On the Approximation of Optimal Realizable Linear Filters Using a Karhunen-Loève Expansion

T. E. Fortmann; B. D.O. Anderson

doi:10.1109/TIT.1973.1055039

On the Approximation of Optimal Realizable Linear Filters Using a Karhunen-Loève Expansion

T. E. Fortmann, B. D.O. Anderson

Research output: Contribution to journal › Letter › peer-review

14 Citations (Scopus)

Abstract

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 Kalmaa-Bucy filter for this model provides an approximate realizable linear estimator which approaches the optimal one as N → ∞. A bound on the truncation error is obtained.

Original language	English
Pages (from-to)	561-564
Number of pages	4
Journal	IEEE Transactions on Information Theory
Volume	19
Issue number	4
DOIs	https://doi.org/10.1109/TIT.1973.1055039
Publication status	Published - Jul 1973
Externally published	Yes

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10.1109/TIT.1973.1055039

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abstract = "The Karhunen-Lo{\`e}ve 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 Kalmaa-Bucy filter for this model provides an approximate realizable linear estimator which approaches the optimal one as N → ∞. A bound on the truncation error is obtained.",

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AB - 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 Kalmaa-Bucy filter for this model provides an approximate realizable linear estimator which approaches the optimal one as N → ∞. A bound on the truncation error is obtained.

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On the Approximation of Optimal Realizable Linear Filters Using a Karhunen-Loève Expansion

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