Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume

Lu Zhang; Janusz Kulon; Yong Yan

doi:10.1109/I2MTC.2015.7151443

Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume

Lu Zhang, Janusz Kulon, Yong Yan

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

Abstract

This paper addresses the problem of estimating the Doppler frequency in Laser Doppler Velocimetry (LDV) systems by taking into account the effect of the particle trajectory via the measurement volume. The dependency of the burst length on the Cramér-Rao lower bound (CRLB) and the Doppler frequency estimation is investigated by employing the 2D model of the Doppler Burst Signal with the Gaussian envelope. The Maximum Likelihood Estimator (MLE) equations are solved for estimates of the Doppler frequency for LDV systems operating in one particle scattering mode. The numerical examples show the performance of the MLE and FFT with various parameter configurations compared with the derived CRLB. The numerical results confirm the validity of the analysis in terms of the relative effect of the particle trajectory, relative measurement time, size of the volume and signal-to-noise ratio on the accuracy of the estimation.

Original language	English
Title of host publication	2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings
Publisher	Institute of Electrical and Electronics Engineers
Pages	1198-1203
Number of pages	6
ISBN (Electronic)	978-1-4799-6114-6
DOIs	https://doi.org/10.1109/I2MTC.2015.7151443
Publication status	Published - 11 May 2015
Event	2015 IEEE International Instrumentation and Measurement Technology Conference: The Measurable of Tomorrow: Providing a Better Perspective on Complex Systems - Palazzo dei Congressi, Pisa, Italy Duration: 11 May 2015 → 14 May 2015

Conference

Conference	2015 IEEE International Instrumentation and Measurement Technology Conference
Abbreviated title	I2MTC
Country/Territory	Italy
City	Pisa
Period	11/05/15 → 14/05/15

Keywords

Power measurement
Volume measurement
Size measurement
Convergence

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10.1109/I2MTC.2015.7151443Licence: CC BY-NC-ND

Cite this

Zhang, L., Kulon, J., & Yan, Y. (2015). Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume. In 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings (pp. 1198-1203). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/I2MTC.2015.7151443

Zhang, Lu ; Kulon, Janusz ; Yan, Yong. / Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency : The effect of a particle trajectory through the measurement volume. 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings. Institute of Electrical and Electronics Engineers, 2015. pp. 1198-1203

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title = "Maximum Likelihood Estimator, FFT Estimator and Cram{\'e}r-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume",

abstract = "This paper addresses the problem of estimating the Doppler frequency in Laser Doppler Velocimetry (LDV) systems by taking into account the effect of the particle trajectory via the measurement volume. The dependency of the burst length on the Cram{\'e}r-Rao lower bound (CRLB) and the Doppler frequency estimation is investigated by employing the 2D model of the Doppler Burst Signal with the Gaussian envelope. The Maximum Likelihood Estimator (MLE) equations are solved for estimates of the Doppler frequency for LDV systems operating in one particle scattering mode. The numerical examples show the performance of the MLE and FFT with various parameter configurations compared with the derived CRLB. The numerical results confirm the validity of the analysis in terms of the relative effect of the particle trajectory, relative measurement time, size of the volume and signal-to-noise ratio on the accuracy of the estimation.",

keywords = "Power measurement, Volume measurement, Size measurement, Convergence ",

author = "Lu Zhang and Janusz Kulon and Yong Yan",

year = "2015",

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language = "English",

pages = "1198--1203",

booktitle = "2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings",

publisher = "Institute of Electrical and Electronics Engineers",

note = "2015 IEEE International Instrumentation and Measurement Technology Conference : The Measurable of Tomorrow: Providing a Better Perspective on Complex Systems, I2MTC ; Conference date: 11-05-2015 Through 14-05-2015",

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Zhang, L, Kulon, J & Yan, Y 2015, Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume. in 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings. Institute of Electrical and Electronics Engineers, pp. 1198-1203, 2015 IEEE International Instrumentation and Measurement Technology Conference, Pisa, Italy, 11/05/15. https://doi.org/10.1109/I2MTC.2015.7151443

Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume. / Zhang, Lu; Kulon, Janusz; Yan, Yong.
2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings. Institute of Electrical and Electronics Engineers, 2015. p. 1198-1203.

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

TY - CHAP

T1 - Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency

T2 - 2015 IEEE International Instrumentation and Measurement Technology Conference

AU - Zhang, Lu

AU - Kulon, Janusz

AU - Yan, Yong

PY - 2015/5/11

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N2 - This paper addresses the problem of estimating the Doppler frequency in Laser Doppler Velocimetry (LDV) systems by taking into account the effect of the particle trajectory via the measurement volume. The dependency of the burst length on the Cramér-Rao lower bound (CRLB) and the Doppler frequency estimation is investigated by employing the 2D model of the Doppler Burst Signal with the Gaussian envelope. The Maximum Likelihood Estimator (MLE) equations are solved for estimates of the Doppler frequency for LDV systems operating in one particle scattering mode. The numerical examples show the performance of the MLE and FFT with various parameter configurations compared with the derived CRLB. The numerical results confirm the validity of the analysis in terms of the relative effect of the particle trajectory, relative measurement time, size of the volume and signal-to-noise ratio on the accuracy of the estimation.

AB - This paper addresses the problem of estimating the Doppler frequency in Laser Doppler Velocimetry (LDV) systems by taking into account the effect of the particle trajectory via the measurement volume. The dependency of the burst length on the Cramér-Rao lower bound (CRLB) and the Doppler frequency estimation is investigated by employing the 2D model of the Doppler Burst Signal with the Gaussian envelope. The Maximum Likelihood Estimator (MLE) equations are solved for estimates of the Doppler frequency for LDV systems operating in one particle scattering mode. The numerical examples show the performance of the MLE and FFT with various parameter configurations compared with the derived CRLB. The numerical results confirm the validity of the analysis in terms of the relative effect of the particle trajectory, relative measurement time, size of the volume and signal-to-noise ratio on the accuracy of the estimation.

KW - Power measurement

KW - Volume measurement

KW - Size measurement

KW - Convergence

U2 - 10.1109/I2MTC.2015.7151443

DO - 10.1109/I2MTC.2015.7151443

M3 - Chapter

SP - 1198

EP - 1203

BT - 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

PB - Institute of Electrical and Electronics Engineers

Y2 - 11 May 2015 through 14 May 2015

ER -

Zhang L, Kulon J, Yan Y. Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume. In 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings. Institute of Electrical and Electronics Engineers. 2015. p. 1198-1203 doi: 10.1109/I2MTC.2015.7151443

Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume

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