Restricted structure optimal linear estimators

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The restricted structure optimal deconvolution filtering, smoothing and prediction problem for multivariable, discrete-time linear signal processing problems is considered. A new class of discrete-time optimal linear estimators is introduced that directly minimises a minimum variance criterion but where the structure is prespecified to have a relatively simple form. The resulting estimator can be of much lower order than a Kalman or Wiener estimator and it minimises the estimation error variance, subject to the constraint referred to above. The numerical optimisation algorithm is simple to implement and the full-order optimal solutions are available as a by-product of the analysis. Moreover, the restricted structure solution may be used to compute both IIR and FIR estimators. A weighted H-2 cost-function is minimised, where the dynamic weighting function can be chosen for robustness improvement. The signal and noise sources can be correlated and the signal channel dynamics can be included in the system model. The algorithm enables low-order optimal estimators to be computed that directly minimise the cost index. The main technical advance is in the pre-processing, which enables the expanded cost expression to be simplified considerably before the numerical solution is obtained. The optimisation provides a direct minimisation over the unknown parameters for the particular estimator structure chosen. This should provide advantages over the simple approximation of a high-order optimal estimator. The results are demonstrated in the estimation of a signal heavily contaminated by both coloured and white noise.
LanguageEnglish
Pages400-410
Number of pages10
JournalIEE Proceedings Vision Image and Signal Processing
Volume151
Issue number5
DOIs
Publication statusPublished - Oct 2004

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Deconvolution
White noise
Cost functions
Error analysis
Byproducts
Costs
Signal processing
Processing

Keywords

  • deconvolution
  • prediction
  • filter

Cite this

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title = "Restricted structure optimal linear estimators",
abstract = "The restricted structure optimal deconvolution filtering, smoothing and prediction problem for multivariable, discrete-time linear signal processing problems is considered. A new class of discrete-time optimal linear estimators is introduced that directly minimises a minimum variance criterion but where the structure is prespecified to have a relatively simple form. The resulting estimator can be of much lower order than a Kalman or Wiener estimator and it minimises the estimation error variance, subject to the constraint referred to above. The numerical optimisation algorithm is simple to implement and the full-order optimal solutions are available as a by-product of the analysis. Moreover, the restricted structure solution may be used to compute both IIR and FIR estimators. A weighted H-2 cost-function is minimised, where the dynamic weighting function can be chosen for robustness improvement. The signal and noise sources can be correlated and the signal channel dynamics can be included in the system model. The algorithm enables low-order optimal estimators to be computed that directly minimise the cost index. The main technical advance is in the pre-processing, which enables the expanded cost expression to be simplified considerably before the numerical solution is obtained. The optimisation provides a direct minimisation over the unknown parameters for the particular estimator structure chosen. This should provide advantages over the simple approximation of a high-order optimal estimator. The results are demonstrated in the estimation of a signal heavily contaminated by both coloured and white noise.",
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Restricted structure optimal linear estimators. / Grimble, M.J.

In: IEE Proceedings Vision Image and Signal Processing, Vol. 151, No. 5, 10.2004, p. 400-410.

Research output: Contribution to journalArticle

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