中文摘要：

在在线非线性自适应滤波应用中，由于基于多核学习的算法具有更高自由度并且能够利用更多数据特征，相比基于单核学习的算法在性能上有很大提升。首先给出具有相同“字典”的多核仿射投影算法，该算法是多核学习方法和仿射投影算法的结合。然后基于相干准则针对多核仿射投影算法的特例，对应不同高斯核带宽，利用相干稀疏准则构造不同“字典”，提出利用自适应 l1-范数正则项来解决归一化多核最小均方非线性自适应滤波算法在非平稳信号下“字典”存在冗余核函数的问题。最后数值仿真结果与比较验证了所提算法的有效性。

英文摘要：

The performance of the multi-kernel learning algorithm possesses higher degree of freedom and uses more features of data,which outperforms the mono-kernel methods in online nonlinear adaptive filtering applications.The multi-kernel affine projection algorithm with the same dictionary is presented,which is an umbrella of multiple-kernel learning and affine projection methods.As the particular case of multi-kernel affine projection building almost distinct dictionary corresponding to different Gaussian kernel band-widths based on coherence sparsification critera,multi-kernel normalized least-mean-square with adaptive l 1-norm regularization for update of dictionary is also proposed to overcome the drawback that the obsolete kernel functions cannot be discarded in non-stationary environment.Simulation results show the effectiveness of the proposed methods.