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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 958474, 13 pages
Research Article

Covariance-Based Estimation from Multisensor Delayed Measurements with Random Parameter Matrices and Correlated Noises

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

Received 18 March 2014; Revised 30 April 2014; Accepted 19 May 2014; Published 16 June 2014

Academic Editor: Suiyang Khoo

Copyright © 2014 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.


The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems subject to randomly delayed measurements with different delay rates. For each sensor, a different binary sequence is used to model the delay process. The measured outputs are perturbed by both random parameter matrices and one-step autocorrelated and cross correlated noises. Using an innovation approach, computationally simple recursive algorithms are obtained for the prediction, filtering, and smoothing problems, without requiring full knowledge of the state-space model generating the signal process, but only the information provided by the delay probabilities and the mean and covariance functions of the processes (signal, random parameter matrices, and noises) involved in the observation model. The accuracy of the estimators is measured by their error covariance matrices, which allow us to analyze the estimator performance in a numerical simulation example that illustrates the feasibility of the proposed algorithms.