Robust statistics based adaptive filtering algorithms for impulsive noise suppression

Abstract

(Uncorrected OCR) Abstract

Abstract of thesis entitled

Robust Statistics Based Adaptive Filtering Algorithms

For Impulsive Noise Suppression

Submitted by Yuexian Zou

for the degree of Doctor of Philosophy at The University of Hong Kong in May 2000

The behavior of an adaptive filter is inherently decided by how its estimation error and the cost function are formulated under certain assumption of the involving signal statistics. This dissertation is concerned with the development of robust adaptive filtering in an impulsive noise environment based on the linear transversal filter (LTF) and the lattice-ladder filer (LLF) structures. Combining the linear adaptive filtering theory and robust statistics estimation techniques, two new cost functions, called the mean M -estimate error (MME) and the sum of weighted M -estimate error (SWME), are proposed. They can be taken as the generalizations of the well-known mean squared error (MSE) and the sum of weighted squares error (SWSE) cost functions when the

involving signals are Gaussian.

Based on the SWME cost function, the resulting optimal weight vector is governed by an M-estimate normal equation and a recursive least M -estimate (RLM) algorithm is derived. The RLM algorithm preserves the fast initial convergence, lower steady-state 11

Abstract

derived. The RLM algorithm preserves the fast initial convergence, lower steady-state error and the robustness to the sudden system change of the recursive least squares (RLS) algorithm under Gaussian noise alone. Meanwhile, it has the ability to suppress impulse noise both in the desired and input signals. In addition, using the MME cost function, stochastic gradient based adaptive algorithms, named the least mean Mestimate (LMM) and its transform dOlnain version, the transform domain least mean Mestimate (TLMM) algorithms have been developed. The LMM and TLMM algorithms can be taken as the generalizations of the least-mean square (LMS) and transform domain normalized LMS (TLMS) algorithms, respectively. These two robust algorithms give similar performance as the LMS and TLMS algorithms under Gaussian noise alone and are able to suppress impulse noise appearing in the desired and input signals. It is noted that the performance and the computational complexity of the RLM, LMM and TLMM algorithms have a close relationship with the estimate of the threshold parameters for the M-estimate functions. A robust and effective recursive method has been suggested in this dissertation to estimate the variance of the estimation error and the required threshold parameters with certain confidence to suppress the impulsive noise. The mean and mean square convergence performances of the RLM and the LMM algorithms are evaluated, respectively, when the impulse noise is assumed to be contaminated Gaussian distribution.

Motivated by the desirable features of the lattice-ladder filter, a new robust adaptive gradient lattice-ladder filtering algorithm is developed by minimizing an MME cost function together with an embedded robust impulse suppressing process, especially for impulses appearing in the filter input. The resultant robust gradient lattice-robust

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Abstract

normalized LMS (RGAL-RNLMS) algorithm perfonns comparably to the conventional GAL-NLMS algorithm under Gaussian noise alone; meanwhile, it has the capability of suppressing the adverse effects due to impulses in the input and the desired signals. The additional computational complexity compared to the GAL-NLMS algorithm is of

O(Nw log Nw) + O(NfI log N,J .

Extensive computer simulation studies are undertaken to evaluate the performance of the RLM, LMM, TLMM and the RGAL-RNLMS algorithms under the additive noise with either a contaminated Gaussian distribution or the symmetric alpha-stable (SaS ) distributions. The results substantiate the analysis and demonstrate the effectiveness and robustness of the developed robust adaptive filtering algorithms in suppressing impulsive noise both in the input and the desired signals of the adaptive filter. In conclusion, the proposed approaches in this dissertation present an attempt for developing robust adaptive filtering algorithms in impulsive noise environments and can be viewed as an extension of the linear adaptive filter theory. They may become reasonable and effective tools to solve adaptive filtering problems in a non-Gaussian environment in practice.

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