Title: A semi-widely linear prediction algorithm for stationary Gaussian quaternion signals
Authors: Rosa Maria Fernandez-Alcala - University of Jaen (Spain) [presenting]
Jesus Navarro-Moreno - University of Jaen (Spain)
Juan Carlos Ruiz-Molina - University of Jaen (Spain)
Jose Domingo Jimenez-Lopez - University of Jaen (Spain)
Abstract: The prediction problem in the quaternion domain is addressed under stationarity, Gaussianity and C-properness hypotheses. A very general formulation of the problem is considered allowing the estimation of any linear or nonlinear functional of the signal. In the proposed methodology, based on a semi-widely linear (SWL) processing, we first consider a SWL version of the Durbin-Levinson algorithm for the one-stage prediction problem. Then, a general recursive prediction algorithm is devised by incorporating the information supplied by the square vector of the observation quaternion process. The proposed solution presents the following advantages in relation to the conventional quaternion widely linear predictor: better performance, matrices with lower dimensions and efficiently implementable. The practical application of this SWL prediction algorithm is illustrated by means of a numerical example where a nonlinear functional of the signal is estimated.