A recursive least M-estimate algorithm for robust adaptive filtering in impulsive noise: fast algorithm and convergence performance analysis

This paper studies the problem of robust adaptive filtering in impulsive noise environment using a recursive least M-estimate algorithm (RLM). The RLM algorithm minimizes a robust M-estimator-based cost function instead of the conventional mean square error function (MSE). Previous work has showed that the RLM algorithm offers improved robustness to impulses over conventional recursive least squares (RLS) algorithm. In this paper, the mean and mean square convergence behaviors of the RLM algorithm under the contaminated Gaussian impulsive noise model is analyzed. A lattice structure-based fast RLM algorithm, called the Huber Prior Error Feedback-Least Squares Lattice (H-PEF-LSL) algorithm is derived. Part of the H-PEF-LSL algorithm was presented in ICASSP 2001. It has an order O(N) arithmetic complexity, where N is the length of the adaptive filter, and can be viewed as a fast implementation of the RLM algorithm based on the modified Huber M-estimate function and the conventional PEF-LSL adaptive filtering algorithm. Simulation results show that the transversal RLM and the H-PEF-LSL algorithms have better performance than the conventional RLS and other RLS-like robust adaptive algorithms tested when the desired and input signals are corrupted by impulsive noise. Furthermore, the theoretical and simulation results on the convergence behaviors agree very well with each other.     

A robust past algorithm for subspace tracking in impulsive noise

The PAST algorithm is an effective and low complexity method for adaptive subspace tracking. However, due to the use of the recursive least squares (RLS) algorithm in estimating the conventional correlation matrix, like other RLS algorithms, it is very sensitive to impulsive noise and the performance can be degraded substantially. To overcome this problem, a new robust correlation matrix estimate, based on robust statistics concept, is proposed in this paper. It is derived from the maximum-likelihood (ML) estimate of a multivariate Gaussian process in contaminated Gaussian noise (CG) similar to the M-estimates in robust statistics. This new estimator is incorporated into the PAST algorithm for robust subspace tracking in impulsive noise. Furthermore, a new restoring mechanism is proposed to combat the hostile effect of long burst of impulses, which sporadically occur in communications systems. The convergence of this new algorithm is analyzed by extending a previous ordinary differential equation (ODE)-based method for PAST. Both theoretical and simulation results show that the proposed algorithm offers improved robustness against impulsive noise over the PAST algorithm. The performance of the new algorithm in nominal Gaussian noise is very close to that of the PAST algorithm.     

The multi-user detection under fading channel

This paper proposes a method of blind multi-user detection algorithm based on signal sub-space estimation under the fading channels in the present of impulse noise. This algorithm adapts recursive least square (RLS) filter that can estimate the coefficients using only the signature waveform. In addition, to strengthen the ability of resisting the impulse noise, a new suppressive factor is induced, which can suppress the amplitude of the impulse, and improve the ability of convergence speed. Simulation results show that new RLS algorithm is more robust against consecutive impulse noise and have better convergence ability than conventional RLS. In addition, Compared to the least mean square (LMS) detector, the new robust RLS sub-space based method has better multi-address-inference (MAI) suppressing performance, especially, when channel degrades.     

在脉冲噪声环境中用于快衰信道估计的改进型算法

该文分析了在存在噪声干扰的情况下,进行估计快衰信道的方法。在无线通信系统中,快衰信道可以采用AR(Auto-Regressive)模型进行预测,而LS (Least Square)算法和自适应Kalman滤波器可以分别对AR模型的参数和信道的冲激响应进行估计,但是这两种算法对噪声干扰非常敏感。该文提出改进型的RLM算法和Kalman 滤波器,并在存在噪声的情况下,使用它们并行对AR参数和信道的冲激响应进行联合估计。仿真结果显示:相比于传统的算法,改进后的算法在联合估计信道时,提高了抵抗大脉冲干扰的能力,加快了待估的参数的收敛速度。     

A New Sequential Block Partial Update Normalized Least Mean M-Estimate Algorithm and its Convergence Performance Analysis

