Departamento de Estadística e Investigación Operativa
URI permanente para esta comunidadhttps://hdl.handle.net/10953/30
En esta Comunidad se recogen los documentos generados por el Departamento de Estadística e Investigación Operativa y que cumplen los requisitos de Copyright para su difusión en acceso abierto.
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Examinando Departamento de Estadística e Investigación Operativa por Autor "Fernández Alcalá, Rosa Mª"
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Ítem Biased Regression Algorithms in the Quaternion Domain(Elsevier, 2024) Ruiz Molina, Juan Carlos; Navarro Moreno, Jesús; Fernández Alcalá, Rosa Mª; Jiménez López, José D.The ill-conditioned matrix problem in quaternion linear regression models is addressed in this paper and several dimension-reduction based regression methods for circumventing this problem are suggested. The algorithms are formulated in a general way and can be easily adapted to different scenarios: widely linear, semi-widely linear and strictly linear processing, in accordance with the properness properties presented by quaternion random vectors. A comparison with existing solutions is carried out by using both laboratory data and a color face database.Ítem Proper Adaptive Filtering in Four-Dimensional Cayley-Dickson Algebras(Elsevier, 2023) Ruiz Molina, Juan Carlos; Navarro Moreno, Jesús; Fernández Alcalá, Rosa Mª; Jiménez López, José D.A family of hypercomplex algebras in four dimensions (4D) is proposed to devise adaptive filters. Such a family, called $\beta$-quaternions, has multiplication rules for the complex units that depend on a parameter $\beta$, and this family contains, as particular cases, both standard Hamilton quaternions and split quaternions. In this framework, two notions of properness for random vectors are introduced and their implications on the statistical processing involved are analyzed. Then, statistical tests to check properness in practice and a method to select the best algebra where the properness conditions could hold are provided. Also, proper adaptive filters are suggested and row and column updating problems are studied. The main advantage of the techniques proposed compared with the standard ones is that a notable reduction in the computational burden is achieved. Finally, simulation examples validate the proper adaptive filters and demonstrate that our scheme performs better than the traditional quaternion domain.Ítem Semi-Widely Linear Estimation Algorithms of Quaternion Signals with Missing Observations and Correlated Noises(Elsevier, 2020) Ruiz Molina, Juan Carlos; Navarro Moreno, Jesús; Fernández Alcalá, Rosa Mª; Jiménez López, José D.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.Ítem Widely Linear Estimation for Multisensor Quaternion Systems with Mixed Uncertainties in the Observations(Elsevier, 2019) Ruiz Molina, Juan Carlos; Navarro Moreno, Jesús; Fernández Alcalá, Rosa Mª; Jiménez López, José D.The optimal widely linear state estimation problem for quaternion systems with multiple sensors and mixed uncertainties in the observations is solved in a unified framework. For that, we devise a unified model to describe the mixed uncertainties of sensor delays, packet dropouts and uncertain observations by using three Bernoulli distributed quaternion random processes. The proposed model is valid for linear discrete-time quaternion stochastic systems measured by multiple sensors and it allows us to provide filtering, prediction and smoothing algorithms for estimating the quaternion state through a widely linear processing. Simulation results are employed to show the superior performance of such algorithms in comparison to standard widely linear methods when mixed uncertainties are present in the observations.