Both the minimum error entropy (MEE) and mixture MEE (MMEE) are extensively employed in distributed adaptive filters, exhibiting their robustness against non-Gaussian noise by capturing high-order statistical information from network data. However, the fixed shape of the Gaussian kernel function existing in MEE and MMEE restricts their flexibility, leading to reduced robustness and deteriorated performance. To address this issue, a novel diffusion generalized minimum total error entropy (DGMTE) algorithm is first proposed in this letter, using a generalized MEE criterion to significantly improve the performance of error-in-variables models-based algorithms under non-Gaussian noise. Moreover, as a special case of DGMTE, a generalized minimum total error entropy (GMTE) algorithm is also proposed, and the local convergence analysis of DGMTE is given. Finally, simulations show the superiorities of DGMTE in comparison with other representative algorithms.

Quaternion adaptive filters (QAFs) are extensively used in processing three- or four-dimensional signals effectively. However, their performance can significantly deteriorate or even diverge when system inputs and outputs are contaminated by complex noises. Therefore, this letter addresses the issue of parameter estimation in the quaternion errors-in-variables (QEIV) in asymmetric noise. First, a novel robust criterion, called improved quaternion minimum error entropy criterion with fiducial points (IQMEEF), is constructed. Then, a minimum total quaternion error entropy algorithm with fiducial points (MTQEEF) is proposed by integrating the IQMEEF criterion with the total least squares (TLS) method, leveraging stochastic gradient and quaternion generalized Hamilton-real (GHR) calculus theory. Finally, simulations validate the superior performance of MTQEEF in the QEIV model under asymmetric noise environments.