Conventional Filtered-x Least Mean Square Research Articles

An extrapolation-based virtual sensing technique of improving the control performance of the FxLMS algorithm in a maritime environment

Several local active noise control (ANC) approaches based on Filtered-x Least Mean Square (FxLMS) algorithm have been designed to mitigate low frequency noise annoyance from undesirable acoustic sources, for which conventional passive techniques are ineffective. A fundamental limitation of local ANC is the small size of quiet zone that is extended around the error microphone. This means that the physical sensor should be mounted at the desired location of noise attenuation, which in most cases is practically inconvenient. In order to extend the zone of quiet close to the ears of a seated passenger who moves gently his head, a number of complicated and computationally heavy virtual sensing algorithms have been developed for ANC. The spatial performance of such a local active sound controller depends not only on the correlation properties of the primary sound field and the adaptation algorithm but also on the microphones spatial arrangement, the size and the number of the control sources. Thus, the objective of this work is to develop a simple, robust and computationally-efficient virtual sensing ANC algorithm of improving the performance of the conventional FxLMS. The main approach to do so is by using a feedforward ANC controller based on the combined solution of first-order pressure prediction technique and a mixed-error design integrating the FXLMS algorithm for enhancing the noise attenuation levels and shaping an extended silence zone. Aim of this work is also to estimate a simplified approach of the virtual secondary path in order to be more challenging in practical and commercial applications, while the ANC system can achieve adequate control performance.In an effort to test the extension degree of the silence zone generated at a fixed virtual location, low computational demand ANC headrest configurations, are investigated. The proposed schemes have been tested through a simulation model, a test rig and an experimental ANC system installed in a cabin mock-up. The computer-modeled and the experimental results demonstrate that the proposed local virtual sensing ANC algorithm maintains stability in all operating points, and works reliably and more effectively than the widely used conventional FxLMS algorithm.

Multi-frequency micro-vibration control with hybrid adaptive control algorithm

As a popular adaptive algorithm for active vibration control (AVC), filtered-x least mean square (FxLMS) algorithm sometimes fails to suppress multiple narrowband disturbance. To control multi-frequency structure vibration, parallel-form FxLMS algorithm can be employed. However, the conventional parallel-form FxLMS does not perform well in the situation of disturbance frequency mismatch and wideband measurement noise. For this issue, the majority of the improvement approaches are based on adaptive frequency estimator. It increased the computational burden of the parallel-form FxLMS algorithm. Therefore, taking the advantage of feedback control, a hybrid adaptive control for AVC is proposed in this paper. And the “posterior” residual error is adopted for better robustness. The convergence analysis of the hybrid AVC algorithm is given. Co-simulations with ADAMS and SIMULINK are implemented to verify the effectiveness in micro-vibration control system. Some comparison experiments are implemented in a micro-vibration AVC experimental system for several typical disturbances. Experimental results confirm the feasibility and effectiveness of the proposed algorithm.

A generalized maximum correntropy criterion based robust sparse adaptive room equalization

An adaptive room equalization scheme is usually employed to compensate for the distortion of sound produced by the room impulse response, thereby offering an improved listening experience. In a conventional adaptive room equalizer, an adaptive filter updated using a filtered-x least mean square (FxLMS) algorithm is used to achieve room equalization. Conventional FxLMS algorithm based room equalizers are not robust to strong disturbances picked up by the reference microphone. A robust adaptive room equalization scheme based on a generalized maximum correntropy criteria has been developed in this paper. The performance has been further enhanced by using a proportionate learning strategy to take advantage of the sparse nature of the room impulse response. The proposed algorithm has been shown to provide enhanced room equalization performance over other methods compared, for various types of noise distributions.

