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Title: Estimation recursive algorithms of hypercomplex signals from delayed observations Authors:  Jose Domingo Jimenez-Lopez - University of Jaen (Spain) [presenting]
Jesus Navarro-Moreno - University of Jaen (Spain)
Abstract: In many practical situations, as in communication mechanisms, robots, signal detectors, electronic devices, among others, intermittent failures in the signal transmission occur, and this fact causes errors in the observations. The state-space model staying within these situations includes Bernoulli random variables in the observation equation, which allows us to approach uncertain, delayed or lost observations. We study the one or two steps delayed observations case, that is, at each instant of time, every quaternion component of the available observation can coincide with the corresponding component of the real observation, or be delayed one or two sampling periods. Moreover, recently many real situations in fields as signal and image processing, quantum and orbital mechanics, graphics computer, attitude control or robotics, among others, are modelled by quaternion signals, because they need orientation and rotation characteristics to be modelled. We approach the linear processing of quaternion signals from delayed observations, proposing recursive algorithms for different estimation problems and considering the complete quaternion, that is, the real component with its three involutions.