Development and convergence analysis of new least‐mean‐square‐based algorithm equipped with exponential‐decay step size and disturbance compensation for active noise control

In real‐world active noise control (ANC) applications, disturbance can be picked up by error sensors and significantly degrade the steady‐state ANC performance. This study proposes two techniques in combination with a least‐mean‐square (LMS) based ANC algorithm, named normalized filtered‐x LMS/commutation error (NFxLMS/CE) algorithm, to deal with the disturbance that is independent of a reference signal. A new stochastic method to analyze convergence properties of the NFxLMS/CE algorithm under influence of the disturbance is first established. Given that the reference signal is persistently exciting of sufficient order, exponential convergence of the algorithm is derived with a step‐size condition. An exponential‐decay step size (EDSS) is then proposed to obtain a new ANC algorithm referred to as EDSS‐NFxLMS/CE algorithm. In addition, a disturbance‐compensation (DC) technique is developed for the EDSS‐NFxLMS/CE algorithm to obtain an EDSS‐NFxLMS/CE_DC algorithm such that the influence of the disturbance can be reduced. It is shown that the EDSS‐NFxLMS/CE_DC algorithm is exponentially convergent. Moreover, computer simulations show that the EDSS‐NFxLMS/CE_DC algorithm can achieve a better ANC performance in terms of convergence rate and level of noise reduction as compared with that using the EDSS‐NFxLMS/CE algorithm without DC and that using NFxLMS/CE_DC algorithm of constant step sizes. These results support the effectiveness of the proposed techniques and EDSS‐NFxLMS/CE_DC algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

基于自适应陷波器的科氏流量计信号频率跟踪新方法

为提高对科氏流量计信号频率随机缓慢变化的持续跟踪能力,以对格型ANF、简化格型ANF和基于SMM的新式ANF三种典型自适应陷波器的性能比较分析为基础,提出了一种科氏流量计信号频率跟踪新方法。该方法对频率、幅值和相位均随机游动变化的科氏流量计信号,首先采用新式ANF快速检测信号频率并作短时频率跟踪,待其收敛后简化格型ANF开始并行工作,在简化格型ANF收敛后取代新式ANF持续跟踪信号频率的变化。仿真结果表明,本文方法比格型ANF方法收敛速度更快、频率跟踪精度更高,比单一采用新式ANF方法计算更为简便,是一种科氏流量计信号处理的有效方法。     

On the design of adaptive notch filters

In instrumentation and other applications, the on‐line estimation of the frequency and amplitude of a noise‐corrupted sinewave is of great practical interest. Recently an adaptive notch filter (ANF) with global convergence properties has been developed, and is a candidate approach to our problem. This paper analyses the transient and noise properties of this ANF and equips the method with design equations. Using frequency ranges greater than (up to 2 decades) and signal/noise ratios less than (down to ?16 dB) those commonly found in the ANF literature, it is verified by extensive simulations that the new frequency estimator has excellent tracking and noise‐rejection properties, provided that the signal/noise ratio is not too small. A comparison is made of its behaviour with that of a phase‐locked loop, a method commonly used in practice. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive filtering‐based multi‐innovation gradient algorithm for input nonlinear systems with autoregressive noise

In this paper, by means of the adaptive filtering technique and the multi‐innovation identification theory, an adaptive filtering‐based multi‐innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi‐innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering‐based multi‐innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm.     

Set‐theoretic adaptive filtering based on data‐driven sparsification

In this article, we propose a fast and efficient algorithm named the adaptive parallel Krylov‐metric projection algorithm. The proposed algorithm is derived from the variable‐metric adaptive projected subgradient method, which has recently been presented as a unified analytic tool for various adaptive filtering algorithms. The proposed algorithm features parallel projection—in a variable‐metric sense—onto multiple closed convex sets containing the optimal filter with high probability. The metric is designed based on (i) sparsification by means of a certain data‐dependent Krylov subspace and (ii) maximal use of the obtained sparse structure for fast convergence. The numerical examples show the advantages of the proposed algorithm over the existing ones in stationary/nonstationary environments. Copyright © 2011 John Wiley & Sons, Ltd.     

