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. © 2009 Springer Science+Business Media, LLC.published_or_final_versionSpringer Open Choice, 01 Dec 201

A normalized gradient algorithm for an adaptive recurrent perceptron

A normalized algorithm for on-line adaptation of a recurrent perceptron is derived. The algorithm builds upon the normalized backpropagation (NBP) algorithm for feedforward neural networks, and provides an adaptive learning rate and normalization for a recurrent perceptron learning algorithm. The algorithm is based upon local linearization about the current point in the state-space of the network. Such a learning rate is normalized by the squared norm of the gradient at the neuron, which extends the notion of normalized linear algorithms to the nonlinear cas

New sequential partial-update least mean M-estimate algorithms for robust adaptive system identification in impulsive noise

The sequential partial-update least mean square (S-LMS)-based algorithms are efficient methods for reducing the arithmetic complexity in adaptive system identification and other industrial informatics applications. They are also attractive in acoustic applications where long impulse responses are encountered. A limitation of these algorithms is their degraded performances in an impulsive noise environment. This paper proposes new robust counterparts for the S-LMS family based on M-estimation. The proposed sequential least mean M-estimate (S-LMM) family of algorithms employ nonlinearity to improve their robustness to impulsive noise. Another contribution of this paper is the presentation of a convergence performance analysis for the S-LMS/S-LMM family for Gaussian inputs and additive Gaussian or contaminated Gaussian noises. The analysis is important for engineers to understand the behaviors of these algorithms and to select appropriate parameters for practical realizations. The theoretical analyses reveal the advantages of input normalization and the M-estimation in combating impulsive noise. Computer simulations on system identification and joint active noise and acoustic echo cancellations in automobiles with double-talk are conducted to verify the theoretical results and the effectiveness of the proposed algorithms. © 2010 IEEE.published_or_final_versio

Active disturbance cancellation in nonlinear dynamical systems using neural networks

A proposal for the use of a time delay CMAC neural network for disturbance cancellation in nonlinear dynamical systems is presented. Appropriate modifications to the CMAC training algorithm are derived which allow convergent adaptation for a variety of secondary signal paths. Analytical bounds on the maximum learning gain are presented which guarantee convergence of the algorithm and provide insight into the necessary reduction in learning gain as a function of the system parameters. Effectiveness of the algorithm is evaluated through mathematical analysis, simulation studies, and experimental application of the technique on an acoustic duct laboratory model

System approach to robust acoustic echo cancellation through semi-blind source separation based on independent component analysis

We live in a dynamic world full of noises and interferences. The conventional acoustic echo cancellation (AEC) framework based on the least mean square (LMS) algorithm by itself lacks the ability to handle many secondary signals that interfere with the adaptive filtering process, e.g., local speech and background noise. In this dissertation, we build a foundation for what we refer to as the system approach to signal enhancement as we focus on the AEC problem. We first propose the residual echo enhancement (REE) technique that utilizes the error recovery nonlinearity (ERN) to "enhances" the filter estimation error prior to the filter adaptation. The single-channel AEC problem can be viewed as a special case of semi-blind source separation (SBSS) where one of the source signals is partially known, i.e., the far-end microphone signal that generates the near-end acoustic echo. SBSS optimized via independent component analysis (ICA) leads to the system combination of the LMS algorithm with the ERN that allows for continuous and stable adaptation even during double talk. Second, we extend the system perspective to the decorrelation problem for AEC, where we show that the REE procedure can be applied effectively in a multi-channel AEC (MCAEC) setting to indirectly assist the recovery of lost AEC performance due to inter-channel correlation, known generally as the "non-uniqueness" problem. We develop a novel, computationally efficient technique of frequency-domain resampling (FDR) that effectively alleviates the non-uniqueness problem directly while introducing minimal distortion to signal quality and statistics. We also apply the system approach to the multi-delay filter (MDF) that suffers from the inter-block correlation problem. Finally, we generalize the MCAEC problem in the SBSS framework and discuss many issues related to the implementation of an SBSS system. We propose a constrained batch-online implementation of SBSS that stabilizes the convergence behavior even in the worst case scenario of a single far-end talker along with the non-uniqueness condition on the far-end mixing system. The proposed techniques are developed from a pragmatic standpoint, motivated by real-world problems in acoustic and audio signal processing. Generalization of the orthogonality principle to the system level of an AEC problem allows us to relate AEC to source separation that seeks to maximize the independence, hence implicitly the orthogonality, not only between the error signal and the far-end signal, but rather, among all signals involved. The system approach, for which the REE paradigm is just one realization, enables the encompassing of many traditional signal enhancement techniques in analytically consistent yet practically effective manner for solving the enhancement problem in a very noisy and disruptive acoustic mixing environment.PhDCommittee Chair: Biing-Hwang Juang; Committee Member: Brani Vidakovic; Committee Member: David V. Anderson; Committee Member: Jeff S. Shamma; Committee Member: Xiaoli M

