A closed-form expanded autocorrelation method for frequency estimation of a sinusoid

• Published in: Signal processing Vol. 92; no. 4; pp. 885 - 892
• Main Authors: Cao, Yan, Wei, Gang, Chen, Fang-Jiong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2012; Elsevier
• Subjects: Algorithms; Applied sciences; Autocorrelation; Autocorrelation lag; Cramer-Rao bounds; Detection, estimation, filtering, equalization, prediction; Estimates; Estimators; Exact sciences and technology; Exact solutions; Frequency estimation; Information, signal and communications theory; Least squares method; Mathematical analysis; Real single sinusoid; Signal and communications theory; Signal, noise; Taylor series expansion; Telecommunications and information theory; Taylor series expansion; Frequency estimation; Real single sinusoid; Autocorrelation lag; Performance evaluation; Cost minimization; Parameter estimation; Signal estimation; Taylor series; Timbre; Algorithm; Time domain method; Covariance; Simulation; Least squares method; Algorithm complexity; Series expansion; Signal processing; Cost function; Autocorrelation; Sinusoidal signal; Cramer Rao inequality
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2011.09.025

A closed-form expanded autocorrelation method for real single-tone frequency estimation is proposed. Firstly, the modified covariance (MC) method based on multiple autocorrelation lags is applied to provide a coarse frequency estimate. Then, a closed-form adjustment term based on a least square cost function is derived to get the fine frequency estimate. Simulation results show that the performance of the proposed algorithm, when compared with several existing closed-form time-domain estimators, is closer to the Cramer–Rao bound (CRB). Moreover, the proposed method has lower computation complexity than other autocorrelation-based approaches, which also use multiple autocorrelation lags. ► Our estimator is closer to CRB than several existing time-domain estimators. ► Our estimator is more computational efficient than two-stage autocorrelation method. ► Our estimator has a closed-form. ► A closed-form expression of the MSE of our estimator is derived.