Minimum Total Quaternion Error Entropy Filtering With Fiducial Points Against Asymmetric Noise

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.