Optimal Centralized, Recursive, and Distributed Fusion for Stochastic Systems with Coupled Noises

  • Hongbin MaEmail author
  • Liping Yan
  • Yuanqing Xia
  • Mengyin Fu


In this chapter, optimal state estimation for linear systems is introduced, where the noises of different sensors are cross-correlated and also coupled with the system noise of the previous step. The main result is that the optimal linear estimation is generated in recursive form (Optimal Recursive Fusion: ORF) and distributed fusion (Optimal Distributed Fusion: ODF). They are both compared with the optimal batch fusion (OBF) algorithm by use of many measures, besides the traditional statistical estimation error and the trace of the estimation error covariances, some measures related to the normalized estimation error square or the Mahalanobis distance are introduced and analyzed. Simulation on a target tracking example is done to show the effectiveness of the presented algorithms and to illustrate the usefulness of the novel measure indices.


  1. 1.
    X.R. Li, Y.M. Zhu, J. Wang, C.Z. Han, Optimal linear estimation fusion-part 1: unified fusion rules. IEEE Trans. Inf. Theory 49(9), 2192–2208 (2003)CrossRefGoogle Scholar
  2. 2.
    Y. Bar-Shalom, Multitarget-Multisensor Tracking: Advanced Applications (Artech House, Norwood, 1990)Google Scholar
  3. 3.
    C.Y. Chong, K.C. Chang, S. Mori, Distributed tracking in distributed sensor networks (1986), pp. 1863–1868Google Scholar
  4. 4.
    Z.S. Duan, X.R. Li, Lossless linear transformation of sensor data for distributed estimation fusion. IEEE Trans. Signal Process. 59(1), 362–372 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    E.B. Song, Y.M. Zhu, J. Zhou, Z.S. You, Optimal Kalman filtering fusion with cross-correlated sensor noises. Automatica 43(8), 1450–1456 (2007)MathSciNetCrossRefGoogle Scholar
  6. 6.
    X.R. Li, Optimal linear estimation fusion-part vii: dynamic systems (2003), pp. 455–462Google Scholar
  7. 7.
    Z.S. Duan, C.Z. Han, T. Tao, Optimal multi-sensor fusion target tracking with correlated measurement noises. IEEE Int. Conf. Syst. Man Cybern. 2, 1272–1278 (2004)Google Scholar
  8. 8.
    Z.S. Duan, X.R. Li, The optimality of a class of distributed estimation fusion algorithm (2008), pp. 1–6Google Scholar
  9. 9.
    J.K. Uhlmann, General data fusion for estimates with unknown cross covariances (1996), pp. 536–547Google Scholar
  10. 10.
    C.Y. Chong, S. Mori, Convex combination and covariance intersection algorithms in distributed fusion (2001), pp. WeA2.11–WeA2.18Google Scholar
  11. 11.
    Y.M. Wang, X.R. Li, Distributed estimation fusion with unavailable cross-correlation. IEEE Trans. Aerosp. Electron. Syst. 48, 259–278 (2012)CrossRefGoogle Scholar
  12. 12.
    S. Sun, Z. Deng, Multi-sensor optimal information fusion Kalman filter. Automatica 40(6), 1017–1023 (2004)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Z.S. Duan, C.Z. Han, Discrete-time linear estimation with correlated noises. Syst. Eng. Electron. 27, 792–794 (2005)Google Scholar
  14. 14.
    Y. Bar-Shalom, X. Li, T. Kirubarajan, Estimation with Applications to Tracking and Navigation: Theory Algorithms and Software (Wiley, New York, 2001)CrossRefGoogle Scholar
  15. 15.
    X.R. Li, Recursibility and optimal linear estimation and filtering, in 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas, 14–17 Dec 2004, pp. 1761–1766Google Scholar
  16. 16.
    Y. Bar-Shalom, K. Birmiwal, Consistency and robustness of pdaf for target tracking in cluttered environments. Automatica 19(4), 431–437 (1983)CrossRefGoogle Scholar
  17. 17.
    X.R. Li, Z.L. Zhao, X.B. Li, Evaluation of estimation algorithms-II: credibility tests. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 42(1), 147–163 (2012)Google Scholar
  18. 18.
    J.H. Stapleton, Linear Stochastical Models (Wiley, New York, 1995)CrossRefGoogle Scholar

Copyright information

© Science Press 2020

Authors and Affiliations

  • Hongbin Ma
    • 1
    Email author
  • Liping Yan
    • 1
  • Yuanqing Xia
    • 1
  • Mengyin Fu
    • 1
  1. 1.School of AutomationBeijing Institute of TechnologyBeijingChina

Personalised recommendations