A piloted adaptive notch filter

In the implementation of an adaptive notch filter using the least mean squares (LMS) algorithm, the zero of the filter is steered toward the input sinusoid based on the gradient information. The convergent may be speeded up if a larger step size is used when the zero of the notch filter is far away from the frequency of the input sinusoid. The gradient provides information on the direction where the zero should be steered but does not provide information on the distance between the zero and the frequency of the sinusoid. Conventional variable step-size algorithms determine the step size based on a (linear/nonlinear) weighted average of the gradient estimate at several sampling instances (time domain averaging). In this paper, we propose a new method for extracting information on the distance between the frequency of the input sinusoid and the zero of the notch. We use three (or more) notches, namely, a main notch and two (or more) pilot notches implemented with minimal additional cost. The pilot notches are used to analyze the gradient estimates at the same sampling instance but at several frequency points as the main notch. Simulation results show that our new piloted notch technique is significantly superior to step-size determination based on a time-averaging technique. Novel theoretical analysis is presented. Our method can be used in conjunction with most existing algorithms to determine the step size.