Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 148461, 18 pages
http://dx.doi.org/10.5402/2011/148461
Research Article

Quadratic Filtering Algorithm Based on Covariances Using Correlated Uncertain Observations Coming from Different Sensors

1Departamento de Estadística, Universidad de Jaén, Paraje Las Lagunillas, 23071 Jaén, Spain
2Departamento de Estadística, Universidad de Granada, Avda, Fuentenueva, 18071 Granada, Spain

Received 29 March 2011; Accepted 1 May 2011

Academic Editors: I. K. Argyros and X. Zhang

Copyright © 2011 R. Caballero-Águila et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The least-squares quadratic estimation problem of signals from observations coming from multiple sensors is addressed when there is a nonzero probability that each observation does not contain the signal to be estimated. We assume that, at each sensor, the uncertainty about the signal being present or missing in the observation is modelled by correlated Bernoulli random variables, whose probabilities are not necessarily the same for all the sensors. A recursive algorithm is derived without requiring the knowledge of the signal state-space model but only the moments (up to the fourth-order ones) of the signal and observation noise, the uncertainty probabilities, and the correlation between the variables modelling the uncertainty. The estimators require the autocovariance and cross-covariance functions of the signal and their second-order powers in a semidegenerate kernel form. The recursive quadratic filtering algorithm is derived from a linear estimation algorithm for a suitably defined augmented system.