About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 716915, 14 pages
http://dx.doi.org/10.1155/2013/716915
Research Article

Adaptive Kalman Estimation in Target Tracking Mixed with Random One-Step Delays, Stochastic-Bias Measurements, and Missing Measurements

School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

Received 5 November 2013; Accepted 21 November 2013

Academic Editor: Lifeng Ma

Copyright © 2013 Sujuan Chen 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.

Linked References

  1. A. Farina, B. Ristic, and L. Timmoneri, “Cramér-Rao bound for nonlinear filtering with Pd< 1 and its application to target tracking,” IEEE Transactions on Signal Processing, vol. 50, no. 8, pp. 1916–1924, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  2. S. Nakamori, R. Caballero-Águila, A. Hermoso-Carazo, and J. Linares-Pérez, “New design of estimators using covariance information with uncertain observations in linear discrete-time systems,” Applied Mathematics and Computation, vol. 135, no. 2-3, pp. 429–441, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan, and S. S. Sastry, “Kalman filtering with intermittent observations,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1453–1464, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  4. Z. Wang, D. W. C. Ho, and X. Liu, “Variance-constrained control for uncertain stochastic systems with missing measurements,” IEEE Transactions on Systems, Man, and Cybernetics A, vol. 35, no. 5, pp. 746–753, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Yang, G. Feng, and J. Ren, “A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems,” IEEE Transactions on Systems, Man and Cybernetics A, vol. 34, no. 3, pp. 406–420, 2004. View at Publisher · View at Google Scholar
  6. S. Nakamori, R. Caballero-Águila, A. Hermoso-Carazo, and J. Linares-Pérez, “Recursive estimators of signals from measurements with stochastic delays using covariance information,” Applied Mathematics and Computation, vol. 162, no. 1, pp. 65–79, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Variance-constrained H filtering for a class of nonlinear time-varying systems with multiple missing measurements: the finite-horizon case,” IEEE Transactions on Signal Processing, vol. 58, no. 5, pp. 2534–2543, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. Kluge, K. Reif, and M. Brokate, “Stochastic stability of the extended Kalman filter with intermittent observations,” IEEE Transactions on Automatic Control, vol. 55, no. 2, pp. 514–518, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  9. Y. Mo and B. Sinopoli, “A characterization of the critical value for Kalman filtering with intermittent observations,” in Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08), pp. 2692–2697, Cancun, Mexico, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Moayedi, Y. K. Foo, and Y. C. Soh, “Adaptive Kalman filtering in networked systems with random sensor delays, multiple packet dropouts and missing measurements,” IEEE Transactions on Signal Processing, vol. 58, no. 3, pp. 1577–1588, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  11. Y. Che, H. Shu, and X. Kan, “Estimation for stochastic nonlinear systems with randomly distributed time-varying delays and missing measurements,” Mathematical Problems in Engineering, vol. 2012, Article ID 890512, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Jinling, W. Zidong, and L. Xiaohui, “Robust state estimation for two-dimensional stochastic time-delay systems with missing measurements and sensor saturation,” Multidimensional Systems and Signal Processing, 2012. View at Publisher · View at Google Scholar
  13. L. Li and Y. Xia, “Stochastic stability of the unscented Kalman filter with intermittent observations,” Automatica, vol. 48, no. 5, pp. 978–981, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. Dong, Z. Wang, and H. Gao, “Distributed filtering for a class of time-varying systems over sensor networks with quantization errors and successive packet dropouts,” IEEE Transactions on Signal Processing, vol. 60, no. 6, pp. 3164–3173, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  15. R. Niu, P. Willett, and Y. Bar-Shalom, “Matrix CRLB scaling due to measurements of uncertain origin,” IEEE Transactions on Signal Processing, vol. 49, no. 7, pp. 1325–1335, 2001. