Application of Quaternion Series Expansion to the Estimation Problem

• Activity Number: 416
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Rosa Fernandez Alcala*+ and Jesus Navarro-Moreno and Juan Carlos Ruiz-Molina
• Companies: University of Jaen and University of Jaen and University of Jaen
• Keywords: linear estimation ; quaternion signals ; series representations ; widely linear processing

Abstract

Series representation for stochastic processes has been widely used to address different estimation problems. In this context, widely linear series expansions are considered to provide a linear estimation for a quaternion signal. This type of signal is a non-commutative expansion of complex signals composed by a scalar real part and a vectorial (three vector) imaginary part, given a unified mean to process three and four- dimensional signals. For a complete second-order description of a quaternion signal, not only correlation information must be taken into account but also the information provided by the complementary correlation functions. In this sense, widely linear series expansions, based on augmented statistics, suppose a useful tool in estimation problem. In particular, a quaternion Karhunen-Loève (doubly orthogonal) expansion is considered here for estimating a functional of a quaternion signal from noisy observations.