Synchronous phase estimation of a signal corrupted by a close sinusoid

The authors consider the problem of initial phase estimation of a signal s(1), given frequency, ω_s, in the presence of additive noise, w(1), and closely spaced sinusoidal interferences, r(1), whose parameters are unknown a priori. The proposed estimator makes use of a special nonlinear preprocessing based on the LMS minimization of distances between instantaneous values of LP-coefficients which are extracted from the augmented moving-average model of an r(1) interference. The preprocessed incoming signal is then synchronously detected to reveal an initial phase. The estimator is then compared to the four-steps adaptive estimator, showing the potentials of the proposed approach for small values of proximity coefficient D=Δf×N, well beyond the resolution of the discrete Fourier transform (DFT), given by 1/N