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Farina, L. Timmoneri, S. Immediata, and B. Ristic, “CRLB with Pd< 1 fused tracks,” in Proceedings of the 8th International Conference on Information Fusion (FUSION '05), pp. 191–196, July 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Boers and H. Driessen, “Results on the modified Riccati equation: target tracking applications,” IEEE Transactions on Aerospace and Electronic Systems, vol. 42, no. 1, pp. 379–384, 2006. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Boers and H. Driessen, “Modified Riccati equation and its application to target tracking,” IEE Proceedings: Radar, Sonar and Navigation, vol. 153, no. 1, pp. 7–12, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Zhang, Q. Chen, H. Yan, and J. Liu, “Robust H filtering for switched stochastic system with missing measurements,” IEEE Transactions on Signal Processing, vol. 57, no. 9, pp. 3466–3474, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  20. A. Censi, “Kalman filtering with intermittent observations: convergence for semi-Markov chains and an intrinsic performance measure,” IEEE Transactions on Automatic Control, vol. 56, no. 2, pp. 376–381, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  21. H. Dong, Z. Wang, and H. Gao, “Distributed H filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4665–4672, 2013. View at Publisher · View at Google Scholar
  22. A. Ray, L. W. Liou, and J. H. Shen, “State estimation using randomly delayed measurements,” Journal of Dynamic Systems, Measurement and Control, vol. 115, no. 1, pp. 19–26, 1993. View at Scopus
  23. J. Nilsson, B. Bernhardsson, and B. Wittenmark, “Stochastic analysis and control of real-time systems with random time delays,” Automatica, vol. 34, no. 1, pp. 57–64, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Z. Wang, F. Yang, D. W. C. Ho, and X. Liu, “Robust H filtering for stochastic time-delay systems with missing measurements,” IEEE Transactions on Signal Processing, vol. 54, no. 7, pp. 2579–2587, 2006. View at Publisher · View at Google Scholar · View at Scopus
  25. F. Yang, Z. Wang, G. Feng, and X. Liu, “Robust filtering with randomly varying sensor delay: the finite-horizon case,” IEEE Transactions on Circuits and Systems I, vol. 56, no. 3, pp. 664–672, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  26. X. Wang, Q. Pan, Y. Liang, and F. Yang, “Gaussian smoothers for nonlinear systems with one-step randomly delayed measurements,” IEEE Transactions on Automatic Control, vol. 58, no. 7, pp. 1828–1835, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  27. S. Elmadssia, K. Saadaoui, and M. Benrejeb, “New delay-dependent stability conditions for linear systems with delay,” Systems Science and Control Engineering, vol. 1, no. 1, pp. 2–11, 2013.
  28. A. T. Alouani, P. Xia, T. R. Rice, and W. D. Blair, “A two-stage Kalman estimator for state estimation in the presence of random bias and for tracking maneuvering targets,” in Proceedings of the 30th IEEE Conference on Decision and Control, pp. 2059–2062, December 1991. View at Scopus
  29. J. Y. Keller and M. Darouach, “Optimal two-stage Kalman filter in the presence of random bias,” Automatica, vol. 33, no. 9, pp. 1745–1748, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  30. M. Ignagni, “Optimal and suboptimal separate-bias Kalman estimators for a stochastic bias,” IEEE Transactions on Automatic Control, vol. 45, no. 3, pp. 547–551, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. B. Xu and Z. Wang, “Biased bearings-only parameter estimation for bistatic system,” Journal of Electronics, vol. 24, no. 3, pp. 326–331, 2007. View at Publisher · View at Google Scholar · View at Scopus
  32. B. Xu, Z. Wu, and Z. Wang, “On the Cramér-Rao lower bound for biased bearings-only maneuvering target tracking,” Signal Processing, vol. 87, no. 12, pp. 3175–3189, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. X. He and D. Zhou, “Robust H-infinity filtering for time-delay systems with missing measurements: a parameter-dependent approach,” Journal of Control Theory and Applications, vol. 5, no. 4, pp. 336–344, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  34. S. Sun, “Optimal linear filters for discrete-time systems with randomly delayed and lost measurements with/without time stamps,” IEEE Transactions on Automatic Control, vol. 58, no. 6, pp. 1551–1556, 2013. View at Publisher · View at Google Scholar · View at MathSciNet