Single-tone frequency estimation using modified autocorrelation and polynomial root-finding

Abstract

Based on a novel extension scheme to autocorrelation with higher lags, this paper devises an unbiased and nearly-optimal estimator for a single real sinusoid in white noise. Specifically, the new autocorrelation functions are utilized to construct a univariate polynomial equation parameterized by the frequency. By comparing all roots of the polynomial equation with the cosine of a coarse estimate, the root corresponding to the sinusoidal frequency can be determined. The frequency variance is derived, which is then employed to find the optimal lag of autocorrelation for attaining the minimum mean square frequency error. Computer simulations are provided to corroborate the theoretical development and contrast with several existing estimators as well as the Cramér–Rao lower bound. The code link of our proposed estimator is available at https://github.com/Amao-Liang/MAPR-Algorithm-for-Single-Tone-Frequency-Estimation.