A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.     

Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.     

Robust Blind Adaptive Channel Equalization in Chaotic Communication Systems

Based on the bounded property and statistics of chaotic signal and the idea of set-membership identification, we propose a set-membership generalized least mean square （SM-GLMS） algorithm with variable step size for blind adaptive channel equalization in chaotic communication systems. The steady state performance of the proposed SM-GLMS algorithm is analysed, and comparison with an extended Kalman filter （EKF）-based adaptive algorithm and variable gain least mean square （VG-LMS） algorithm is performed for blind adaptive channel equalization. Simulations show that the proposed SM-GLMS algorithm can provide more significant steady state performance improvement than the EKF-based adaptive algorithm and VG-LMS algorithm.     

Speech endpoint detection in real noise environments

A method of speech endpoint detection in environments of complicated additive noise is presented. Based on the analysis of noise, an adaptive model of stationary noise is proposed to detect the section where the signal is nonstationary. Then the voice is detected in this section by its harmonic structure, and the accurate endpoint is searched using energy. Compared with the typical algorithms, this algorithm operates reliably in most real noise environments.     

Small moving target interference suppression detection method in space-time Doppler frequency shift domain

Active sonar can separate clutter, reverberation, and moving targets in the Doppler frequency shift domain using Doppler sensitive signals, but time and Doppler leakages of strong interference can inundate weak targets at low signal-to-interference ratios. Therefore, a small moving target interference suppression detection method based on an adaptive least mean square(LMS) algorithm and wide-band ambiguity function(WAF) is proposed. First, an adaptive notch filter based on LMS is used to suppres...     

Minimum mean square error method for stripe nonuniformity correction

Stripe nonuniformity is very typical in line infrared focal plane (IRFPA) and uncooled starring IRFPA. We develop the minimum mean square error (MMSE) method for stripe nonuniformity correction (NUC). The goal of the MMSE method is to determine the optimal NUC parameters for making the corrected image the closest to the ideal image. Moreover, this method can be achieved in one frame, making it more competitive than other scene-based NUC algorithms. We also demonstrate the calibration results of our algorithm using real and virtual infrared image sequences. The experiments verify the positive effect of our algorithm.     

An adaptive time delay estimati on algorithm based onquadratic weighting of the frequency domain

Time delay estimation (TDE) plays an important role in many engineering appli-cations. A new time delay estimation configuration, the quadratic weighting of the frequency domain adaptive TDE model, is put forward. The quadratic weighting of the frequency domainSCOT (Smoothed Coherence Transform) and ML (Maximum Likelihood) adaptive TDE algo-rithms are presented, respectively. The variance of the quadratic weighting of the frequency domain SCOT algorithm is derived. Then the proposed algorithms are applied in the TDE of helicopter passive acoustic location. The simulation results are presented which verify that the proposed algorithm has better performance in the low signal to noise ratio.     

An approach to the detection of underwater remote target

An approach to the detection of underwater remote target by estimating its backscattering coefficient is presented. The key to this approach is that the echo signal is represented in state-variable model and the back-scattering coefficients of target are contained in dynamic noise of this model, thus underwater target can be detected by estimating this dynamic noise, i.e., deconvolving this model. When all noise statistics are a priori known, an optimum deconvolution algorithm based on the optimum state filter is derived, or else, an adaptive deconvolution algorithm based on the adaptive state filter of alternatively estimating the vector state and the noise statistics is developed. In the final simulation test, an echo signal with SNR equal to -6.1 dB is proceeded using the aforementioned two deconvolution algorithms, respectively, and the results demonstrate good performance of the approach.     

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper,the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks(DNNs) with stochastic perturbation is studied.Based on the Lyapunov stability theory,stochastic analysis approach and an efficient impulsive delay differential inequality,some new exponential synchronization criteria expressed in the form of the linear matrix inequality(LMI) are derived.The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square,but also can control the exponential synchronization rate.Furthermore,to estimate the stable region of the synchronization error dynamics,a novel optimization control algorithm is proposed,which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively.Simulation results finally demonstrate the effectiveness of the proposed method.     

Prediction of chaotic systems with multidimensional recurrent least squares support vector machines

In this paper, we propose a multidimensional version of recurrent least squares support vector machines （MDRLS- SVM） to solve the problem about the prediction of chaotic system. To acquire better prediction performance, the high-dimensional space, which provides more information on the system than the scalar time series, is first reconstructed utilizing Takens＇s embedding theorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in the high- dimensional space, and the prediction performance can be improved from the point of view of reconstructed embedding phase space. In addition, the MDRLS-SVM algorithm is analysed in the context of noise, and we also find that the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.     

