Estimation-based synthesis of H∞-optimal adaptive FIR filtersfor 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

Estimation-based multi-channel adaptive algorithm for filtered-LMS problems

This paper presents an estimation-based adaptive filtering algorithm for the multi-channel Filtered-LMS problems where a number of adaptively controlled secondary sources use multiple reference signals to cancel the effect of a number of primary sources (i.e. disturbance sources) as seen by a number of error sensors. We show that our estimation based approach easily extends to the multi-channel case, and that it maintains all of the stability and performance features of the single-channel solution. The problem of noise cancellation in a one dimensional acoustic duct, and a structural vibration control problem are chosen to examine the main characteristics of the proposed multi-channel adaptive algorithm. The performance of the new multi-channel adaptive algorithm is compared to the performance of a multi-channel implementation of the FAMS algorithm in these cases, and it is shown that the new algorithm provides a faster response, with improved transient behavior and steady-state performance

An LMI formulation for the estimation-based approach to the design of adaptive filters

We present a linear matrix inequalities (LMI) formulation for the estimation-based approach to the design of adaptive FIR and IIR filters. LMI provide a convenient framework for the synthesis of multiobjective (H_2/H∞) control problems. Therefore, the H∞ disturbance attenuation criterion in the estimation-based adaptive algorithm can be easily augmented with the appropriate H2 performance constraints. The question of internal stability of the overall system is also directly addressed as a by-product of the Lyapunov-based nature of the LMI formulation. We use an active noise cancellation scenario to study the main features of the proposed LMI solution

Estimation-based synthesis of H_∞-optimal adaptive equalizers over wireless channels

This paper presents a systematic synthesis procedure for H_∞-optimal adaptive FIR equalizers over a time-varying wireless channel. The channel is assumed to be frequency selective with Rayleigh fading. The proposed equalizer structure consists of the series connection of an adaptive FIR filter and a fixed equalizer (designed for the nominal channel). Adaptation of the weight vector of the adaptive FIR filter is achieved using the H_∞-optimal solution of an estimation-based interpretation of the channel equalization problem. Due to its H_∞-optimality, the proposed solution is robust to exogenous disturbances, and enables fast adaptation (i.e., a short training period) without compromising the steady-state performance of the equalization. Preliminary simulation are presented to support the above claims

An Estimation-Based Approach to the Design of Adaptive IIR Filters 1

We present an estimation-based approach to the design of adaptive IIR filters. We also use this approach to design adaptive filters when a feedback signal from the output of the adaptive filter contaminates the reference signal. We use an H, criterion to cast the problem as a nonlinear H, filtering problem, and present an approximate linear H, filtering solution. This linear filtering solution is then used to ada.pt the adaptive IIR Filter. The presentation of the proposed adaptive algorithm is done in the context of an adaptive Active Noise Cancellation (ANC) problem. Simulations are used to examine the performance of the proposed estimation-based adaptive algorithm.

An H∞-Optimal Alternative to the FxLMS Algorithm

We study a general setting of active noise cancellation problems from the H∞ point of view and present a solution that optimally limits the worst case energy gain from the interfering measurement errors, external disturbances, and initial condition uncertainty to the residual noise. The optimal bounding of this energy gain is the main characteristic of the proposed solution. To impose a nite impulse response (FIR) structure on the controller, we suggest an adaptation scheme for the weight vector of an FIR filter that approximates the H∞-optimal solution. Our discussions in this paper explain; (i) why and how this new adaptive scheme generalizes previous results on the H∞-optimality of the LMS algorithm, (ii) why it is an alternative for the widely used Filtered-X Least-Mean-Squares (FxLMS) algorithm, and (iii) how the formulation provides an appropriate framework to address the issues of modeling error and robustness. Simulations are used to compare the performance of the proposed (approximate) H∞-optimal adaptivescheme with the FxLMS algorithm

Estimation-Based Synthesis of H∞-Optimal Adaptive FIR Filters for Filtered-LMS Problems

This paper presents a systematic synthesis procedure for-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 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