Unbiased estimation of a sinusoid in colored noise via adapted notch filters

Standard notch models for the estimation of a sinusoid in noise are characterized by two poles on the unit circle and two zeros aligned with the poles. These models provide biased estimates of the unknown frequency, the bias increasing with the zero-pole distance. On the other hand, keeping the zeros far from the poles has the beneficial effect of making the identification algorithm less sensitive to the adopted initialization. In this paper we remove the pole-zero alignment constraint. The extra degree of freedom thus obtained is used to alleviate the traditional trade-off between unbiasedness of the estimates and robustness against poor initializations. The proposed technique applies to the case of both white and colored additive noise. (C) 1997 Elsevier Science Ltd.