An Adaptive Multiple Target Tracking Filter Using the EM Algorithm

EM 알고리즘을 이용한 적응다중표적추적필터

  • Published : 2001.09.01

Abstract

Tracking the targets of interest has been one of the major research areas in radar surveillance system. We formulate the tracking problem as an incomplete data problem and apply the EM algorithm to obtain the MAP estimate. The resulting filter has a recursive structure analogous to the Kalman filter. The difference is that the measurement-update deals with multiple measurements and the parameter-update can estimate the system parameters. Through extensive experiments, it turns out that the proposed system is better than PDAF and NNF in tracking the targets. Also, the performance degrades gracefully as the disturbances become stronger.

Keywords

References

  1. S .S. Blackman. Multiple-Target Tracking with Radar Applications. Artech House, Inc, 1986
  2. M. I. Skolnik. Introduction to Radar Systems. McGraw-Hill, New York, NY, USA, 1980
  3. N. Levanon. Radar Principles. A Wiley-Interscience Publication, New York, NY, USA, 1988
  4. T. E. Fortmann, Y. Bar-Shalom, and M. Scheffe. Sonar tracking of multiple targets using joint probabilistic data association. IEEE Journal of Oceanic Engineering, OE-8(3):173-- 183, Jul 1983
  5. Y. Bar-Shalom. Extension of the probabilistic data association filter in multi-target tracking. In Proceedings of the 5th Symposium on Nonlinear Estimation, pages 16--21, Sep. 1974
  6. Y. Bar-Shalom and E. Tse. Tracking in a cluttered environment with probabilistic data association. Automation, 11:451--460, Sep. 1975
  7. Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, Inc, 1988
  8. Y. Bar-Shalom and X. R. Li. Estimation and tracking: principles, techniques, and software. Artech House, Inc, 1993
  9. Y. Bar-Shalom and X. R. Li. Multitarget-Multisensor Tracking: Principles and Techniques. YBS Publishing, Storrs, CT, 1995
  10. D. Sengupta and R. A. Iltis. Neural solution to the multitarget tracking data association problem. IEEE Trans. Aerosp. Electron. Syst., AES-25:96--108, Jan. 1989 https://doi.org/10.1109/7.18666
  11. Henry Leung. Neural network data association with application to multiple-target tracking. Opt. Eng., 35(3):693--700, Mar. 1996 https://doi.org/10.1117/1.600661
  12. Gilles P. Mauroy and Edward W. Kamen. Multiple target tracking using recurrent neural networks. In Proceedings of ICNN'97, 1997 https://doi.org/10.1109/ICNN.1997.614223
  13. M. Winter and G. Favier. A neural solution for multitarget tracking based on a maximum likelihood approach. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pages 1141--1144, May 1998 https://doi.org/10.1109/ICASSP.1998.675471
  14. J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. In Proceedings of the National Academy of Science, pages 2554--2558, 1982 https://doi.org/10.1073/pnas.79.8.2554
  15. J. J. Hopfield and D. W. Tank. Neural computation of decisions in optimization problems. Biological Cybernetics, 52:141--152, 1985 https://doi.org/10.1007/BF00339943
  16. Y. W. Lee and H. Jeong. A MAP estimate of optimal data association for multi-target tracking. In Proceedings of ICSPAT, 1997
  17. H. Jeong and J. H. Park. Multiple target tracking using constrained MAP data association. Electronics Letters, 35(1):25--26, Jan. 1999 https://doi.org/10.1049/el:19990002
  18. A. P. Dempster, N. M. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B, 39(1):1--38, 1997
  19. G. J. McLachlan and T. Krishnan. The EM Algorithm and Extensions. A Wiley-Interscience Publication, 1996
  20. D. Avitzour. A maximum likelihood approach to data association. IEEE Trans. Aerosp. Electron. Syst., 28(2):560--565, Apr. 1992 https://doi.org/10.1109/7.144581
  21. H. Gauvrit, J. P. Le Cadre, and C.Jauffret. A formulation of multitarget tracking as an incomplete data problem. IEEE Trans. Aerosp. Electron. Syst., 33(4):1242--1257, Oct. 1997 https://doi.org/10.1109/7.625121
  22. K. J. Molnar and J. W. Modestino. Application of the EM algorithm for the multitarget/multisensor tracking problem. IEEE Trans. Signal Processing, 46(1):115-- 129, Jan 1998 https://doi.org/10.1109/78.651193
  23. L. Frenkel and M. Feder. Recursive expectation-maximization (EM) algorithms for time-varying parameters with applications to multiple target tracking. IEEE Trans. Signal Processing, 47(2):306--320, Feb. 1999 https://doi.org/10.1109/78.740104
  24. R. E. Kalman. A new approach to linear filtering and prediction problems. Trans. ASME, (J. Basic Eng.,)), 82:34--45, Mar 1960
  25. R. E. Kalman and R. Bucy. New results in linear filtering and prediction theory. Trans. ASME, (J. Basic Eng.,)), 83:95--108, Mar 1961
  26. M. Grewal and A. Andrews. Kalman Filtering : Theory and Practice. Prentice-Hall, Englewood Cliffs, NJ 07632, USA, 1993
  27. P. Green. On use of the {EM} algorithm for penalized likelihood estimation. J. Roy. Statist. Soc. Ser. B, 52(3):443--452, 1990
  28. X. L. Meng and D. B. Rubin. Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80:267--278, 1993 https://doi.org/10.1093/biomet/80.2.267
  29. M. Skolnik, editor. Radar Handbook. McGraw-Hill, New York, NY, USA, 1990
  30. D. G. Luenberger. Optimization by Vector Space Methods. John Wiley & Son, Inc., 1969
  31. Max Woodbury. Inverting modified matrices. Memorandum Report 42, Statistical Research Group, Princeton, 1950
  32. Alston S. Householder. The Theory of Matrices in Numerical Analysis. Dover Publications, New York, 1975
  33. X. L. Meng and D. B. Rubin. Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. Journal of the American Statistical Association, 86:899--909, 1991 https://doi.org/10.2307/2290503
  34. T. Orchard and M. A. Woodbury. A missing information principle: Theory and application. In Proceedings of the Statistical Computing Section, pages 41--45. American Statistical Association, 1972