Filtered weight FxLMS adaptation algorithm: Analysis,design and implementation

In the Filtered‐x Least‐Mean‐Square (FxLMS)‐based Active Noise Control (ANC), the convergence speed of the adaptation process has a direct relationship to a scalar parameter, called the step size. There is a theoretical upper‐bound for the step size beyond which the system becomes unstable. However, the step size is usually set to a number smaller than its upper‐bound in practice. This is because for relatively large step sizes, the adaptation process becomes very sensitive to any non‐stationary change in acoustic noise. Owing to this trade‐off, real‐time implementation of high‐performance ANC systems becomes challenging. To overcome this problem, this paper develops a novel ANC algorithm in which a recursive filter compensates for influences of the step size increase on the system performance. It is shown that this filter can efficiently increase the step size upper‐bound; consequently, the performance of the system is improved. This improvement is demonstrated using computer simulation. Also, experimental results shows the preference of the proposed algorithm to the traditional FxLMS‐based ANC algorithm in practice. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive notch filters are local adaptive observers

Several continuous‐time frequency estimators for a measured sinusoidal signal, which have been proposed in the literature, are reviewed, reinterpreted and compared both theoretically and by simulations. It is argued that adaptive notch filters are feedback algorithms that contain a local adaptive observer in the feedback loop. It is shown that the adaptive notch filter (ANF), which was originally conceived as a discrete‐time ANF, is basically equivalent to the recently proposed adapted frequency locked loop called orthogonal signal generator. They both require a sufficiently slow frequency estimation and can be interpreted as third‐order adaptive observers. They exhibit local convergence properties for the estimation errors, that is, the convergence to zero is guaranteed provided that their initial error is sufficiently small. Three adaptive observers, which were independently proposed in 2002, are third‐order frequency estimators whose estimation errors are exponentially convergent to zero from any initial condition and for any value of frequency, amplitude and phase in the measured sinusoidal signal. They have the additional advantage of not requiring the frequency estimation dynamics to be sufficiently slow. Conversely, they may be interpreted as adaptive notch filters. Second‐order frequency estimators have been proposed as well: they may be interpreted as adaptive reduced‐order observers. Copyright © 2015 John Wiley & Sons, Ltd.     

Selective partial update and set‐membership improved proportionate normalized subband adaptive filter algorithms

In this article, the concept of proportionate adaptation is extended to the selective partial update (SPU) and set‐membership (SM) normalized subband adaptive filters (NSAFs), and three proportionate normalized subband adaptive filter algorithms are established. The proposed algorithms are the improved proportionate NSAF (IPNSAF), the SPU improved proportionate NSAF (SPU‐IPNSAF), and the SM‐IPNSAF which are suitable for sparse system identification. When the impulse response of the echo path is sparse, the IPNSAF algorithm has faster convergence than NSAF. The performance of IPNSAF is also suitable for dispersive impulse responses. In SPU‐IPNSAF, the filter coefficients are partially updated rather than the entire filter at every adaptation which reduces the computational complexity of IPNSAF. The SM‐IPNSAF exhibits good performance with significant reduction in the overall computational complexity compared with the ordinary IPNSAF. The simulation results show good performance of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd.     

FPGA‐based embedded platform for fiber optic gyroscope signal denoising

This paper presents System on Chip (SoC) implementation of a proposed denoising algorithm for fiber optic gyroscope (FOG) signal. The SoC is developed using an Auxillary Processing Unit of the proposed algorithm and implemented in the Xilinx Virtex‐5‐FXT‐1136 field programmable gate array. SoC implementation of this application is first of its kind. The proposed algorithm namely adaptive moving average‐based dual‐mode Kalman filter (AMADMKF) is a hybrid of adaptive moving average and Kalman filter (KF) technique. The performance of the proposed AMADMKF algorithm is compared with the discrete wavelet transform and KF of different gains. Allan variance analysis, standard deviation and signal to noise ratio (SNR) are used to measure the efficiency of the algorithm. The experimental result shows that AMADMKF algorithm reduces the standard deviation or drift of the signal by an order of 100 and improves the SNR approximately by 80 dB. The Allan variance analysis result shows that this algorithm also reduces different types of random errors of the signal significantly. The proposed algorithm is found to be the best suited algorithm for denoising the FOG signal in both the static and dynamic environments. Copyright © 2013 John Wiley & Sons, Ltd.     

基于变步长LMS自适应陷波算法的电气信号频率测量

提出一种基于二阶无限冲击响应(IIR)变步长自适应数字陷波滤波器的电气信号频率跟踪测量算法。论述了陷波滤波器能够滤除信号中特定的频率,而其他的频率成分不受影响的原理;最小均方LMS(LeastMeanSquare)自适应陷波算法是将被谐波和随机噪声污染的电气信号通过基波陷波器,根据陷波器输出误差采用变步长因子的递推LMS自适应修正陷波器参数和跟踪频率的变化。实例中,给出了给定变步长迭代公式的常数以计算出频率,并采用频率稳定时的测量、频率波动时的测量、电机运行频率测量的3种仿真结果表明所提出的频率跟踪测量算法效果良好。     

