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postgraduate thesis: Robust statistics based adaptive filtering algorithms for impulsive noise suppression
Title  Robust statistics based adaptive filtering algorithms for impulsive noise suppression 

Authors  
Issue Date  2000 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Zou, Y. [鄒月嫻]. (2000). Robust statistics based adaptive filtering algorithms for impulsive noise suppression. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. 
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 latticeladder 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 wellknown 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 Mestimate normal equation and a recursive least M estimate (RLM) algorithm is derived. The RLM algorithm preserves the fast initial convergence, lower steadystate 11
Abstract
derived. The RLM algorithm preserves the fast initial convergence, lower steadystate 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 leastmean 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 Mestimate 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 latticeladder filter, a new robust adaptive gradient latticeladder 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 latticerobust
111
Abstract
normalized LMS (RGALRNLMS) algorithm perfonns comparably to the conventional GALNLMS 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 GALNLMS 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 RGALRNLMS algorithms under the additive noise with either a contaminated Gaussian distribution or the symmetric alphastable (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 nonGaussian environment in practice.
IV 
Degree  Doctor of Philosophy 
Subject  Adaptive filters. Signal processing  Statistical methods. Robust statistics. 
Dept/Program  Electrical and Electronic Engineering 
DC Field  Value  Language 

dc.contributor.author  Zou, Yuexian   
dc.contributor.author  鄒月嫻  zh_HK 
dc.date.issued  2000   
dc.identifier.citation  Zou, Y. [鄒月嫻]. (2000). Robust statistics based adaptive filtering algorithms for impulsive noise suppression. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.   
dc.description.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 latticeladder 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 wellknown 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 Mestimate normal equation and a recursive least M estimate (RLM) algorithm is derived. The RLM algorithm preserves the fast initial convergence, lower steadystate 11 Abstract derived. The RLM algorithm preserves the fast initial convergence, lower steadystate 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 leastmean 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 Mestimate 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 latticeladder filter, a new robust adaptive gradient latticeladder 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 latticerobust 111 Abstract normalized LMS (RGALRNLMS) algorithm perfonns comparably to the conventional GALNLMS 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 GALNLMS 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 RGALRNLMS algorithms under the additive noise with either a contaminated Gaussian distribution or the symmetric alphastable (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 nonGaussian environment in practice. IV   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.source.uri  http://hub.hku.hk/bib/B22823736   
dc.subject.lcsh  Adaptive filters.   
dc.subject.lcsh  Signal processing  Statistical methods.   
dc.subject.lcsh  Robust statistics.   
dc.title  Robust statistics based adaptive filtering algorithms for impulsive noise suppression   
dc.type  PG_Thesis   
dc.identifier.hkul  b2282373   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Electrical and Electronic Engineering   
dc.description.nature  abstract   
dc.description.nature  toc   