Research On The Adaptive Filtering Algorithms Based On Kernel Method In Impulsive Interference

The traditional linear adaptive filtering algorithms have shown powerful computation in dealing with the linear problems. However, in general, the real-world complex applications such as system identification, voice echo cancellation, time series prediction, most of them, the relationship between input and output is nonlinear. The traditional linear method is difficult to deal with them. The kernel method is a powerful tool for extending an algorithm from linear to nonlinear case. Recently, kernel method has been used in the design of nonlinear filter increasingly. Most existing kernel adaptive filtering algorithms(such as kernel least mean square algorithm) are derived in the premise that the background noise is assumed to be Gaussian white noise. These algorithms suffer from performance degeneration, when the unknown system is interfered by impulsive noise. In other word, these algorithms are not robust against impulsive noise. This thesis mainly studies on the robust kernel adaptive filtering algorithm in impulsive interference, which is of great practical significance.Firstly, in the research of linear adaptive filtering algorithms, the least logarithmic absolute difference(LLAD) algorithm has been proved to be robust against impulsive noise. In this thesis, the kernel method and LLAD algorithm are combined to derive the kernel least logarithmic absolute difference(KLLAD) algorithm. In order to prove the robustness of the proposed algorithm, the proposed algorithm is applied to nonlinear system identification experiments. Simulation results show that the KLLAD algorithm is robust against impulsive noise and has lower steady-state error than its corresponding linear algorithm.Secondly, when the impulsive noise appears, the sign of prediction error is used to update the weight vector of the LLAD algorithm, which results in low convergence speed. This thesis proposes a normalized least mean square algorithm based on the arctangent cost function(Arc-NLMS). The weight update of the proposed algorithm stops automatically in the presence of impulsive noise. Thus, this eliminates the likelihood of updating the weight vector based on wrong information resulting from impulsive noise. The proposed algorithm is applied to linear system identification experiment which is interfered severely by the impulse. Simulations results show that the proposed algorithm is robust against impulsive noise and has a fast convergence speed. Because of the good performance of the Arc-NLMS algorithm, the kernel method and Arc-NLMS are combined to derive a kernel adaptive filtering algorithm to solve the nonlinear problems. Then, the quantized method is applied to the proposed kernel adaptive filtering algorithm to reduce its computational complexity. The proposed algorithm is applied to nonlinear system identification experiment. Simulation results show that the proposed algorithm is robust against impulsive noise and has lower computational complexity.