一种改进的去除灰度图像椒盐噪声方法的研究

针对传统中值滤波算法（SM）在滤除高密度椒盐噪声时存在滤除不完全和使边缘细节变得模糊的不足,提出了一种改进自适应中值滤波法,该方法在计算像素点4邻域均值与检测点的灰度差值后,将此差值同一个自适应调整的阈值进行比较,若差值大于阈值则为噪声,否则为信号点。实验表明,该方法比传统方法去噪效果较好,对噪声密度在30％以上的图像,去噪后可使图像峰值信噪比（PSNR）达到20dB以上,均方误差（MSE）在100以内。     

Self‐tuning weighted fusion Kalman filter for ARMA signal with colored measurement noise and its convergence analysis

For the multisensor single‐channel autoregressive moving average (ARMA) signal with colored measurement noise, when the partial model parameters and the noise variance are unknown, a self‐tuning fusion Kalman filter weighted by scalar is presented based on the ARMA innovation model by the modern time series analysis method. With the application of the recursive instrumental variable algorithm and the Gevers–Wouters iterative algorithm with dead band, the information fusion estimators for the unknown model parameters and noise variance are obtained, and their consistence is proved by the existence and continuity theorem of implicit function. Then, substituting them into the optimal weighted fusion Kalman filter, one can obtain the corresponding self‐tuning weighted fusion Kalman filter. Further, with the application of the dynamic variance error system analysis method, the convergence of the self‐tuning Lyapunov equations for filtering error cross‐covariances is proved. With the application of the dynamic error system analysis method, it is rigorously proved that the self‐tuning weighted fusion Kalman filter converges to the optimal weighted fusion Kalman filter in a realization; that is, it has asymptotic optimality. A simulation example shows its effectiveness.Copyright © 2012 John Wiley & Sons, Ltd.     

A 0.6‐V sub‐mW X‐band RFSOI CMOS LNA with novel complementary current‐reused technique

A fully integrated 0.6 V low‐noise amplifier (LNA) for X‐band receiver application based on 0.18 μm RFSOI CMOS technology is presented in this paper. To achieve low noise and high gain with the constraint of low voltage and low power consumption, a novel modified complementary current‐reused LNA using forward body bias technique is proposed. A diode connected MOSFET forward bias technique is employed to minimize the body leakage and improve the noise performance. A notch filter isolator is constructed to improve the linearity of low voltage. The measured results show that the proposed LNA achieves a power gain of 11.2 dB and a noise figure of 3.8 dB, while consuming a DC current of only 1.6 mA at supply voltage of 0.6 V. Copyright © 2017 John Wiley & Sons, Ltd.     

Zero‐attracting variable‐step‐size least mean square algorithms for adaptive sparse channel estimation

Recently, sparsity‐aware least mean square (LMS) algorithms have been proposed to improve the performance of the standard LMS algorithm for various sparse signals, such as the well‐known zero‐attracting LMS (ZA‐LMS) algorithm and its reweighted ZA‐LMS (RZA‐LMS) algorithm. To utilize the sparsity of the channels in wireless communication and one of the inherent advantages of the RZA‐LMS algorithm, we propose an adaptive reweighted zero‐attracting sigmoid functioned variable‐step‐size LMS (ARZA‐SVSS‐LMS) algorithm by the use of variable‐step‐size techniques and parameter adjustment method. As a result, the proposed ARZA‐SVSS‐LMS algorithm can achieve faster convergence speed and better steady‐state performance, which are verified in a sparse channel and compared with those of other popular LMS algorithms. The simulation results show that the proposed ARZA‐SVSS‐LMS algorithm outperforms the standard LMS algorithm and the previously proposed sparsity‐aware algorithms for dealing with sparse signals. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance characterization of a non‐linear system as both an adaptive notch filter and a phase‐locked loop

The behaviour of a non‐linear dynamical system is described. The system may be characterized as an adaptive notch filter, or alternatively, as a phase‐locked loop. Either way, the system has the inherent capability of directly providing estimates of the parameters of the extracted sinusoidal component of its input signal, namely its amplitude, phase and frequency. The structure and mathematical properties of the system are presented for two cases of fixed‐frequency and varying‐frequency operation. The effects of parameter setting of the system on its performance are studied in detail using computer simulations. Transient and steady‐state behaviour of the system are studied in the presence of noise. Simplicity of structure, high noise immunity and robustness and the capability of direct estimation of amplitude, phase and frequency are the salient features of the system when envisaged as an adaptive notch filter or a phase‐locked loop. Copyright © 2004 John Wiley & Sons, Ltd.     

