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Single-tone frequency estimation based on reformed covariance for half-length autocorrelation

Sienkowski Sergiusz, Krajewski Mariusz

Metrology and Measurement Systems

2020

Vol. 27, nr 3

473--493

This paper presents a new simple and accurate frequency estimator of a sinusoidal signal based on the signal autocorrelation function (ACF). Such an estimator was termed as the reformed covariance for half-length autocorrelation (RC-HLA). The designed estimator was compared with frequency estimators well-known from the literature, such as the modified covariance for half-length autocorrelation (MC-HLA), reformed Pisarenko harmonic decomposition for half-length autocorrelation (RPHD-HLA), modified Pisarenko harmonic decomposition for half-length autocorrelation (MPHD-HLA), zero-crossing (ZC), and iterative interpolated DFT (IpDFT-IR) estimators. We determined the samples of the ACF of a sinusoidal signal disturbed by Gaussian noise (simulations studies) and the samples of the ACF of a sinusoidal voltage (experimental studies), calculated estimators based on the obtained samples, and computed the mean squared error (MSE) to compare the estimators. The errors were juxtaposed with the Cramér-Rao lower bound (CRLB). The research results have shown that the proposed estimator is one of the most accurate, especially for SNR>25dB. Then the RC-HLA estimator errors are comparable to the MPHD-HLA estimator errors. However, the biggest advantage of the developed estimator is the ability to quickly and accurately determine the frequency based on samples collected from no more than five signal periods. In this case, the RC-HLA estimator is the most accurate of the estimators tested.