Available online at www.sciencedirect.com Journal of the Franklin Institute 350 (2013) 598–616 Optimal state estimation over communication channels with random delays Magdi S. Mahmoud a,n , Bo Liu b a Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia b Computer, Electrical and Mathematical Science & Engineering Department, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia Received 24 April 2012; received in revised form 11 November 2012; accepted 19 December 2012 Available online 29 January 2013 Abstract This paper is concerned with the optimal estimation of linear systems over unreliable communication channels with random delays. The measurements are delivered without time stamp, and the probabilities of time delays are assumed to be known. Since the estimation is time-driven, the actual time delays are converted into virtual time delays among the formulation. The receiver of estimation node stores the sum of arrived measurements between two adjacent processing time instants and also counts the number of arrived measurements. The original linear system is modeled as an extended system with uncertain observation to capture the feature of communication, then the optimal estimation algorithm of systems with uncertain observations is proposed. Additionally, a numerical simulation is presented to show the performance of this work. & 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. 1. Introduction It is assumed that the measurements to be processed are transmitted without delay and drop in classical estimation theory [1,2]. However, many applications developed in recent years have incurred unreliable delivery of signals, thus corresponding communication constraints should be considered in system design, for example, finite bandwidth constraints [3], time delay and clock asynchronism constraints [4]. The most popular www.elsevier.com/locate/jfranklin 0016-0032/$32.00 & 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfranklin.2012.12.021 n Corresponding author. Tel.: þ966 542019258; fax: þ966 38602965. E-mail addresses: magdim@yahoo.com, msmahmoud@kfupm.edu.sa (M.S. Mahmoud), bo.liu.777@gmail.com (B. Liu).