SDPLL-Based Frequency Estimation of a Sinusoid in Colored Noise

Abstract

The problem of frequency estimation of a single sinusoid observed in colored noise is addressed. Our estimator is based on the operation of the sinusoidal digital phase-locked loop (SDPLL) which carries the frequency information in its phase error after the noisy sinusoid has been acquired by the SDPLL. We show by computer simulations that this frequency estimator beats the Cramer-Rao bound (CRB) on the frequency error variance for moderate and high SNRs when the colored noise has a general low-pass filtered (LPF) characteristic, thereby outperforming, in terms of frequency error variance, several existing techniques some of which are, in addition, computationally demanding. Moreover, the present approach generalizes on existing work that addresses different methods of sinusoid frequency estimation involving specific colored noise models such as the moving average (MA) noise model. An insightful theoretical analysis is presented to support the practical findings.

Keywords

• Sinusoidal digital phase-locked loop (SDPLL); Cramer-Rao bound (CRB); colored noise; frequency error variance; signal-to-noise ratio (SNR).