Kernel Least Mean Square Algorithm with Shrinkage Variable Step Size Approach

A novel kernel least mean square algorithm (KLMS) that uses a shrinkage variable step size is developed. In traditional KLMS, the step size is usually set a constant value for different cases, and this fixed step size methodology leads to undesirable performance in general. To address this problem, a variable step size is obtained by minimizing the energy of the noise-free a posteriori error signal which is obtained by using a known - minimization formulation. According to this approach, a shrinkage KLMS (SKLMS) algorithm is proposed. The SKLMS algorithm outperforms the original KLMS algorithm in terms of the steady-state misalignment. Simulation results show that the proposed algorithm display outstanding performance in chaos time series prediction and nonlinear system identification in terms of testing MSE as compared to the traditional LMS, KLMS, shrinkage LMS, affine projection(AP), and shrinkage AP algorithms.