Simplified Gradient Adaptive Harmonic IIR Notch Filter for Frequency Estimation and Tracking

This paper proposes a new adaptive harmonic IIR notch filter utilizing the simplified gradient update to achieve robust frequency estimation and tracking. The developed algorithm has ability to prevent the adaptive algorithm from converging to its local minima of the MSE function due to signal fundamental frequency switches in the tracking process. In addition, a formula to determine the stability bound for applying the least mean squares (LMS) algorithm is derived. Computer simulations validate the developed algorithm. A simple scheme (10) is first devised to monitor the global minimum of the MSE function; and it will reset the adaptive parameter using its new estimation whenever a possible local minimum is detected. In this paper, a new simplified gradient algorithm based on the direct form II structure (11) is proposed for the adaptive harmonic IIR filter. The proposed algorithm has less computation requirement. The stability bound for convergence in mean is derived. The computer simulations validate the developed algorithm.