Li Wenling, Wang Zidong, Hu Jun, Du Junping, Sheng Weiguo
IEEE Trans Neural Netw Learn Syst. 2024 Mar;35(3):4339-4346. doi: 10.1109/TNNLS.2022.3199679. Epub 2024 Feb 29.
This brief is concerned with the problem of kernel adaptive filtering for a complex network. First, a coupled kernel least mean square (KLMS) algorithm is developed for each node to uncover its nonlinear measurement function by using a series of input-output data. Subsequently, an upper bound is derived for the step-size of the coupled KLMS algorithm to guarantee the mean square convergence. It is shown that the upper bound is dependent on the coupling weights of the complex network. Especially, an optimal step size is obtained to achieve the fastest convergence speed and a suboptimal step size is presented for the purpose of practical implementations. Besides, a coupled kernel recursive least square (KRLS) algorithm is further proposed to improve the filtering performance. Finally, simulations are provided to verify the validity of the theoretical results.
本简报关注复杂网络的核自适应滤波问题。首先，为每个节点开发了一种耦合核最小均方（KLMS）算法，通过一系列输入输出数据来揭示其非线性测量函数。随后，推导了耦合KLMS算法步长的上界，以保证均方收敛。结果表明，该上界取决于复杂网络的耦合权重。特别地，获得了一个最优步长以实现最快的收敛速度，并提出了一个次优步长用于实际应用。此外，进一步提出了一种耦合核递归最小二乘（KRLS）算法以提高滤波性能。最后，通过仿真验证了理论结果的有效性。
