A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).
Zhe LI
Southeast University
Yili XIA
Southeast University
Qian WANG
Southeast University
Wenjiang PEI
Southeast University
Jinguang HAO
Ludong University
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Zhe LI, Yili XIA, Qian WANG, Wenjiang PEI, Jinguang HAO, "A Novel Four-Point Model Based Unit-Norm Constrained Least Squares Method for Single-Tone Frequency Estimation" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 2, pp. 404-414, February 2019, doi: 10.1587/transfun.E102.A.404.
Abstract: A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.404/_p
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@ARTICLE{e102-a_2_404,
author={Zhe LI, Yili XIA, Qian WANG, Wenjiang PEI, Jinguang HAO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Novel Four-Point Model Based Unit-Norm Constrained Least Squares Method for Single-Tone Frequency Estimation},
year={2019},
volume={E102-A},
number={2},
pages={404-414},
abstract={A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).},
keywords={},
doi={10.1587/transfun.E102.A.404},
ISSN={1745-1337},
month={February},}
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TY - JOUR
TI - A Novel Four-Point Model Based Unit-Norm Constrained Least Squares Method for Single-Tone Frequency Estimation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 404
EP - 414
AU - Zhe LI
AU - Yili XIA
AU - Qian WANG
AU - Wenjiang PEI
AU - Jinguang HAO
PY - 2019
DO - 10.1587/transfun.E102.A.404
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2019
AB - A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).
ER -