The Research Of Kernel-based Adaptive Filtering Algorithm

The adaptive filtering algorithm has become important subject areas of signal processing. The least-mean-squares (LMS) algorithm is one of the most famous linear online algorithms. LMS algorithms, proposed by widrow and hoff in 1960, become useful in very wide range for it's simple and practicability. But nonlinear systems problems areas has obtained more attention in achieving communication, radar and other areas as scientific and academic development, the linear filtering algorithm has bad performance in dealing with nonlinear problem. And the traditional nonlinear problems algorithm, as nerve network, though has the good performance for the nonlinear problems, but with the complicated computation and local minimum value. so it is not practical.The basic principle of kernel method provides effective way for our algorithm to construct nonlinear algorithm by linear algorithm. This paper based on linear adaptive filtering algorithm, through the basic principle of kernel method, construct kernel-based adaptive filtering algorithm. The algorithm is an nonlinear adaptive filter algorithm essentially, not only have the nonlinear signal processing capability as nerve network, but also have the lower computation as linear adaptive filter algorithm.The innovative works of this paper are showed as follows:(1) We propose two kinds of kernel-based adaptive filtering algorithm. Through the kernel method principle, we can map the least mean square algorithm to a high dimensional feature space and make adaptive training in this high dimensional feature space, in addition to make use of normalization and variable Step-Size update equation. Then, map the output data back to the original space. By this means, we get the kernel-based normalized least mean square algorithm. Simulation results show the algorithm have stronger capability of nonlinear signal processing.(2) Research kernel-based NLMS adaptive filtering algorithm we proposed in adaptive noise cancel. Practiced kernel-based adaptive filtering algorithm in the adaptive noise canceller for audio frequency, realized canceling the noise signal, through simulation results check the performance.