核递归最小二乘(KRLS, kernel recursive least squares)算法以其快速的收敛速度和较高的滤波精度等优点而闻名于核自适应滤波器(KAFs, kernel adaptive filters)的算法中，然而其发展却受到线性增长结构和巨大计算复杂度的限制。为了缓解这些问题，基于概率密度秩量化取样的Nystr?m的核递归最小二乘方法(NysKRLS-PRQ, kernel recursive least squares with the Nystr?m method based on probability density rank-based quantization sampling)被提出，该算法以牺牲一定的滤波精度为代价来降低KRLS的计算复杂度。为进一步提高NysKRLS-PRQ的滤波精度，提出了基于最近中心PRQ取样Nystr?m方法的核递归最小二乘(NNKRLS-PRQ, kernel recursive least squares with nearest PRQ Nystr?m method)算法。在NNKRLS-PRQ中，特征空间中的输入向量被分为 个不相交的簇。根据输入向量的分布情况以及高斯核函数的置信概率，NNKRLS-PRQ能够自适应地从对应的簇中选择合适的样本来映射输入向量。通过仿真实验证明了NNKRLS-PRQ算法的优越性。

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.

TN911.7

国家自然科学(62071391)；重庆市自然科学(cstc2020jcyj-msxmX0234)；中央高校基本科研业务费(2020jd001)。