A family of real single-tone frequency estimators using higher-order sample covariance lags

In this paper, the problem of frequency estimation of a single sinusoid immersed in white noise is addressed. Inspired by the Pisarenko Harmonic Decomposer (PHD) estimator, which makes use of the sample covariance of the observations with lags 1 and 2, we propose a family of estimators using higher lags p and 2p of the sample covariance. The proposed estimator outperforms the PHD, except for frequencies close to the edges kπ/p. As a means to sidestep this problem, two different estimators with different lags can be appropriately combined. A statistical analysis of the proposed method in terms of the Mean Square Error of the frequency estimate is presented. Computer simulations are included to validate the theoretical analysis of the novel estimator and to compare its performance to that of PHD and to the Cramer-Rao Lower Bound.