Estimation-based synthesis of H infinity-optimal adaptive FIR filters for filtered-LMS problems

This paper presents a systematic synthesis procedure for H-infinity-optimal adaptive FIR filters in the context of an active noise cancellation (ANC) problem. An estimation interpretation of the adaptive control problem is in troduced first, Based on this interpretation, an H-infinity estimation prob lem is formulated, and its finite horizon prediction (filtering) solution i s discussed. The solution minimizes the maximum energy gain from the distur bances to the predicted (filtered) estimation error and serves as the adapt ation criterion for the weight vector in the adaptive FIR filter. We refer to this adaptation scheme as estimation-based adaptive filtering (EBAF), We show that the steady-state gain vector in the EBAF algorithm approaches th at of the classical (normalized) filtered-X LMS algorithm. The error terms, however, are shown to be different. Thus, these classical algorithms can b e considered to be approximations of our algorithm. We examine the performance of the proposed EBAF algorithm (both experimenta lly and in simulation) in an active noise cancellation problem of a one-dim ensional (1-D) acoustic duct for both narrowband and broadband cases. Compa risons to the results from a conventional filtered-LMS (FxLMS) algorithm sh ow faster convergence without compromising steady-state performance and/or robustness of the algorithm to feedback contamination of the reference sign al.