Two-stage optimisation algorithm for adaptive IIR notch filter

The performances of the linear prediction (LP) algorithm and the indirect plain gradient (IPG) algorithm for the adaptive infinite-impulse-response (IIR) notch filter are theoretically studied, and the two phenomena in these two algorithms are revealed. First, the LP algorithm has a faster convergence speed than the IPG algorithm when the initial adjusted value is far away from the optimal solution. Secondly, the IPG algorithm has a much smaller estimation bias and mean squared error than the LP algorithm in a steady state. On the basis of these facts, a two-stage optimisation algorithm is proposed to make full use of the advantages of both the LP algorithm and the IPG algorithm. Simulation results show that the proposed algorithm can improve the convergence rate while keeping the same steady state as the IPG algorithm.