The Nonlinear Assignment Problem in Experimental High Energy Physics

  • Jean-Francois Pusztaszeri
Part of the Combinatorial Optimization book series (COOP, volume 7)


This chapter describes a mathematical programming approach to solve the data association phase of the multiple-target tracking problem, and its implementation in the context of pattern recognition in High Energy Physics. The approach can be easily integrated within existing parameter estimation methods of dynamic systems commonly used in practice, and in particular within the framework of Kalman filtering. It also provides the only alternative to exhaustive search when optimality conditions of estimation methods are violated and when strict quality requirements are in place.

While it has been developed for a specific High Energy Physics experiment (ALEPH), the approach presented here is general enough to extend, with only little additional modeling effort, to other multiple-target tracking applications with similar operational requirements.


Extend Kalman Filter Data Association Primary Vertex Vertex Detector Hadronic Event 
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.


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  1. [Bar-Shalom and Fortmann, 1988]
    Bar-Shalom, Y. and Fortmann, T. E. (1988). Tracking and Data Association. Mathematics in Science and Engineering, Academic Press.Google Scholar
  2. [Bar-Shalom et al., 1980]
    Bar-Shalom, Y., Fortmann, T. E., and Scheffe, M. (1980). Joint probabilistic data association filter for multiple targets in clutter. In Proc. Conf. on Information Science and Systems. Princeton, NJ.Google Scholar
  3. [Blackman, 1986]
    Blackman, S. S. (1986). Multiple-Target Tracking with Radar Applications. Artech House.Google Scholar
  4. [Chang et al., 1994a]
    Chang, K.-C., Mori, S., and Chong, C.-Y. (1994a). Evaluating a multiple-hypothesis multitarget tracking algorithm. IEEE Transactions on Aerospace and Electronic Systems, 30(1).Google Scholar
  5. [Chang et al., 1994b]
    Chang, K.-C., Mori, S., and Chong, C.-Y. (1994b). Performance evaluation of track initiation in dense target environments. IEEE Transactions on Aerospace and Electronic Systems, 30(1).Google Scholar
  6. [Comas et al., 1996]
    Comas, P., Knobloch, J., and Pusztaszeri, J.-F. (1996). Aleph event reconstruction manual. Technical Report 96–010, CERN. ALEPH Collaboration.Google Scholar
  7. [Cox and Miller, 1995]
    Cox, I. J. and Miller, M. L. (1995). On finding ranked assignments with applications to multitarget tracking and motion correspondence. IEEE Transactions on Aerospace and Electronic Systems, 31(1).Google Scholar
  8. [D. Decamp, 1991]
    D. Decamp, e. a. C. (1991). Measurement of the charged particle multiplicity distribution in hadronic z decays. Physics Letters B, 273:181–192.CrossRefGoogle Scholar
  9. [Denby et al., 1990]
    Denby, B., Lessner, E., and Lindsey, C. S. (1990). Tests of track segment and vertex finding with neural networks. In Proceedings of the Conference on Computing in High Energy Physics - CHEP90, Santa Fe, U.S.A., April 8–13. World Scientific.Google Scholar
  10. [Drevermann et al., 1995]
    Drevermann, H., Kuhn, D., and Nilsson, B. S. (1995). Event display. In Proceedings of the CERN School of Computing, CERN-ECP, number 95–25.Google Scholar
  11. [F. Abe, 1995]
    F. Abe, e. a. C. C. (1995). Observation of top quark production in ppbar collisions with the cdf detector at fermilab. Technical Report PUB022E, Fermi National Laboratory, Batavia, U.S.A. CDF preprint.Google Scholar
  12. [Frühwirth, 1987]
    Frühwirth, R. (1987). Applications of kalman filtering to track and vertex fitting. Nuclear Instr. & Methods, A262:444–450.CrossRefGoogle Scholar
  13. [G. Batignani, 1992]
    G. Batignani, e. a. (1992). Experience with the aleph silicon vertex detector. Nuclear Instr. & Methods, A315:121–124.CrossRefGoogle Scholar
  14. [Group, 1994]
    Group, P. D. (1994). Review of particle properties. Physical Review D, Particles and Fields, 50(1).Google Scholar
  15. [Gyulassy and Harlander, 1991]
