Kernel adaptive filters implement a nonlinear transfer function using kernel methods. In these methods, the signal is mapped to a high-dimensional linear feature space, a reproducing kernel Hilbert space (RKHS), and a nonlinear function is approximated as a sum over kernels, whose domain is the RKHS. If this is done in a universal reproducing kernel, e.g. Gaussian kernel, a kernel method can be a universal approximator for a nonlinear function. Kernel methods have the advantage of having convex loss functions, with no local minima, and of being only moderately complex to implement.

In this project, different adaptive kernel filtering algorithms are developed. These algorithms are widely applied in the regression problem, such as the function estimation, and the chaotic time-series prediction, e.g. Lorenz time-series prediction.