Improved adaptive recursive even mirror Fourier nonlinear filter for nonlinear active noise control

In this paper, we analyze the theoretical mechanism for the effectiveness of recursive filters including both linear and nonlinear feedforward and feedback subsections to accurately approximate nonlinear distributions in the active noise control (ANC) system. As a result, we improve the recursive even mirror Fourier nonlinear (REMFN) filter by adding an additional linear section termed REMFNL filter together with its channel reduced form (CRREMFNL) to explore better control performance. As for the linear feedback section introduced, we have studied the bound-input bound-output (BIBO) stability condition for the REMFNL filter and designed a stable control scheme to guarantee the filter satisfying the stability criteria. The performance of the proposed filters equipped with a filtered-x least mean square (FXLMS) algorithm is validated through analyses of computational complexity and simulations of various nonlinearities for nonlinear ANC (NANC) systems. Simulation results demonstrate that the proposed REMFNL and CRREMFNL filters can achieve better performance over the bilinear, recursive second-order Volterra (RSOV), recursive functional link artificial neural network (RFLANN) and standard REMFN filters based on the FXLMS algorithm, which often outperform the conventional Volterra FXLMS (VFXLMS) and filtered-s least mean square (FSLMS) algorithms.

Channel self-adjusting filtered-x LMS algorithm for active control of vehicle road noise

Current active road noise control (ARNC) systems, configured with the standard filtered-x least mean square (FxLMS) algorithm, are not sufficient enough to yield an ideal noise reduction over a broad frequency range. This is because ARNC systems generally employ multiple reference signals, which has an inherent limitation of the channel-dependent convergence behaviour due to dynamic characteristics amongst reference signals. In this study, an effective ARNC system with the channel self-adjusting FxLMS (CSFxLMS) algorithm by incorporating the self-adjusting parameter on each reference signal path is proposed, which is to minimise the effect of its dynamics characteristics in different reference channels. To validate the effectiveness of the proposed algorithm, numerical simulations using measured road noise response is conducted. Results show that the performance of the proposed CSFxLMS algorithm is significantly better as compared to the conventional FxLMS algorithm, and is able to achieve around 5 dBA reductions at the driver's ear position.

Multiple Iteration of Weight Updates for Least Mean Square Adaptive Filter in Active Noise Control Application

The method of least mean square (LMS) is the commonly used algorithm in Adaptive filter due to its simplicity and robustness in implementation. In Active Noise Control application, a filtered reference signal is used prior to LMS algorithm to overcome the constraint on stability and convergence performance of the system due to the existence of the auxiliary path. This is known as Filtered-X LMS algorithm. In conventional Filtered-X LMS algorithm, each filter weight is updated once on every audio sample. This paper proposes the improved version of Filtered-X LMS algorithm with the use of multiple iteration of filter weight on every sample of audio signal. The proposed work uses field programmable gate arrays to realize real-time simulation on hardware for the noise signal of 500 Hz. Results from the real-time hardware simulations have shown much faster error convergence and better adaptation performance for different selections of learning constant μ, as compared with the conventional method.

A unified framework for adaptive inverse power control

In this paper, a unified framework for adaptive inverse power control is developed. It is based on a modified filtered-x least mean square (MFxLMS) algorithm that is proposed and analyzed. A practical version of the algorithm for closed loop power control is also developed. The filtered-x least mean square (FxLMS) algorithm is widely used for inverse control such as noise cancelation. This is the first paper to apply the algorithm for power control. We have modified the conventional FxLMS algorithm by adding absolute value blocks since power control does not need phase information. The modification makes the algorithm more robust and requires fewer bits to be transmitted in the feedback link. The main contribution of the paper is that the proposed algorithm can be seen as generalized inverse control to be used in power control research. It gives a unified framework for several existing algorithms, linking them to the least mean square (LMS) literature. Numerical results are provided, comparing the performance of the proposed algorithm to existing practical algorithms used, e.g., in Third Generation Partnership Project (3GPP) long-term evolution (LTE) systems.

Variable Step Size for Improving Convergence of FxLMS Algorithm

Several approaches have been introduced for active noise control (ANC) systems. The most popular adaptation algorithm used for Active Noise Control(ANC) applications is the Filtered-x Least Mean Square (FxLMS) algorithm. In this paper, FxLMS algorithm with variable step size to improve the convergence of ANC system has been proposed. This algorithm is mostly preferred, because it used as controller in adaptation filter to update the filter coefficients. This new algorithm is based onarc-tangent function and it will improve the convergence as well as a reduction in noise compared with conventional FxLMS. The convergence and noise reduction rate are analyzed with the help of MATLAB. Simulation results show that the convergence speed and noise reduction of the variable step algorithm are superior to conventional FxLMS algorithm.

Computationally efficient algorithm for high sampling-frequency operation of active noise control

In high sampling-frequency operation of active noise control (ANC) system the length of the secondary path estimate and the ANC filter are very long. This increases the computational complexity of the conventional filtered-x least mean square (FXLMS) algorithm. To reduce the computational complexity of long order ANC system using FXLMS algorithm, frequency domain block ANC algorithms have been proposed in past. These full block frequency domain ANC algorithms are associated with some disadvantages such as large block delay, quantization error due to computation of large size transforms and implementation difficulties in existing low-end DSP hardware. To overcome these shortcomings, the partitioned block ANC algorithm is newly proposed where the long length filters in ANC are divided into a number of equal partitions and suitably assembled to perform the FXLMS algorithm in the frequency domain. The complexity of this proposed frequency domain partitioned block FXLMS (FPBFXLMS) algorithm is quite reduced compared to the conventional FXLMS algorithm. It is further reduced by merging one fast Fourier transform (FFT)-inverse fast Fourier transform (IFFT) combination to derive the reduced structure FPBFXLMS (RFPBFXLMS) algorithm. Computational complexity analysis for different orders of filter and partition size are presented. Systematic computer simulations are carried out for both the proposed partitioned block ANC algorithms to show its accuracy compared to the time domain FXLMS algorithm.

A Computationally Efficient Multichannel Active Road Noise Control System

A multichannel active noise control (ANC) system has been developed for a vehicle application, which employs loudspeakers to reduce the low-frequency road noise. Six accelerometers were attached to the vehicle structure to provide the reference signal for the feedforward control strategy, and two loudspeakers and two microphones were applied to attenuate acoustic noise near the headrest of the driver's seat. To avoid large computational burden caused by the conventional time-domain filtered-x least mean square (FXLMS) algorithm, a time-frequency domain FXLMS (TF-FXLMS) algorithm is proposed. The proposed algorithm calculates the gradient estimate and filtered reference signal in the frequency domain to reduce the computational requirement, while also updates the control signals in the time domain to avoid delay. A comprehensive computational complexity analysis is conducted to demonstrate that the proposed algorithm requires significantly lower computational cost as compared to the conventional FXLMS algorithm.

Combined Feedforward–Feedback Active Control of Road Noise Inside a Vehicle Cabin

Conventional active control of road noise inside a vehicle cabin generally uses a pure feedforward control system with the conventional filtered-x least mean square (FXLMS) algorithm. While it can yield satisfactory noise reduction when the reference signal is well correlated with the targeted noise, in practice, it is not always possible to obtain a reference signal that is highly coherent with a broadband response typically seen in road noise. To address this problem, an active noise control (ANC) system with a combined feedforward–feedback controller is proposed to improve the performance of attenuating road noise. To take full advantage of the feedforward control, a subband (SFXLMS) algorithm, which can achieve more noise attenuation over a broad frequency range, is used to replace the conventional FXLMS algorithm. Meanwhile, a feedback controller, based on internal model control (IMC) architecture, is introduced to reduce the road noise components that have strong response but are poorly correlated with the reference signals. The proposed combined feedforward–feedback ANC system has been demonstrated by a simulation model with six reference accelerometers, two control loudspeakers and one error microphone, using actual data measured from a test vehicle. Results show that the performance of the proposed combined controller is significantly better than using either a feedforward controller only or a feedback controller only, and is able to achieve about 4 dBA of overall sound pressure level reduction.

