The hybrid cramér-rao bound and the generalized Gaussian linear estimation problem

Y. Noam; H. Messer

doi:10.1109/SAM.2008.4606898

The hybrid cramér-rao bound and the generalized Gaussian linear estimation problem

Y. Noam, H. Messer

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper explores the Hybrid Cramér-Rao Lower-bound (HCRLB) for a Gaussian generalized linear estimation problem in which some of the unknown parameters are deterministic while the other are random. In general, the HCRLB on the non-Bayesian parameters is not asymptotically tight. However, we show that for the generalized Gaussian linear estimation problem, the HCRLB of the deterministic parameters coincides with the CRLB, so it is an asymptotically tight bound. In addition, we show that the ML/MAP estimator [1] is asymptotically efficient for the non-Bayesian parameters while providing optimal estimate of the Bayesian parameters. The results are demonstrated on a signal processing example. It is shown the Hybrid estimation can increase spectral resolution if some prior knowledge is available only on a subset of the parameters.

Original language	English
Title of host publication	SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop
Pages	395-399
Number of pages	5
DOIs	https://doi.org/10.1109/SAM.2008.4606898
State	Published - 2008
Externally published	Yes
Event	SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop - Darmstadt, Germany Duration: 21 Jul 2008 → 23 Jul 2008

Publication series

Name	SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop

Conference

Conference	SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop
Country/Territory	Germany
City	Darmstadt
Period	21/07/08 → 23/07/08

Access to Document

10.1109/SAM.2008.4606898

Cite this

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title = "The hybrid cram{\'e}r-rao bound and the generalized Gaussian linear estimation problem",

abstract = "This paper explores the Hybrid Cram{\'e}r-Rao Lower-bound (HCRLB) for a Gaussian generalized linear estimation problem in which some of the unknown parameters are deterministic while the other are random. In general, the HCRLB on the non-Bayesian parameters is not asymptotically tight. However, we show that for the generalized Gaussian linear estimation problem, the HCRLB of the deterministic parameters coincides with the CRLB, so it is an asymptotically tight bound. In addition, we show that the ML/MAP estimator [1] is asymptotically efficient for the non-Bayesian parameters while providing optimal estimate of the Bayesian parameters. The results are demonstrated on a signal processing example. It is shown the Hybrid estimation can increase spectral resolution if some prior knowledge is available only on a subset of the parameters.",

author = "Y. Noam and H. Messer",

year = "2008",

doi = "10.1109/SAM.2008.4606898",

language = "אנגלית",

isbn = "9781424422418",

series = "SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop",

pages = "395--399",

booktitle = "SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop",

}

Noam, Y & Messer, H 2008, The hybrid cramér-rao bound and the generalized Gaussian linear estimation problem. in SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop., 4606898, SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop, pp. 395-399, SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop, Darmstadt, Germany, 21/07/08. https://doi.org/10.1109/SAM.2008.4606898

The hybrid cramér-rao bound and the generalized Gaussian linear estimation problem. / Noam, Y.; Messer, H.
SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop. 2008. p. 395-399 4606898 (SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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The hybrid cramér-rao bound and the generalized Gaussian linear estimation problem

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