基于P范数的核最小对数绝对差自适应滤波算法

为了进一步提高在a稳定分布噪声背景下非线性自适应滤波算法的收敛速度,本文提出了一种新的基于p范数的核最小对数绝对差自适应滤波算法(kernel least logarithm absolute difference algorithm based on p-norm, P-KLLAD).该算法结合核最小对数绝对差算法和p范数,一方面利用最小对数绝对差准则保证了算法在a稳定分布噪声环境下良好的鲁棒性,另一方面在误差的绝对值上添加p范数,通过p范数和一个正常数a来控制算法的陡峭程度,从而提高该算法的收敛速度.在非线性系统辨识和Mackey-Glass混沌时间序列预测的仿真结果表明,本文算法在保证鲁棒性能的同时提高了收敛速度,并且在收敛速度和鲁棒性方面优于核最小均方误差算法、核分式低次幂算法、核最小对数绝对差算法和核最小平均p范数算法.     

Design and analysis of a BLPC vocoder-based adaptive feedback cancellation with probe noise

The band-limited linear predictive coding (BLPC) vocoder-based adaptive feedback cancellation (AFC) removes the high-frequency bias, while the low frequency bias persists between the desired input signal and the loudspeaker signal in the estimate of the feedback path. In this paper, we present a BLPC vocoder-based adaptive feedback canceller with probe noise with an objective of reducing the low-frequency bias in digital hearing-aids. A step-wise mathematical analysis of the proposed feedback canceller is presented employing the recursive least square and normalized least mean square adaptive algorithms. It is observed that the optimal solution of the feedback path is unbiased for an unshaped probe noise, but is biased for a shaped probe signal; the bias term does not consist of correlation between the desired input and the loudspeaker output. The identifiability conditions are analysed and it is shown that a delay, greater than or equal to the length of the adaptive filter, must be introduced in the forward path to achieve an unbiased feedback path estimate. Algorithm analysis and computer simulations presented in this paper justify the reason for selecting the proposed design over the existing BLPC vocoder-based feedback cancellation algorithm.     

用于混沌时间序列自适应预测的一种少参数二阶Volterra滤波器

研究了二阶Volterra滤波器的一种乘积耦合近似实现结构及其非线性NLMS自适应算法,并用这种少参数二阶Volterra滤波器(RPSOVF)研究了一些混沌信号的非线性自适应预测性能.仿真研究结果表明:所给出的非线性NLMS自适应算法能够保证这种RPSOVF的稳定性和收敛性,且RPSOVF用这种非线性NLMS自适应算法能够自适应预测一些混沌时间序列. 关键词： 混沌 非线性自适应预测 Volterra滤波器 非线性NLMS自适应算法     

Experimental evaluation of leaky least-mean-square algorithms for active noise reduction in communication headsets

An adaptive leaky normalized least-mean-square (NLMS) algorithm has been developed to optimize stability and performance of active noise cancellation systems. The research addresses LMS filter performance issues related to insufficient excitation, nonstationary noise fields, and time-varying signal-to-noise ratio. The adaptive leaky NLMS algorithm is based on a Lyapunov tuning approach in which three candidate algorithms, each of which is a function of the instantaneous measured reference input, measurement noise variance, and filter length, are shown to provide varying degrees of tradeoff between stability and noise reduction performance. Each algorithm is evaluated experimentally for reduction of low frequency noise in communication headsets, and stability and noise reduction performance are compared with that of traditional NLMS and fixed-leakage NLMS algorithms. Acoustic measurements are made in a specially designed acoustic test cell which is based on the original work of Ryan et al. ["Enclosure for low frequency assessment of active noise reducing circumaural headsets and hearing protection," Can. Acoust. 21, 19-20 (1993)] and which provides a highly controlled and uniform acoustic environment. The stability and performance of the active noise reduction system, including a prototype communication headset, are investigated for a variety of noise sources ranging from stationary tonal noise to highly nonstationary measured F-16 aircraft noise over a 20 dB dynamic range. Results demonstrate significant improvements in stability of Lyapunov-tuned LMS algorithms over traditional leaky or nonleaky normalized algorithms, while providing noise reduction performance equivalent to that of the NLMS algorithm for idealized noise fields.     

Improving robustness of filtered-x least mean p-power algorithm for active attenuation of standard symmetric-α-stable impulsive noise

The paper concerns active control of impulsive noise having peaky distribution with heavy tail. Such impulsive noise can be modeled using non-Gaussian stable process for which second order moments do not exist. The most famous filtered-x least mean square (FxLMS) algorithm for active noise control (ANC) systems is based on the minimization of variance (second order moment) of error signal, and hence, becomes unstable for the impulsive noise. In order to improve the robustness of adaptive algorithms for processes having distributions with heavy tails (i.e. signals with outliers), either (1) a robust optimization criterion may be used to derive the adaptive algorithm or (2) the large amplitude samples may be ignored or replaced by an appropriate threshold value. Among the existing algorithms for ANC of impulsive noise, one is based on the minimizing least mean p-power (LMP) of the error signal, resulting in FxLMP algorithm (approach 1). The other is based on modifying; on the basis of statistical properties; the reference signal in the update equation of the FxLMS algorithm (approach 2). In this paper we propose two solutions to improve the robustness of the FxLMP algorithm. In first proposed algorithm, the reference and the error signals are thresholded before being used in the update equation of FxLMP algorithm. As another solution to improve the performance of FxLMP algorithm, a modified normalized step size is proposed. The computer simulations are carried out, which demonstrate the effectiveness of the proposed algorithms.     

