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Cited by 496

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A New Approach to Linear Filtering and Prediction Problems

·2009·Control Theory
DOI 10.1109/9780470544334.ch9
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Abstract

The clssical filleting and prediclion problem is re-examined using the Bode-Shannon representation of random processes and the ?stat-tran-sition? method of analysis of dynamic systems. New result are: (1) The formulation and Methods of solution of the problm apply, without modification to stationary and nonstationary stalistics end to growing-memory and infinile -memory filters. (2) A nonlinear difference (or differential) equalion is dericed for the covariance matrix of the optimal estimalion error. From the solution of this equation the coefficients of the difference, (or differential) equation of the optimal linear filter are obtained without further caleulations. (3) Tke fillering problem is shoum to be the dual of the nois-free regulator problem. The new method developed here, is applied to do well-known problems, confirming and extending, earlier results. The discussion is largely, self-contatained, and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.

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Metadata

Venue
Control Theory
Publisher
IEEE
Published
2009
DOI
10.1109/9780470544334.ch9
OpenAlex
W1786529921
Cited by
496
References
0
FWCI
27.00
Type
book chapter
Language
en
Open access
closed

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CoChat. (2026). Citation check: A New Approach to Linear Filtering and Prediction Problems. https://app.cochat.ai/papers/10.1109/9780470544334.ch9
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A New Approach to Linear Filtering and Prediction Problems. (2009). Control Theory. https://doi.org/10.1109/9780470544334.ch9

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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.