Cramer-Rao Lower Bound for Harmonic and Subharmonic Estimation

Recently, Zarowski and Kmpyvnytskyy developed a modified iterative cosinor algorithm (MICA) for the estimation of the parameters of sinusoidal signals with harmonics and subharmonics contaminated by AWGN, and derived the Cramer-Rao lower bound (CRLB) for the estimation of fundamental frequency component of such signals. However, their derivation was based on the assumption that the noise variance is known a priori. This paper presents a new derivation of CRLB bound for the case that the noise variance is unknown. The derivations also include the CRLB bounds for the estimation of harmonic and subharmonic amplitudes, noise variance as well as the SNR of the contaminated signal. Numerical simulation results are given to verify and interpret the derived CRLB bounds, together with the evaluation of estimation performance