    Gyulassy, M. and Harlander, M. (1991). Elastic tracking and neural networks for complex pattern recognition. Computer Physics Communications, 66:31–46.zbMATHCrossRefGoogle Scholar
  16. [Kalman and Bucy, 1961]
    Kalman, R. and Bucy, R. (1961). New results in linear filtering and prediction. Journal of Basic Engineering, 83D:360–368.MathSciNetCrossRefGoogle Scholar
  17. [Li and Bar-Shalom, 1991]
    Li, X. R. and Bar-Shalom, Y. (1991). Stability evaluation and track life of the pdaf for tracking in clutter. IEEE Transactions on Automatic Control, 36(5).Google Scholar
  18. [Li and Bar-Shalom, 1994]
    Li, X. R. and Bar-Shalom, Y. (1994). Detection threshold selection for tracking performance optimization. IEEE Transactions on Aerospace and Electronic Systems, 30(3).Google Scholar
  19. [Morefield, 1977]
    Morefield, C. L. (1977). Application of 0–1 integer programming to multitarget tracking problems. IEEE Transactions on Automatic Control, AC-22(3).Google Scholar
  20. [Nagarajan et al., 1987]
    Nagarajan, V., Chidambara, M. R., and Sharma, R. N. (1987). Combinatorial problems in multitarget tracking — a comprehensive solution. IEE Proceedings, 134(1).Google Scholar
  21. [Okun, 1985]
    Okun, L. B. (1985). Particle Physics. Harwood Academic Publishers.Google Scholar
  22. [Peterson, 1989]
    Peterson, C. (1989). Track finding with neural networks. Nuclear Instruments & Methods, A279:537–545.CrossRefGoogle Scholar
  23. [Peterson and Anderson, 1987]
    Peterson, C. and Anderson, J. R. (1987). A mean field theory learning algorithm for neural networks. Complex Systems Publications, 66:31–46.Google Scholar
  24. [Poore, 1994]
    Poore, A. B. (1994). Multidimensional assignment formulation of data association problems arising from multitarget tracking and multisensor data fusion. Computational Optimization and Applications, 3:27–57.MathSciNetzbMATHCrossRefGoogle Scholar
  25. [Poore and Rijavec, 1994a]
    Poore, A. B. and Rijavec, N. (1994a). A lagrangian relaxation algorithm for multidimensional assignment problems arising from multitarget tracking. SIAM Journal of Optimization, 3(3):339–361.MathSciNetGoogle Scholar
  26. [Poore and Rijavec, 1994b]
    Poore, A. B. and Rijavec, N. (1994b). A numerical study of some data association problems arising in multitarget tracking. In Hager, W. W., Hearn, D. W., and Pardalos, P. M., editors, Large Scale Optimization: State of the Art, pages 339–361. Kluwer Academic Publishers B. V., Boston.CrossRefGoogle Scholar
  27. [Pusztaszeri, 1996]
    Pusztaszeri, J.-F. (1996). Combinatorial Algorithms for Pattern Recognition in Composite Tracking Chambers. PhD thesis, Swiss Federal Institute of Technology.Google Scholar
  28. [Pusztaszeri et al., 1996]
    Pusztaszeri, J.-F., Rensing, P., and Liebling, T. (1996). Tracking elementary particles near their primary vertex: a combinatorial approach. Journal of Global Optimization, 9:41–64.MathSciNetzbMATHCrossRefGoogle Scholar
  29. [Reid, 1979]
    Reid, D. B. (1979). An algorithm for tracking multiple targets. IEEE Transactions on Automatic Control, AC-24(6).Google Scholar
  30. [Scott, 1963]
    Scott, W. T. (1963). The theory of small-angle multiple scattering of fast charged particles. Reviews of Modern Physics, 35(2).Google Scholar
  31. [Smith and Buechler, 1975]
    Smith, P. and Buechler, G. (1975). A branching algorithm for discriminating and tracking multiple objects. IEEE Transactions on Automatic Control, AC-20:101–104.zbMATHCrossRefGoogle Scholar
  32. [Stimpfl-Abele and Garrido, 1991]
    Stimpfl-Abele, G. and Garrido, L. (1991). Fast track finding with neural networks. Computer Physics Communications, 64:46–56.CrossRefGoogle Scholar
  33. [Trunk and Wilson, 1981]
    Trunk, G. V. and Wilson, J. D. (1981). Track initiation of occasionally unresolved radar targets. IEEE Transactions on Aerospace and Electronic Systems, AES-17(1).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Jean-Francois Pusztaszeri
    • 1
  1. 1.Logistics DivisionSabre, Inc.USA

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