Adaptive HR filtering via a recursive total instrumental variable algorithm

Adaptive IIR filtering in the case where noise exists in both the input and output of the system amounts to solving over-determined normal equations. In this paper a recursive total instrumental-variable (RTIV) algorithm is proposed for tracking the total least-squares (TLS) solution of the normal equations in the over-determined instrumental-variable methods. It is shown that the weight vector in the RTIV algorithm converges to the direction parallel to the singular vector associated with the smallest singular value of the augmented cross-correlation matrix. Moreover, the estimated parameters of the adaptive IIR filter are optimal in the TLS sense and its noise rejection capability is superior to that of the least-squares based algorithms. The appealing behavior of the RTIV algorithm for noisy adaptive IIR filtering is substantiated by simulation results.