基于分数阶最大相关熵算法的混沌时间序列预测

为提高最大相关熵算法对混沌时间序列的预测速度和精度,提出了一种新的分数阶最大相关熵算法.在采用最大相关熵准则的基础上,利用分数阶微分设计了一种新的权重更新方法.在alpha噪声环境下,采用新的分数阶最大相关熵算法对Mackey-Glass和Lorenz两类具有代表性的混沌时间序列进行预测,并分析了分数阶的阶数对混沌时间序列预测性能的影响.仿真结果表明:与最小均方算法、最大相关熵算法以及分数阶最小均方算法三类自适应滤波算法相比,所提分数阶最大相关熵算法在混沌时间序列预测中能够有效地抑制非高斯脉冲噪声干扰的影响,具有较快收的敛速度和较低的稳态误差.     

A novel feedback active noise control for broadband chaotic noise and random noise

The feedback active noise control (ANC) can be seen as a predictor, the conventional method based on filtered-x least mean square (FXLMS) algorithm can only be useful for linear and tonal noise, but for nonlinear and broadband noise, it is useless. The feedback ANC using functional link artificial neural networks (FLANN) based on filtered-s least mean square (FSLMS) algorithm can reduce some nonlinear noise such as chaotic noise, but the noise cancellation performance is not very well, at the same time, it is not useful to random noise. To solve the problem above, a new feedback ANC using wavelet packet FXLMS (WPFXLMS) algorithm is proposed in this paper. By decomposing the broadband noise into several band-limited parts which are predictable and each part is controlled independently, the proposed algorithm can not only suppress the chaotic noise, but also mitigate the random noise. Compared with FXLMS and FSLMS algorithms, proposed WPFXLMS algorithm also holds the best performance on noise cancellation. Numerous simulations are conducted to demonstrate the effectiveness of the proposed WPFXLMS algorithm.     

非高斯冲激干扰下基于Softplus函数的核自适应滤波算法

针对非高斯环境下一般自适应滤波算法性能严重下降问题,本文提出了一种基于Softplus函数的核分式低次幂自适应滤波算法(kernel fractional lower algorithm based on Softplus function,SP-KFLP),该算法将Softplus函数与核分式低次幂准则相结合,利用输出误差的非线性饱和特性通过随机梯度下降法更新权重.一方面利用Softplus函数的特点在保证了SP-KFLP算法具有良好的抗脉冲干扰性能的同时提高了其收敛速度;另一方面将低次幂误差的倒数作为权重向量更新公式的系数,利用误差突增使得权重向量不更新的方法来抵制冲激噪声,并对其均方收敛性进行了分析.在系统辨识环境下的仿真表明,该算法很好地兼顾了收敛速度和跟踪性能稳定误差的矛盾,在收敛速度和抗脉冲干扰鲁棒性方面优于核最小均方误差算法、核分式低次幂算法和S型核分式低次幂自适应滤波算法.     

Improving performance of FxRLS algorithm for active noise control of impulsive noise

Active noise control (ANC) systems employing adaptive filters suffer from stability issues in the presence of impulsive noise. New impulsive noise control algorithms based on filtered-x recursive least square (FxRLS) algorithm are presented. The FxRLS algorithm gives better convergence than the filtered-x least mean square (FxLMS) algorithm and its variants but lacks robustness in the presence of high impulsive noise. In order to improve the robustness of FxRLS algorithm for ANC of impulsive noise, two modifications are suggested. First proposed modification clips the reference and error signals while, the second modification incorporates energy of the error signal in the gain of FxRLS (MGFxRLS) algorithm. The results demonstrate improved stability and robustness of proposed modifications in the FxRLS algorithm. However, another limitation associated with the FxRLS algorithm is its computationally complex nature. In order to reduce the computational load, a hybrid algorithm based on proposed MGFxRLS and normalized step size FxLMS (NSS-FXLMS) is also developed in this paper. The proposed hybrid algorithm combines the stability of NSS-FxLMS algorithm with the fast convergence speed of the proposed MGFxRLS algorithm. The results of the proposed hybrid algorithm prove that its convergence speed is faster than that of NSS-FxLMS algorithm with computational complexity lesser than that of FxRLS algorithm.