Quaternion-Valued Adaptive Filtering via Nesterov’s Extrapolation

A new quaternion-valued adaptive filtering algorithm based on extrapolated weight methods is proposed. The proposed algorithm belongs to the class of conjugate direction algorithms [1]. This class of extrapolation (momentum) based algorithms is preferred to RLS-based algorithms when the matrix inversion should be avoided, e.g. in the case of non-vector signals, sparse signals or non-stationary signals. This paper introduces Nesterov's optimal gradient methods in widely linear quaternion adaptive filtering. The resulting class of algorithm is shown to both have similar computational complexity and comparable performance to WLQRLS; however, the proposed method is more stable and outperforms WLQRLS in the non-stationary case.