State estimation with delayed measurements incorporating time-delay uncertainty

State estimation with delayed measurements incorporating time-delay uncertainty

For access to this article, please select a purchase option:

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This study is concerned with the problem of state estimation using delayed measurements, especially when the delay is uncertain. In real-world applications, measurements are often randomly delayed, and hence not immediately available to the filter when taken by a sensor. By modelling uncertain delay as a probabilistic density function, the effect of uncertain delayed measurements is accounted for by the proposed estimator, combined with the augmented state Kalman filter. Use of the uncertain delay model resolves the randomness of the delay, and the augmentation is used to handle the delayed measurements. Consequently, the proposed algorithm is able to provide consistent estimates, regardless of the uncertainty of the delay. Monte Carlo simulations using one-dimensional particle were conducted with three kinds of representative uncertainty models, based on Gaussian, gamma and uniform distributions. The simulations verified the reliability and consistency of the proposed estimator.


    1. 1)
    2. 2)
      • Larsen, T.D., Andersen, N.A., Ravn, O., Poulsen, N.K.: `Incorporation of time delayed measurements in a discrete-time kalman filter', Proc. 37th IEEE Conf. Decision and Control, December 1998, Tampa, Florida, USA, p. 3972–3977.
    3. 3)
    4. 4)
    5. 5)
      • Zhang, K., Li, X.R., Zhu, Y.: `Optimal update with out-of-sequence measurements for distributed filtering', Proc. Fifth Int. Conf. Information Fusion, July 2002, Annapolis, MD, USA, p. 1519–1526.
    6. 6)
    7. 7)
      • van der Merwe, R., Wan, E.A., Julier, S.I.: `Sigma-point Kalman filters for nonlinear estimation and sensor-fusion – applications to integrated navigation –', Proc. AIAA Guidance, Navigation, and Control Conf. and Exhibit, August 2004, Providence, Rhode Island, USA, p. 16–19.
    8. 8)
      • Leonard, J.J., Rikoski, R.J.: Experimental Robotics VII, ser. Lecture notes in control and information sciences, 2001, 271, Chapter: Incorporation of delayed decision making into stochastic mapping, pp. 533–542.
    9. 9)
      • Y. Bar–Shalom , T.E. Fortmann . (1988) , ser. Mathematics in science and engineering.
    10. 10)
    11. 11)
      • Julier, S.J., Uhlmann, J.K.: `Fusion of time delayed measurements with uncertain time delays', Proc. 2005 American Control Conf., 8–10 June 2005, Portland, OR, USA, p. 4028–4033.
    12. 12)
    13. 13)
      • Chen, D., Fu, X., Ding, W., Li, H., Xi, N., Wang, Y.: `Shifted gamma distribution and long-range prediction of round trip time delay for internet-based teleoperation', Proc. 2008 IEEE Int. Conf. Robotics and Biomimetics, 21–26 February 2009, Bangkok, Thailand, p. 1261–1266.
    14. 14)
      • Choi, M., Choi, J., Park, J., Chung, W.K.: `State estimation with delayed measurements considering uncertainty of time delay', Proc. 2009 IEEE Int. Conf. Robotics and Automation, 12–17 May 2009, Kobe, Japan, p. 3987–3992.
    15. 15)
      • Raptis, P., Vitsas, V., Banchs, A., Paparrizos, K.: `Delay distribution analysis of IEEE 802.11 with variable packet length', Proc. IEEE 65th Vehicular Technology Conf., 22–25 April 2007, p. 830–834.
    16. 16)
      • Y. Bar–Shalom , X.R. Li , T. Kirubarajan . (2001) Estimation with applications to tracking and navigation: theory algorithms and software.
    17. 17)
      • Bailey, T., Nieto, J., Guivant, J., Stevens, M., Nebot, E.: `Consistency of the EKF-SLAM algorithm', Proc. 2006 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, 9–15 October 2006, Beijing, China, p. 3562–3568.

Related content

This is a required field
Please enter a valid email address