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Cramér-Rao bounds and non-linear least squares for a seven parameter dual channel sinewave model
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-2718-0262
2007 (English)In: 2007 IEEE Instrumentation and Measurement Technology Conference, IEEE , 2007, 79-84 p.Conference paper, Published paper (Refereed)
Abstract [en]

The Cramer-Rao bound (CRB) is a lower bound on the error variance of any estimator. For a Gaussian scenario, the CRB is derived for a seven parameter dual channel sine wave model; a model with relevance in applications like impedance measurements and the estimation of particle size and velocity by laser anemometry. Three different parameterizations are considered: the common quadrature/in-phase and amplitude-phase models, as well as a relative amplitude-phase model. The CRB indicates the achievable error variance of an unbiased estimator as a function of the signal-to-noise ratio, number of samples, and noise power. An non-optimal non-linear least squares fit of the signal model to the collected data is employed. The problem at hand is separable and can be solved by a one dimensional search followed by a linear least-squares fit of the remaining parameters. The performance of the method is investigated by aid of a simulation study, and the outcome is compared with the corresponding CRB. For high signal-to-noise ratios, the performance of the proposed method is close to optimal with an error variance close to the predictions made by the CRB.

Place, publisher, year, edition, pages
IEEE , 2007. 79-84 p.
Series
IEEE Instrumentation and Measurement Technology Conference, ISSN 1091-5281
Keyword [en]
Cramer-Rao bound, sinewave fit, seven-parameter model, line spectral analysis, non-linear least-squares, IEEE standards 1057 & 1241
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-34931ISI: 000251296800016Scopus ID: 2-s2.0-34648824705ISBN: 978-1-4244-0588-6 (print)OAI: oai:DiVA.org:kth-34931DiVA: diva2:428853
Conference
2007 IEEE Instrumentation and Measurement Technology, IMTC 2007 - Synergy of Science and Technology in Instrumentation and Measurement; Warsaw; Poland; 1 May 2007 through 3 May 2007
Note

QC 20110701

Available from: 2011-07-01 Created: 2011-06-17 Last updated: 2014-11-11Bibliographically approved

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Händel, Peter

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  • apa
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