Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 258065, 18 pages
Research Article

A New Estimation Algorithm from Measurements with Multiple-Step Random Delays and Packet Dropouts

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

Received 18 November 2009; Accepted 24 February 2010

Academic Editor: Jyh Horng Chou

Copyright © 2010 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 least-squares linear estimation problem using covariance information is addressed in discrete-time linear stochastic systems with bounded random observation delays which can lead to bounded packet dropouts. A recursive algorithm, including the computation of predictor, filter, and fixed-point smoother, is obtained by an innovation approach. The random delays are modeled by introducing some Bernoulli random variables with known distributions in the system description. The derivation of the proposed estimation algorithm does not require full knowledge of the state-space model generating the signal to be estimated, but only the delay probabilities and the covariance functions of the processes involved in the observation equation.