An Affine Projection Algorithm with Multi-scale Kernels Learning

In order to improve the ability of noise elimination and channel equalization of strong non-linear signals, a Multi-scale Kernels learning Affine Projection filtering Algorithm based on Surprise Criterion (SC-MKAPA) is proposed on the basis of kernel learning adaptive filtering method. Based on the kernel affine projection filtering algorithm, the structure of the kernel combination function is improved, and the bandwidths of several different Gaussian kernels are taken as variable parameters to participate in the update of the filter together with the weighted coefficients.The calculation results are sparsed by using the surprise criterion, and the surprise measure is improved according to the constraints of the affine projection algorithm, which simplifies the variance term and reduces the calculation complexity. The algorithm is applied to noise cancellation, channel equalization, and Mackey Glass (MG) time series prediction. The simulation results are compared with the traditional adaptive filtering algorithm and the kernel learning adaptive filtering algorithm, it proves the superiority of the proposed algorithm.