Combinations of adaptive filters

Adaptive filters are at the core of many signal processing applications, ranging from acoustic noise supression to echo cancelation [1], array beamforming [2], channel equalization [3], to more recent sensor network applications in surveillance, target localization, and tracking. A trending approach in this direction is to recur to in-network distributed processing in which individual nodes implement adaptation rules and diffuse their estimation to the network [4], [5].The work of Jerónimo Arenas-García and Luis Azpicueta-Ruiz was partially supported by the Spanish Ministry of Economy and Competitiveness (under projects TEC2011-22480 and PRI-PIBIN-2011-1266. The work of Magno M.T. Silva was partially supported by CNPq under Grant 304275/2014-0 and by FAPESP under Grant 2012/24835-1. The work of Vítor H. Nascimento was partially supported by CNPq under grant 306268/2014-0 and FAPESP under grant 2014/04256-2. The work of Ali Sayed was supported in part by NSF grants CCF-1011918 and ECCS-1407712. We are grateful to the colleagues with whom we have shared discussions and coauthorship of papers along this research line, especially Prof. Aníbal R. Figueiras-Vidal

Robust Adaptation and Learning Over Networks

This doctoral dissertation centers on robust adaptive networks. Robust adaptation strategies are devised to solve typical network inference tasks such as estimation and detection in a decentralized manner in the presence of impulsive contamination. Typical in wireless communication environments, an impulsive noise process can be described as one whose realizations contain sparse, random samples of amplitude much higher than nominally accounted for. An attractive feature that these robust adaptive strategies enjoy is that neither their development nor operation hinges on the availability of exact knowledge of the noise distribution: The robust adaptive strategies are capable of learning it on-the-fly and adapting their parameters accordingly. Forgoing data fusion centers, the network agents employing these strategies rely solely on local interactions and in-network processing to perform inference tasks, which renders networks more reliable, resilient to node and link failure, scalable, and resource efficient. Distributed cooperative processing finds applications in many areas including wireless sensor networks in smart-home, environmental, and industrial monitoring; healthcare; and military surveillance. Since adaptive systems based on the mean-square-error criterion see their performance degrade in the presence of non-Gaussian noise, the robust adaptive strategies developed in this dissertation harness nonlinear data processing and robust statistics instead to mitigate the detrimental effects of impulsive noise. To this end, a robust adaptive filtering algorithm is developed that employs an adaptive error nonlinearity. The error nonlinearity is chosen to be a convex combination of preselected basis functions where the combination coefficients are adapted jointly with the estimate of the parameter of interest such that the mean-square-error relative to the optimal error nonlinearity is minimized in each iteration. Then, a robust diffusion adaptation algorithm of the adapt-then-combine variety is developed as an extension of its stand-alone counterpart for distributed estimation over networks where the measurements may be corrupted by impulsive noise. Each node in the network runs a combination of its neighbors’ estimates through one iteration of a local robust adaptive filter update to ameliorate the effects of contamination, leading to better overall network performance matching that of a centralized strategy at steady-state. Finally, the robust diffusion adaptation algorithm is extended further to solve the problem of distributed detection over adaptive networks where the measurements may be corrupted by impulsive noise. The estimates generated by the robust algorithm are used as basis for the design of robust local detectors, where the form of the test- statistics and the rule for the computation of the detection thresholds are motivated by the analysis of the algorithm dynamics. Each node in the network cooperates with its neighbors, utilizing their estimates, to update its local detector. Effectively, information pertaining to the event of interest percolates across the network, leading to enhanced detection performance. The transient and steady-state behavior of the developed algorithms are analyzed in the mean and mean-square sense using the energy conservation framework. The performance of the algorithm is also examined in the context of distributed detection. Performance is validated extensively through numerical simulations in an impulsive noise scenario, revealing the robustness of the proposed strategies in comparison with state-of-the-art algorithms as well as good agreement between theory and practice

Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation