Tracking Analysis and Improvement of Broadband Kalman Filter Using the Two-Echo-Path Model as a Rapid Tunnel

A time-domain Kalman filter, namely the broadband Kalman filter, was proposed for acoustic system identification to bridge between the exact Kalman filter and normalized least-mean-square algorithm. The broadband Kalman filter was found to exhibit both fast convergence and robustness to noise disturbance. However, its tracking capability is degraded especially when the observation noise variance is approximated by the error variance. We present the theoretical analysis of the tracking capability of the broadband Kalman filter by resorting to its steady-state predicted system distance and corresponding step size. In addition, a two-echo-path approach is employed to improve the tracking. Simulation results agree with the theoretical prediction and demonstrated that the algorithm's reconvergence ability is significantly improved with the two-echo-path model using speech as input.