Online Learning Algorithms for Quaternion ARMA Model

In recent years, quaternion algebra has attracted considerable attention in the signal processing community. As a natural representation of 3D and 4D signals, quaternion allows for a reduction in the number of parameters and operations involved, and can bring insights that would not be acquired by real-and complexvalued representations. Due to these elegant properties, quaternion adaptive signal processing algorithms have developed rapidly and have achieved satisfactory performance in a wide range of applications [1]-[8]. Despite the existence of many quaternion algorithms, we notice that so far, there is no learning algorithm for the ARMA model in the quaternion domain.