Maximum Total Quaternion Generalized Correntropy Adaptive Filtering

Quaternion adaptive filters have been widely used in processing three-dimensional (3-D) and 4-D signals. To improve the filtering performance of quaternion adaptive filtering algorithms when both the input and output signals are disturbed by non-Gaussian noises, this brief addresses the issue of quaternion parameter estimation in the quaternion errors-in-variables (QEIV) model. First a novel maximum total quaternion generalized correntropy (MTQGC) criterion is proposed to resist non-Gaussian noises. And the stochastic gradient method is used to implement the quaternion parameter estimation. Then, combined with the total least squares (TLS) method, an MTQGC algorithm is proposed using quaternion generalized Hamilton-real (GHR) calculus. Moreover, the convergence condition of the proposed MTQGC algorithm is obtained. Finally, simulations demonstrate the improved filtering performance in the QEIV model.