A novel robust frequency domain widely linear quaternion adaptive filtering algorithm

Abstract

This paper proposes a novel robust frequency-domain widely linear quaternion adaptive filtering algorithm (QGMFD) based on the hyperbolic tangent Geman-McClure function, which is designed to remove outliers from the dataset within the hyperbolic tangent framework. The algorithm significantly reduces the interference of impulsive noise on the system and effectively addresses the performance degradation of traditional frequency-domain widely linear quaternion adaptive filters (FDAF) when processing colored input signals in an impulsive noise environment. Additionally, a theoretical analysis of the proposed QGMFD is provided, and its computational complexity is compared with that of other algorithms. Finally, the simulation results for system identification and prediction demonstrate that the proposed QGMFD outperforms other algorithms in processing colored signals under impulsive noise.