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Title: A widely linear system for quaternion estimation Authors:  Juan Carlos Ruiz-Molina - University of Jaen (Spain) [presenting]
Jesus Navarro-Moreno - University of Jaen (Spain)
Rosa Maria Fernandez-Alcala - University of Jaen (Spain)
Jose Domingo Jimenez-Lopez - University of Jaen (Spain)
Abstract: A Karhunen-Loeve series expansion is presented for quaternion representation and its potential application in the quaternion MMSE estimation problem is shown. The optimal implementation of the technique needs the computation of the true eigenvalues and eigenfunctions of an integral equation. This task can be very involved and sometimes even impossible. We avoid this shortcoming solving numerically the integral equation involved via the Rayleigh-Ritz method. Then the resulting approximate series expansion is used to propose a new form of the estimator. A numerical example illustrates the performance of the suggested solution.