Tracking analysis of a constrained adaptive notch filter

The asymptotic tracking properties of an adaptive notch filter with pole-zeros constraints for the cancellation or retrieval of multiple time-varying sine waves in additive noise are analyzed. The methods of Ljung and Gunnarsson (see Automatica, vol.26, no.1, p.7-21, Jan. 1990) are used in order to analyze the asymptotic mean-square parameter error, when the variations in the underlying frequencies and the gain of the algorithm are assumed to be sufficiently small. A closed-form expression for the mean square error (MSE) is derived as a function of the tuning variables of the algorithm. The results give insight into the operational properties of the algorithm and are used in order to minimize the MSE with respect to the tuning variables