Research On Adaptive Filtering Algorithm Based On Minimum Error Entropy

Adaptive filtering algorithm is one of the most influential research hotspots in the world. The traditional adaptive filtering algorithm, such as the least mean square algorithm(LMS algorithm) has widely used in domain of engineering fields of adaptive signal processing and machine learning, due to its simple structure, stable performance and low computational complexity. The LMS algorithms perform well in Gaussian noise environment. However, in non-Gaussian noise environment, they perform very poorly. Therefore, when faced with the practical application in non-Gaussian noise situation, how to build some robustness algorithms has become a crucial issue that should be researched on adaptive filtering algorithm.This thesis focuses on the minimum error entropy(MEE), and proposes some robustness adaptive filtering algorithms, which effectively overcome the shortage of traditional adaptive filtering algorithms in non-Gaussian noise situations. The contributions of this thesis are summarized as follows:Firstly, the sparse channel normally presents in communication systems. Since and the traditional sparse adaptive filtering algorithm only has the best performance in Gaussian environment, based on MEE criterion, this thesis proposes two types of algorithms for non-Gaussian noise environment:1) Three sparse adaptive filtering algorithms, incorporating an 1l-norm, a reweighted 1l- norm and the correntropy induced metric(CIM) into the minimum error entropy respectively, have been developed to solve the sparse channel parameter estimation problem under non-Gaussian noise environment. The convergence has been analyzed and experiment results indicate that, under non-Gaussian noise environment, the proposed algorithm has excellent performance in solving the sparse channel parameter estimation problems.2) By introducing the concept of the proportional adaptive, a proportionate adaptive filtering algorithm, which uses MEE to replace MSE as an adaptive criterion, has been proposed. Based on the energy conservation relationship, the sufficient condition for the mean square stability of the algorithm are obtained. Simulation results show that this algorithm exhibits the robustness and strong tracking capability under the impulse noise interference.Secondly, aiming at the problem that the tradition MEE algorithm frequently requires a compromise between convergence speed and accuracy, an improved algorithm, based on adaptive convex combination filter under MEE, has been proposed, which can achieve fast convergence speed while keeping a good accuracy. Simulation results demonstrate the superior performance of the proposed algorithm.This thesis, based on the minimum error entropy criterion, has proposed sparse adaptive filtering algorithm with sparsity penalty constraints, sparse proportionate adaptive filtering algorithm and convex combination adaptive filtering algorithm. The convergence of these algorithms has been analyzed. Experimental results show that the proposed methods have excellent convergence performance under non-Gaussian situations.