Nonlinear Adaptive Filtering with a Family of Kernel Affine Projection Algorithms

In this chapter, the family of kernel affine projection algorithms with coherence criterion is presented. The proportionality principle is translated to the kernel-based version. A new algorithm called Kernel Proportionate Affine Projection Algorithm (KPAPA) is proposed. It is proved that the additional computational increase burden is independent of the order of the algorithm, being dependent only on the order of the kernel expansion. The Dichotomous Coordinate Descent (DCD) method and an example of an efficient implementation of KAPA using DCD are presented. This chapter also discusses the influence of the coherence value, the step size value, and the dictionary size on the performance of KAPA and KPAPA algorithms. The effectiveness of the proposed algorithms and the effect of different parameters are confirmed by computer simulations for nonlinear system identification application.