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.

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

This paper proposes two gradient-based adaptive algorithms, called the least mean M estimate and the transform domain least mean M-estimate (TLMM) algorithms, for robust adaptive filtering in impulse noise. A robust M-estimator is used as the objective function to suppress the adverse effects of impulse noise on the filter weights. They have a computational complexity of order O(N) and can be viewed, respectively, as the generalization of the least mean square and the transform-domain least mean square algorithms. A robust method fur estimating the required thresholds in the M-estimator is also given. Simulation results show that the TLMM algorithm, in particular, is more robust and effective than other commonly used algorithms in suppressing the adverse effects of the impulses.

/pdf/least-mean-m-estimate-algorithms-for-robust-adaptive-3eowp06q2t.pdf

Least mean M-estimate algorithms for robust adaptive filtering in impulse noise

This paper proposes a recursive least M-estimate (RLM) algorithm for robust adaptive filtering in impulse noise. It employs an M-estimate cost function, which is able to suppress the effect of impulses on the filter weights. Simulation results showed that the RLM algorithm performs better than the conventional RLS, NRLS, and the OSFKF algorithms when the desired and input signals are corrupted by impulses. Its initial convergence, steady-state error, computational complexity, and robustness to sudden system change are comparable to the conventional RLS algorithm in the presence of Gaussian noise alone.

/pdf/a-recursive-least-m-estimate-rlm-adaptive-filter-for-robust-4ks3m9da9b.pdf

A recursive least M-estimate (RLM) adaptive filter for robust filtering in impulse 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.

/pdf/new-sequential-partial-update-least-mean-m-estimate-4w55u1il7v.pdf

New Sequential Partial-Update Least Mean M-Estimate Algorithms for Robust Adaptive System Identification in Impulsive Noise

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.

/pdf/on-the-performance-analysis-of-the-least-mean-m-estimate-and-1mjrmgoba6.pdf

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 deals with the derivation of a new adaptive filtering algorithm, which takes into consideration the often encountered case of impulsive perturbations. The proposed method is a combination of a RLS-based algorithm and the Order Statistic (OS) filter, and can be seen as an extension of the LMS-type Order Statistic filter (OSLMS). In order to obtain a computational burden comparable to the OSLMS filter, our derivation is based on a fast version of the RLS algorithm-the Fast Kalman filter. We will show that the new algorithm is not a coarse extension of the OSLMS filter and that care should be taken when performing the order statistic filtering operation.

https://ieeexplore.ieee.org/iel3/3834/11196/00540366.pdf

D. Ottaviani

Papers

Order statistic fast Kalman filter