A filtered-x weighted accumulated LMS algorithm: Stochastic analysis and simulations for narrowband active noise control system

In narrowband active noise control (NANC) systems, several modifications of the well-known filtered-x least-mean-square (FXLMS) algorithm have been proposed for improved operation. The filtered-x weighted accumulated LMS (FXWALMS) algorithm is a variant of the FXLMS algorithm obtained by introducing the momentum LMS (MLMS) algorithm into the conventional FXLMS algorithm. The version with momentum term of the adaptive algorithm is used in practical implementations aiming to increase convergence with moderate computational cost. In order to better understand the influence of the FXWALMS algorithm on the NANC system, statistical performance of such an algorithm is investigated in both the transient and steady-state behaviors. Different equations which describe the convergence behaviors of the mean and mean squared estimation errors for the discrete Fourier coefficients (DFCs) of the secondary source are derived and discussed in detail. Using related difference equations, the steady-state expressions for DFCs estimation mean square error and the residual noise mean square error are developed in closed forms. Moreover, a modified FXWALMS (MFXWALMS) algorithm is proposed to improve the overall performance of the system. Extensive simulations are conducted to prove the effectiveness of analytical results and the superior performance of the MFXWALMS algorithm in various scenarios.

A nonlinear active noise control algorithm for virtual microphones controlling chaotic noise

In active noise control (ANC) systems, virtual microphones provide a means of projecting the zone of quiet away from the physical microphone to a remote location. To date, linear ANC algorithms, such as the filtered-x least mean square (FXLMS) algorithm, have been used with virtual sensing techniques. In this paper, a nonlinear ANC algorithm is developed for a virtual microphone by integrating the remote microphone technique with the filtered-s least mean square (FSLMS) algorithm. The proposed algorithm is evaluated experimentally in the cancellation of chaotic noise in a one-dimensional duct. The secondary paths evaluated experimentally exhibit non-minimum phase response and hence poor performance is obtained with the conventional FXLMS algorithm compared to the proposed FSLMS based algorithm. This is because the latter is capable of predicting the chaotic signal found in many physical processes responsible for noise. In addition, the proposed algorithm is shown to outperform the FXLMS based remote microphone technique under the causality constraint (when the propagation delay of the secondary path is greater than the primary path). A number of experimental results are presented in this paper to compare the performance of the FSLMS algorithm based virtual ANC algorithm with the FXLMS based virtual ANC algorithm.

Particle Swarm Optimization Based Active Noise Control Algorithm Without Secondary Path Identification

In this paper, particle swarm optimization (PSO) algorithm, which is a nongradient but simple evolutionary computing-type algorithm, is proposed for developing an efficient active noise control (ANC) system. The ANC is conventionally used to control low-frequency acoustic noise by employing a gradient-optimization-based filtered-X least mean square (FXLMS) algorithm. Hence, there is a possibility that the performance of the ANC may be trapped by local minima problem. In addition, the conventional FXLMS algorithm needs prior identification of the secondary path. The proposed PSO-based ANC algorithm does not require the estimation of secondary path transfer function unlike FXLMS algorithm and, hence, is immune to time-varying nature of the secondary path. In this investigation, a small modification is incorporated in the conventional PSO algorithm to develop a conditional reinitialized PSO algorithm to suit to the time-varying plants of the ANC system. Systematic computer simulation studies are carried out to evaluate the performance of the new PSO-based ANC algorithm.

Two-Degree-of-Freedom Active Noise Control Design Based on System Identification Result using Subspace Method.

We have proposed the two-degree-of-freedom active noise control (2DOF-ANC) system, especially for active control of road noise inside automobiles. In this 2DOF-ANC system, the feedforward part is a conventional filtered-x LMS (least mean square) adaptive control and the feedback part is based on an Internal Model Control (IMC). The purpose of this paper is to apply the subspace method to the identification of an IIR (infinite impulse response) model for an acoustic field in the proposed 2DOF-ANC system. The IIR model is used to synthesize the feedback controller based on IMC and to reduce the number of arithmetic operations in feedforward control. The subspace method allows us to quantitatively determine the number of parameters in the IIR model. The effectiveness of the subspace method in the proposed 2DOF-ANC system is demonstrated through computer simulations using actual vehicle data measured in the experiment which simulates road noise in the cabin.