Semi-Widely Linear Estimation Algorithms of Quaternion Signals with Missing Observations and Correlated Noises

Abstract

The paper deals with the estimation problem of a discrete-time vectorial quaternion signal which is observed through a linear dynamic system with intermittent observations and autocorrelated and cross-correlated noises. Under $\mathbb{C}^{\eta}$-properness conditions, a semi-widely linear processing is considered to provide filtering, fixed-point and fixed-lag smoothing algorithms for estimating the quaternion state. The proposed solutions give a substantial reduction in computational burden in relation to the widely linear estimation techniques, this benefit being impossible to be fully captured by using a real number framework. The feasibility and performance of the aforementioned algorithms are illustrated by means of simulation examples.