Abstract:The development of the kernel recursive least squares (KRLS) algorithm, popular with the fastest convergence rate and best filtering accuracy in kernel adaptive filters (KAFs), is limited by the linear growing structure and enormous computational complexity. To alleviate these issues, KRLS with the Nystr?m method (NysKRLS) based on probability density rank-based quantization sampling (NysKRLS-PRQ) has been proposed to alleviate the complexity of KRLS at the cost of decreasing accuracy. To further improve the accuracy of NysKRLS-PRQ, we propose KRLS with nearest PRQ Nystr?m method (NNKRLS-PRQ) algorithm was proposed. The input vectors of NNKRLS-PRQ in the feature space are organized by p disjoint clusters. According to the distribution situation of input vectors and the confidence probability of the Gaussian kernel, NNKRLS-PRQ adaptively chooses proper samples selected from the corresponding cluster to project the input vector. The simulations prove the superiorities of NKMNKRLS.