Issue: 4 )