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

This paper presents a systematic synthesis procedure for H∞-optimal adaptive FIR filters in the context of an active noise cancellation (ANC) problem. An estimation interpretation of the adaptive control problem is introduced first. Based on this interpretation, an H∞ estimation problem is formulated, and its finite horizon prediction (filtering) solution is discussed. The solution minimizes the maximum energy gain from the disturbances to the predicted (filtered) estimation error and serves as the adaptation 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 that of the classical (normalized) filtered-X LMS algorithm. The error terms, however, are shown to be different. Thus, these classical algorithms can be considered to be approximations of our algorithm. We examine the performance of the proposed EBAF algorithm (both experimentally and in simulation) in an active noise cancellation problem of a one-dimensional (1-D) acoustic duct for both narrowband and broadband cases. Comparisons to the results from a conventional filtered-LMS (FxLMS) algorithm show faster convergence without compromising steady-state performance and/or robustness of the algorithm to feedback contamination of the reference signal