Objective Functions for Bayesian Control-Theoretic Sensor Management, II: MНC-Like Approximation

  • Ronald Mahler
Part of the Cooperative Systems book series (COSY, volume 3)


Multisensor-multitarget sensor management is at root a problem in nonlinear control theory. Single-sensor, single-target control typically employs a Kalman filter to predict future target states, in conjunction with a core objective function (usually, a Mahalanobis distance) that dynamically positions the sensor Field of View (FoV) over predicted target position. An earlier (1996) paper proposed a foundation for sensor management based on the Bayes recursive filter for the entire multisensor-multitarget system, used in conjunction with a multi-target Kullback-Leibler objective function. This chapter proposes a potentially computationally tractable approximation of this approach. We analyze possible single-step and multistep objective functions: general multitarget Csiszár information-theoretic functionals and “geometric” functionals, used with various optimization strategies (maxi-min, maxi-mean, and “maxi-null”). We show that some of these objective functions lead to potentially tractable sensor management algorithms when used in conjunction with МНС (multi-hypothesis correlator) algorithms.


Objective Function Data Fusion Cooperative Control Sensor Management Multitarget Tracking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Y. Bar-Shalom and X.-R. Li. Estimation and Tracking: Principles, Techniques, and Software. Artech House, Ann Arbor, 1993.MATHGoogle Scholar
  2. [2]
    I. Csiszár. Information-type measures of difference of probability distributions and indirect observations. Studia Scientarum Mathematicarum Hungarica, 2: 299–318, 1967.MATHGoogle Scholar
  3. [3]
    I. Csiszár. Information measures: a critical survey. In Trans. Seventh Conf. on Info. Theor., Stat. Dec. Func.’s and the Eighth Euro. Meeting of Statisticians, pages 73–86, Tech. Univ. Prague, Prague, 1978.Google Scholar
  4. [4]
    D.J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes. Springer-Verlag, 1988.Google Scholar
  5. [5]
    A. L. Gibbs and F. E. Su. On choosing and bounding probability metrics. Int’l Stat. Rev., 70: 419–435, 2002.MATHCrossRefGoogle Scholar
  6. [6]
    I.R. Goodman, R.P.S. Mahler, and H.T. Nguyen. Mathematics of Data Fusion. Kluwer Academic Publishers, New York, 1997.MATHGoogle Scholar
  7. [7]
    Y.C. Ho and R.C.K. Lee. A Bayesian approach to problems in stochastic estimation and control. IEEE Trans. Automatic Contr., 9: 333–339, 1964.MathSciNetCrossRefGoogle Scholar
  8. [8]
    A. H. Jazwinski. Stochastic Processes and Filtering Theory. Academic Press, New York, 1970.MATHGoogle Scholar
  9. [9]
    R. Mahler. Information theory and data fusion. In Proc. Eighth Nat’l Symp. on Sensor Fusion, volume I (Unclassified), pages 279–292, Dallas TX, March 1995.Google Scholar
  10. [10]
    R. Mahler. Global optimal sensor allocation. In Proc. Ninth Nat’l Symp. on Sensor Fusion, volume I (Unclassified), pages 347–366, Naval Postgraduate School, Monterey CA, March 1996.Google Scholar
  11. [11]
    R. Mahler. A unified foundation for data fusion. In F. A. Sadjadi, editor, Selected Papers on Sensor and Data Fusion, volume MS-124 of SPIE Proc., pages 325–345. 1996. Reprinted from Seventh Joint Service Data Fusion Symposium, Laurel, MD, 1994, pp. 154–174.Google Scholar
  12. [12]
    R. Mahler. Global posterior densities for sensor management. In M. K. Kasten and L. A. Stockum, editors, Acquisition, Tracking, and Pointing XII, volume 3365 of SPIE Proc., pages 252–263. 1998.Google Scholar
  13. [13]
    R. Mahler. An Introduction to Multisource-Multitarget Statistics and Its Applications. Lockheed Martin Technical Monograph, 2000. 114 pages.Google Scholar
  14. [14]
    R. Mahler. Engineering statistics for multi-object tracking. In Proc. 2001 IEEE Workshop on Multi-Object Tracking, pages 53–60, Vancouver, July 2001.Google Scholar
  15. [15]
    R. Mahler. Multitarget moments and their application to multitarget tracking. In Proc. Workshop on Estimation, Tracking, and Fusion: A Tribute to Yaakov Bar-Shalom, pages 134-166, Naval Postgraduate School, Monterey, CA, May 2001.Google Scholar
  16. [16]
    R. Mahler. An extended first-order Bayes filter for force aggregation. In O. Drummond, editor, editor, Signal and Data Processing of Small Targets 2002, volume 4728 of SPIS Proc., pages 196–207. 2002.Google Scholar
  17. [17]
    R. Mahler. Random set theory for target tracking and identification. In D. L. Hall and J. Llinas, editors, Handbook of Multisensor Data Fusion, chapter 14. CRC Press, Boca Raton, FL, 2002.Google Scholar
  18. [18]
    R. Mahler. Objective functions for Bayesian control-theoretic sensor management, I: Multitarget first-moment approximation. In Proc. 2003 IEEE Aerospace Conference. Big Sky MT, March 2003.Google Scholar
  19. [19]
    R. Mahler and R. Prasanth. Technologies leading to unified multiagent collection and coordination. In S. Butenko, R. Murphey, and P.M. Pardalos, editors, Cooperative Control: Models, Applications, and Algorithsms, pages 215–251. Kluwer Academic Publisheres, 2003.Google Scholar
  20. [20]
    G. Mathéron. Random Sets and Integral Geometry. J. Wiley, 1975.Google Scholar
  21. [21]
    L. H. Ryder. Quantum Field Theory. Cambridge U. Press, 2 edition, 1996.MATHGoogle Scholar
  22. [22]
    H. W. Sorenson. Recursive estimation for nonlinear dynamic systems. In J. C. Spall, editor, Bayesian Analysis of Statistical Time Series and Dynamic Models. Marcel Dekker, New York, 1988.Google Scholar
  23. [23]
    D. Stoyan, W.S. Kendall, and J. Meche. Stochastic Geometry and Its Applications. John Wiley & Sons, 2 edition, 1995.MATHGoogle Scholar
  24. [24]
    T. Zajic and R. Mahler. Practical information-based data fusion performance evaluation. In I. Kadar, editor, Signal Processing, Sensor Fusion, and Target Recognition VIII, volume 3720 of SPIE Proc., pages 92–103. 1999.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Ronald Mahler
    • 1
  1. 1.Lockheed Martin NE&SS Tactical SystemsEaganUSA

Personalised recommendations