Prediction of wide-sense stationary quaternion random signals

An efficient widely linear prediction algorithm is introduced for the class of wide-sense stationary quaternion signals. Specifically, using second order statistics information in the quaternion domain, a multivariate Durbin–Levison-like algorithm is derived. The proposed solution can be applied under a very general formulation of the problem, allowing for the estimation of a function of the quaternion signal which is observed through a system with both additive/multiplicative noises.

► A prediction algorithm is given for wide sense stationary quaternion random signals.
► The formulation is very general and includes a great variety of estimation problems.
► The proposed methodology is based on a widely linear processing.
► Simulations on both synthetic and real-world data support our approach.