Hybrid affine projection algorithm

In this work, we put forward a new adaptation criterion, namely the hybrid criterion (HC), which is a mixture of the traditional mean square error (MSE) and the maximum correntropy criterion (MCC). The HC criterion is developed from the viewpoint of the least trimmed squares (LTS) estimator, a high breakdown estimator that can avoid undue influence from outliers. In the LTS estimator, the data are divided (by ranking) into two categories: the normal data and the outliers, and the outlier data are purely discarded. In order to improve the robustness of the LTS, some data with large values, which may contain some useful information, are also thrown away. Instead of purely throwing away those data, the new criterion applies the robust MCC criterion on the large data, and hence can efficiently utilize them to further improve the performance. We apply the HC criterion to adaptive filtering and develop the hybrid affine projection algorithm (HAPA) and kernel hybrid affine projection algorithm (KHAPA). Simulation results show that the proposed algorithms perform very well.