Wigner–Ville Distribution with Multiple Quaternion Correlations via the Offset Linear Canonical Transform

Statistical methods for quaternion enhancement, which are based on multiple quaternion correlations, have found extensive applications in areas such as unmanned aerial vehicle positioning and multiplicative noise removal. However, research on the Wigner-Ville distribution associated with the quaternionic offset linear canonical transform (WVD-QOLCT) fields only utilizes one quaternion correlation based on the conjugate of all imaginary parts of quaternions. In this study, to fully exploit the multiple correlations inherent in quaternions, we propose a novel Wigner–Ville distribution with multiple quaternion correlations via the offset linear canonical transform (WVD-QCOLCT), which introduces the multiple correlation characteristics of quaternions into the WVD-QOLCT. Subsequently, we derive some properties of the WVD-QCOLCT, such as the inverse, the relationship between multiple quaternion correlations in the WVD-QCOLCT, and the uncertainty principle. Finally, a detection algorithm for quaternion signals is proposed to evaluate the performance of the WVD-QCOLCT.