This paper proposes a new sequential block partial update normalized least mean square (SBP-NLMS) algorithm and its nonlinear extension, the SBP-normalized least mean M-estimate (SBP–NLMM) algorithm, for adaptive filtering. These algorithms both utilize the sequential partial update strategy as in the sequential least mean square (S–LMS) algorithm to reduce the computational complexity. Particularly, the SBP–NLMM algorithm minimizes the M-estimate function for improved robustness to impulsive outliers over the SBP–NLMS algorithm. The convergence behaviors of these two algorithms under Gaussian inputs and Gaussian and contaminated Gaussian (CG) noises are analyzed and new analytical expressions describing the mean and mean square convergence behaviors are derived. The robustness of the proposed SBP–NLMM algorithm to impulsive noise and the accuracy of the performance analysis are verified by computer simulations.     

On the Performance Analysis of the Least Mean M-Estimate and Normalized Least Mean M-Estimate Algorithms with Gaussian Inputs and Additive Gaussian and Contaminated Gaussian Noises

This paper studies the convergence analysis of the least mean M-estimate (LMM) and normalized least mean M-estimate (NLMM) algorithms with Gaussian inputs and additive Gaussian and contaminated Gaussian noises. These algorithms are based on the M-estimate cost function and employ error nonlinearity to achieve improved robustness in impulsive noise environment over their conventional LMS and NLMS counterparts. Using the Price’s theorem and an extension of the method proposed in Bershad (IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-34(4), 793–806, 1986; IEEE Transactions on Acoustics, Speech, and Signal Processing, 35(5), 636–644, 1987), we first derive new expressions of the decoupled difference equations which describe the mean and mean square convergence behaviors of these algorithms for Gaussian inputs and additive Gaussian noise. These new expressions, which are expressed in terms of the generalized Abelian integral functions, closely resemble those for the LMS algorithm and allow us to interpret the convergence performance and determine the step size stability bound of the studied algorithms. Next, using an extension of the Price’s theorem for Gaussian mixture, similar results are obtained for additive contaminated Gaussian noise case. The theoretical analysis and the practical advantages of the LMM/NLMM algorithms are verified through computer simulations.     

自适应滤波算法在微弱振动测量中的应用

将递归最小二乘自适应滤波算法应用于激光多普勒测振技术中,搭建了相应的微弱振动测量装置。模拟仿真与实验中,通过与设计的切比雪夫低通滤波算法对比,结果表明:该递归最小二乘自适应滤波算法能够有效抑制随机高斯白噪声,还原出原始信号;能够对简谐振动信号实现有效滤波,并且可以还原出淹没在噪声中的低频20 Hz信号;文中算法可以去除语音噪声,使声音更加纯净,增强语音信号,以此验证了该算法在外差振动测量中的可行性。该算法简单易用、收敛性强、速度快,尤其对于随机噪声的去除比普通的低通滤波器更加有效。     

自适应序贯M估计算法及其性能分析

针对复杂噪声环境下的参数估计问题,提出了一种稳健的自适应序贯M估计算法(Adaptive Recursive M-Estimation,ARME),并从理论分析和Monte Carlo实验仿真两方面分析了该算法的收敛性、渐进无偏特性和稳健性.理论分析和仿真试验表明:在高斯白噪声背景下,ARME具有与序贯最小二乘算法(Recursive Least Square,RLS)相近的性能;在有突出干扰等非高斯噪声背景下,与RLS相比,ARME的参数估计收敛速度更快,估计误差更小,而且在稳健性上大大优于RLS.     

Low Complexity Linear Channel Estimation for MIMO Communication Systems

Channel estimation is employed to get the current knowledge of channel states for an optimum detection in fading environments. In this paper, a new recursive multiple input multiple output (MIMO) channel estimation is proposed which is based on the recursive least square solution. The proposed recursive algorithm utilizes short training sequence on one hand and requires low computational complexity on the other hand. The algorithm is evaluated on a MIMO communication system through simulations. It is realized that the proposed algorithm provides fast convergence as compared to recursive least square (RLS) and robust variable forgetting factor RLS (RVFF-RLS) adaptive algorithms while utilizing lesser computational cost and provides independency on forgetting factor.     

