Noninvasive system identification for multichannel broadband active noise control

Many real-world applications of active noise control are characterized by transfer functions that vary significantly and unpredictably. The controller's transfer-function models must adapt to these variations. Presented here is a class of adaptive filters that accomplish quasiperiodic system identification updates for feedforward control by using blocks of input-output histories. The algorithms form a one-dimensional family linking normalized least-mean squares (LMS) adaptive filters and block recursive least-squares, termed "block projection" algorithms, and generalize the noninvasive system identification studied by Sommerfeldt and Tichy. The system identification proceeds noninvasively, producing nonparametric impulse responses. Simulations show that the algorithm's convergence is faster than that of normalized LMS, even after the additional overhead of computing the update is taken into account. Both the multichannel generalization and application of these algorithms to system identification are novel. Simulations of the algorithms' performance using measured data are presented here, while experimental results of an implemented algorithm are contained in the companion paper.