Research On Robust Kernel Adaptive Filtering Algorithm Based On Information Entropy

In the information processing domain,increasing focus has been engaged in the adaptive filtering algorithms,which can online adjust the filter parameters adaptively.Considering that the traditional linear adaptive filtering algorithm are not suitable for the complex nonlinear model,various nonlinear adaptive filtering algorithms have been derived on the basis of linear adaptive filtering algorithms.Among them,since the kernelbased adaptive filtering algorithms are capable of adopting the Reproducing Kernel Hilbert Space theory to provide linearity in calculation,they have received widespread attention because of its strong ability to process nonlinear signals.The kernel adaptive filters can predict and process the data online from the continuous arrival of the observation data.They have been widely utilized in various fields,including channel equalization,image processing and acoustic echo cancellation.With the complexity of the application scenario,the interference from non-Gaussian environmental noise becomes more obvious.Therefore,the improvement of the robustness for kernel adaptive filtering algorithm has also been the research key point.To address the same problem of non-Gaussian environmental noise,this thesis mainly aims to have a research on the robust kernel adaptive filtering algorithms on the basis of the information entropy,derive new expression through the innovation of cost function and increase the ability of coping with the non-Gaussian environment noise.Therefore,the content of this thesis can be briefly introduced as follows:First,the minimum error entropy is applied to the conventional kernel recursive least squares algorithm,and the novel kernel recursive minimum error entropy algorithm is derived.The stability of the proposed algorithm and its excellent ability of dealing with non-Gaussian noise are proved by convergence analysis and simulation experiments.Besides,by applying the M-estimate regression to the traditional kernel recursive least squares algorithm,a series of robust kernel recursive least squares algorithms are derived.Then,analysis of the computational complexity and several simulations under different types of non-Gaussian noise prove that the algorithms are insensitive to nonGaussian noise.Finally,the M-estimate is applied to the kernel recursive maximum correntropy algorithm to further reach the robustness improvement.Then,a series of robust kernel recursive maximum correntropy algorithm are proposed.When comparing with other conventional algorithms,the proposed algorithms have better performance against the non-Gaussian noise in real data processing.