Science in China Series F: Information Sciences

, Volume 47, Issue 6, pp 728–740 | Cite as

Linear minimum variance estimation fusion



This paper shows that a general multisensor unbiased linearly weighted estimation fusion essentially is the linear minimum variance (LMV) estimation with linear equality constraint, and the general estimation fusion formula is developed by extending the Gauss-Markov estimation to the random parameter under estimation. First, we formulate the problem of distributed estimation fusion in the LMV setting. In this setting, the fused estimator is a weighted sum of local estimates with a matrix weight. We show that the set of weights is optimal if and only if it is a solution of a matrix quadratic optimization problem subject to a convex linear equality constraint. Second, we present a unique solution to the above optimization problem, which depends only on the covariance matrix C k . Third, if a priori information, the expectation and covariance, of the estimated quantity is unknown, a necessary and sufficient condition for the above LMV fusion becoming the best unbiased LMV estimation with known prior information as the above is presented. We also discuss the generality and usefulness of the LMV fusion formulas developed. Finally, we provide an off-line recursion of C k for a class of multisensor linear systems with coupled measurement noises.


fusion distributed estimation linear minimum variance estimation 


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  1. 1.
    Bar-Shalom, Y., On the track-to-track correlation problem, IEEE Trans. Automatic Control, 1981, AC-26: 571–572.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bar-Shalom, Y., The effect of the common process noise on the two-sensor fused-track covariance, IEEE Trans. Aerospace and Electronic Systems, 1986, AES-22: 803–805.CrossRefGoogle Scholar
  3. 3.
    Bar-Shalom, Y. (ed.), Multitarget-Multisensor Tracking: Advanced Applications, Vol. 1 and Vol. 2, Norwood, MA: Atech House, 1990, 1992.Google Scholar
  4. 4.
    Chong, C. Y., Chang, K. C., Mori, S., Distributed tracking in distributed sensor networks, in Proc. 1986 American Control Conf., Seattle, WA, 1986.Google Scholar
  5. 5.
    Chong, C. Y., Chang, K. C., Mori, S., Tracking multiple targets with distributed acoustic sensors, in Proc. 1987 American Control Conf., Minneapolis, MN, 1987.Google Scholar
  6. 6.
    Chong, C. Y., Mori, S., Chang, K. C., Distributed multitarget multisensor tracking, in Multitarget-Multisensor Tracking: Advanced Applications (ed. Bar. Shalom, Y.), Vol. 1, Norwood, MA: Atech House, 1990.Google Scholar
  7. 7.
    Hashmipour, H. R., Roy, S., Laub, A. J., Decentralized structure for parallel Kalman filtering, IEEE Transactions on Automatic Control, 1988, 33(1): 88–93.CrossRefGoogle Scholar
  8. 8.
    Bar-Shalom, Y., Li, X. R., Multitarget-multisensor tracking: Principles and techniques, Storrs, CT: YBS Publishing, 1995.Google Scholar
  9. 9.
    Bjorck, A., Numerical Methods for Least Squares Problems, Philadelphia, PA: SIAM, 1996.Google Scholar
  10. 10.
    Lawson, C. L., Hanson, R. J., Solving Least Squares Problems, Philadelphia, PA: SIAM, 1995.MATHGoogle Scholar
  11. 11.
    Wismer, D. A., Chattergy, R., Introduction to Nonlinear Optimization, New York: Elsevier North-Holland, 1978.MATHGoogle Scholar
  12. 12.
    Zhu, Y. M., Multisensor Decision and Estimation Fusion, Boston: Kluwer Academic Publishers, 2003.Google Scholar
  13. 13.
    Li, X. R., Zhu, Y. M., Wang, J. et al., Optimal linear estimation fusion-part I: unified fusion rules, IEEE Transactions on Information Theory, 2003, IT-49: 2192–2208.CrossRefGoogle Scholar
  14. 14.
    Ben-Israel, A., Greville, T. N. E., Generalized Inverses: Theory and Applications (2nd ed.), New York: John Wiley & Sons, 2002.Google Scholar
  15. 15.
    Kailath, T., Sayed, A. H., Hassibi, B., Linear Estimation, NJ: Prentice Hall, 2000.Google Scholar
  16. 16.
    Chen, H. F., Recursive Estimation and Control for Stochastic Systems, New York: Wiley, 1985.Google Scholar

Copyright information

© Science in China Press 2004

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduChina
  2. 2.Department of Electronic EngineeringUniversity of New OrleansNew OrleansUSA
  3. 3.Department of Electronic EngineeringBeijing Institute of TechnologyBeijingChina

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