EM-based recursive estimation of channel parameters

Recursive (online) expectation-maximization (EM) algorithm along with stochastic approximation is employed in this paper to estimate unknown time-invariant/variant parameters. The impulse response of a linear system (channel) is modeled as an unknown deterministic vector/process and as a Gaussian vector/process with unknown stochastic characteristics. Using these models which are embedded in white or colored Gaussian noise, different types of recursive least squares (RLS), Kalman filtering and smoothing and combined RLS and Kalman-type algorithms are derived directly from the recursive EM algorithm. The estimation of unknown parameters also generates new recursive algorithms for situations, such as additive colored noise modeled by an autoregressive process. The recursive EM algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods     

基于RLS算法实现激光陀螺抖动信号剥除

为了减小陀螺输出数据的时延,以满足机械抖动激光陀螺在快速跟踪中的应用,基于递归最小二乘(RLS)自适应滤波技术实现了激光陀螺抖动信号的剥除。首先对RLS自适应对消去抖算法进行了理论分析,其次通过通用串行总线接口将A/D采集的抖动反馈信号和激光陀螺计数脉冲信号传至上位机,最后基于MATLAB编写了RLS自适应程序,实现了激光陀螺抖动信号的剥除。剥除后的陀螺信号再经过11阶的有限脉冲响应滤波器和陀螺输出直接经过31阶的滤波器剩余的脉冲数基本相当,而时间延迟却明显减小。结果表明,该算法具有较快的收敛速度且能够有效去除激光陀螺计数脉冲中的抖动成分。     

用于自适应数字波束形成的稳健子阵异步RLS算法

提出了一种修正的递归最小二乘自适应算法--稳健子阵异步递推最小二乘算法(MSARLS)--用于自适应数字波束形成.该算法综合运用稳健估计和子阵异步递推技术.改进后的算法,不但大大减少了运算量,而且增强了算法抗突发强干扰的性能.另还给出了计算的理论分析和计算机仿真结果.     

An algorithm for efficient, unbiased, equation-error infiniteimpulse response adaptive filtering

An algorithm for efficiently adjusting the coefficients of equation-error infinite impulse response (IIR) adaptive filters is described. Unlike the recursive least squares (RLS) algorithm, the proposed algorithm yields unbiased filter coefficients. Simulations involving the identification of unknown pole-zero systems demonstrate the algorithm's improved performance over the equation-error RLS algorithm     

基于滑动窗与韧性函数的递归最小p范数滤波方法

稳定分布可以更好地描述实际应用中所遇到的具有显著脉冲特性的随机信号和噪声。与其它统计模型不同, 稳定分布没有统一闭式的概率密度函数,其二阶及二阶以上统计量均不存在。针对系统中存在独立SS噪声与高斯噪声,该文基于SSG分布模型,提出了一种混合噪声环境下基于滑动窗与韧性函数自适应广义递归最小p范数滤波算法,并对算法进行了分析。计算机模拟和分析表明,这种算法是一种在SSG分布背景噪声条件下具有良好鲁棒性的方法。     

An efficient recursive total least squares algorithm for FIRadaptive filtering

An algorithm for recursively computing the total least squares (TLS) solution to the adaptive filtering problem is described. This algorithm requires O(N) multiplications per iteration to effectively track the N-dimensional eigenvector associated with the minimum eigenvalue of an augmented sample covariance matrix. It is shown that the recursive least squares (RLS) algorithm generates biased adaptive filter coefficients when the filter input vector contains additive noise. The TLS solution on the other hand, is seen to produce unbiased solutions. Examples of standard adaptive filtering applications that result in noise being added to the adaptive filter input vector are cited. Computer simulations comparing the relative performance of RLS and recursive TLS are described     

