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Optimal linear estimators for systems with random measurement delays

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Abstract

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.

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Authors and Affiliations

  1. School of Electronic Engineering, Heilongjiang University, Harbin Heilongjiang, 150080, China

    Shuli Sun & Tian Tian

Authors
  1. Shuli Sun
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  2. Tian Tian
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Corresponding author

Correspondence to Shuli Sun.

Additional information

This work was supported by the Natural Science Foundation of China (No. 60874062), the Program for New Century Excellent Talents in University (No. NCET-10-0133) and that in Heilongjiang Province (No.1154-NCET-01).

Shuli SUN received his B.S. degree in Department of Mathematics and M.E. degree in Department of Automation from Heilongjiang University, China, in 1996 and 1999, respectively. He received his Ph.D. degree in School of Astronautics from Harbin Institute of Technology, China, in 2004. He is a research fellow in Nanyang Technological University, Singapore, from 2006 to 2007. Since 2006, he has been a professor in the School of Electronic Engineering of Heilongjiang University, China. His research interests are in the areas of state estimation, signal processing, information fusion and sensor network.

Tian TIAN received her B.E. degrees in Communication from Jilin University of Technology in 2004, and M.E. degree in Control Theory and Control Engineering from Heilongjiang University, China, in 2010. Her research interests include state estimation and time delay systems.

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Sun, S., Tian, T. Optimal linear estimators for systems with random measurement delays. J. Control Theory Appl. 9, 76–82 (2011). https://doi.org/10.1007/s11768-011-0244-7

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  • DOI: https://doi.org/10.1007/s11768-011-0244-7

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