基于时间尺度变换策略的幅频测量用自适应陷波器算法

现有电力信号幅频测量算法在动态条件下的测量精度和响应时间方面还有待改善,为此提出了基于时间尺度变换的自适应陷波器(adaptive notch filter,ANF)算法进行幅频测量。该算法对时间进行尺度变换,得到新时间尺度下的ANF动态方程,能够消除频率参数和滤波器之间的非线性耦合,将状态估计方程等价为线性时不变系统,并进行离散化处理。该算法能够有效消除谐波和噪声干扰,快速准确地测量动态变化的幅值和频率。算例结果验证了该方法的有效性,可满足在线测量的要求。     

Design and performance analysis of LMS algorithm based adaptive filter embedded with CFAR detector under non‐homogeneous clutter scenarios

The paper presents performance analysis of least‐mean‐square algorithm based adaptive filter embedded with constant false alarm rate (CFAR) detector for the purpose of better detection of target under non‐homogeneous clutter environment in radar application. The objective of this paper is to develop a method by redesigning the radar detector in such a way to emphasize the target response and de‐emphasize the clutter response. The hardware implementation using pipeline technique for the adaptive filter reveals its capability to support high sampling frequency, which is an ardent necessity for high performance radar. The moderate area‐delay‐product and low power consumption have made it suitable for hardware realization for such application. The extensive MATLAB simulation of proposed design shows remarkable improvement of detection performance in terms of signal‐to‐noise ratio of 17 dB considering probability of detection at 0.8 over the generic cell averaging CFAR (CA‐CFAR). Copyright © 2015 John Wiley & Sons, Ltd.     

A new two‐microphone Gauss‐Seidel pseudo affine projection algorithm for speech quality enhancement

This study addresses the problem of speech quality enhancement by adaptive and nonadaptive filtering algorithms. The well‐known two‐microphone forward blind source separation (TM‐FBSS) structure has been largely studied in the literature. Several two‐microphone algorithms combined with TM‐FBSS have been recently proposed. In this study, we propose 2 contributions: In the first, a new two‐microphone Gauss‐Seidel pseudo affine projection (TM‐GSPAP) algorithm is combined with TM‐FBSS. In the second, we propose to use the new TM‐GSPAP algorithm in speech enhancement. Furthermore, we show the efficiency of the proposed TM‐GSPAP algorithm in speech enhancement when highly noisy observations are available. To validate the good performances of our algorithm, we have evaluated the adaptive filtering properties in computational complexity and convergence speed performance by system mismatch criteria. A fair comparison with adaptive and nonadaptive noise reduction algorithms are also presented. The adaptive algorithms are the well‐known two‐microphone normalized least mean square algorithm, and the recently published two‐microphone pseudo affine projection algorithm. The nonadaptive algorithms are the one‐microphone spectral subtraction and the two‐microphone Wiener filter algorithm. We evalute the quality of the output speech signal in each algorithm by several objective and subjective criteria as the segmental signal‐to‐noise ratio, cepstral distance, perceptual evaluation of speech quality, and the mean opinion score. Finally, we validate the superior performances of the proposed algorithm with physically measured signals.     

Large error recovery for a class of frequency tracking algorithms

The performance of a recently proposed high-order adaptive notch filter (HANF) for frequency estimation and tracking is studied. An analysis technique utilizing approximations with linear filters is employed to derive closed-form performance expressions for a noisy sinusoidal input signal. Important performance measures, such as stability, noise rejection, statistical efficiency, and tracking ability, are studied in detail, and rules for the design variables are given. A study is presented where the performance of HANF is compared with the performance of a minimal order adaptive notch filter (ANF), as well as with a frequency tracker based on least squares-modelling—the multiple frequency tracker (MFT). The study reveals that HANF is a competitive alternative to ANF, but also that, in general, the MFT is the method of choice. © 1998 John Wiley & Sons, Ltd.     

A study on adaptive noise canceller using linear phase filter

In this paper, we propose a new adaptive noise canceller using a linear phase filter. The linear model in which an arbitrary signal is defined by the output signal of a linear system at the white signal input is used. The noise is suppressed by the estimated linear system and the signal‐to‐noise ratio is improved. At this point, to minimize the distortion of the signal due to the nonlinearity of the phase shift, the linear phase filter has been newly introduced. The transfer function of the linear system is an arbitrary minimum phase rational transfer function that has poles and zeros. It has the feature of not being specified for all pole models. The adaptive algorithm is a gradient‐based algorithm with few computational complexities. The features of the proposed adaptive noise canceller are that the inverse filter of the adaptive filter is stable, the convergence of the algorithm is guaranteed, the distortion of the signal is minimal, and there is no restriction on the transfer function of the linear system. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 178(1): 50–55, 2012; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21116