基于l1-范数约束的递归互相关熵的稀疏系统辨识

为了有效解决脉冲噪声环境下的稀疏系统辨识(Sparse system identification, SSI)问题,以l1 -范数为约束构建稀疏递归互相关熵准则(Recursive maximum correntropy criterion, RMCC)算法来解决脉冲噪声对于辨识性能的影响。结合带遗忘算子的互相关熵准则和l1 -范数作为代价函数,推导出一种递归形式的算法,其相对于传统的最大相关熵算法具有快的收敛速度及小的稳态误差。仿真实验结果表明:该算法对于脉冲噪声干扰环境下的SSI问题具有强的鲁棒性。      

Adaptive robust impulse noise filtering

It is well known that when data is contaminated by non-Gaussian noise, conventional linear systems may perform poorly. The paper presents an adaptive robust filter (adaptive preprocessor) for canceling impulsive components when the nominal process (or background noise) is a correlated, possibly nonstationary, Gaussian process. The proposed preprocessor does not require iterative and/or batch processing or prior knowledge about the nominal Gaussian process; consequently, it can be implemented in real time and adapt to changes in the environment. Based on simulation results, the proposed adaptive preprocessor shows superior performances over presently available techniques for cleaning impulse noise. Using the proposed adaptive preprocessor to clean the impulsive components in received data samples, conventional linear systems based on the Gaussian assumption can work in an impulsive environment with little if any modification. The technique is applicable to a wide range of problems, such as detection, power spectral estimation, and jamming or clutter suppression in impulsive environments     

On the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment

This paper studies the convergence performance of the transform domain normalized least mean square (TDNLMS) algorithm with general nonlinearity and the transform domain normalized least mean M-estimate (TDNLMM) algorithm in Gaussian inputs and additive Gaussian and impulsive noise environment. The TDNLMM algorithm, which is derived from robust M-estimation, has the advantage of improved performance over the conventional TDNLMS algorithm in combating impulsive noises. Using Price’s theorem and its extension, the above algorithms can be treated in a single framework respectively for Gaussian and impulsive noise environments. Further, by introducing new special integral functions, related expectations can be evaluated so as to obtain decoupled difference equations which describe the mean and mean square behaviors of the TDNLMS and TDNLMM algorithms. These analytical results reveal the advantages of the TDNLMM algorithm in impulsive noise environment, and are in good agreement with computer simulation results.     

Adaptive blind channel estimation by least squares smoothing

A least squares smoothing (LSS) approach is presented for the blind estimation of single-input multiple-output (SIMO) finite impulse response systems. By exploiting the isomorphic relation between the input and output subspaces, this geometrical approach identifies the channel from a specially formed least squares smoothing error of the channel output. LSS has the finite sample convergence property, i.e., in the absence of noise, the channel is estimated perfectly with only a finite number of data samples. Referred to as the adaptive least squares smoothing (A-LSS) algorithm, the adaptive implementation has a high convergence rate and low computation cost with no matrix operations. A-LSS is order recursive and is implemented in part using a lattice filter. It has the advantage that when the channel order varies, channel estimates can be obtained without structural change of the implementation. For uncorrelated input sequence, the proposed algorithm performs direct deconvolution as a by-product     

Fast adaptive blind beamforming algorithm for antenna array in CDMA systems

In this paper, the maximum signal-to-interference-plus-noise ratio (MSINR) beamforming problem in antenna-array CDMA systems is considered. In this paper, a modified MSINR criterion presented in a previous paper is interpreted as an unconstrained scalar cost function. By applying recursive least squares (RLS) to minimize the cost function, a novel blind adaptive beamforming algorithm to estimate the beamforming vector, which optimally combines the desired signal contributions from different antenna elements while suppressing noise and interference, is derived. Neither the knowledge of the channel conditions (fading coefficients, signature sequences and timing of interferers, statistics of other noises, etc.) nor training sequence is required. Compared with previously published adaptive beamforming algorithms based on the stochastic-gradient method, it has faster convergence and better tracking capability in the time-varying environment. Simulation results in various signal environments are presented to show the performance of the proposed algorithm.