ETRI Journal

  • 제35권5호
  • /
  • Pages.849-858
  • /
  • 2013
  • /
  • 1225-6463(pISSN)
  • /
  • 2233-7326(eISSN)
한국전자통신연구원 (Electronics and Telecommunications Research Institute)
권호 표지
DOI QR코드

DOI QR Code

Stochastic Differential Equations for Modeling of High Maneuvering Target Tracking

  • Hajiramezanali, Mohammadehsan (Department of Electrical Engineering, Amirkabir University of Technology) ;
  • Fouladi, Seyyed Hamed (Department of Electrical Engineering, Amirkabir University of Technology) ;
  • Ritcey, James A. (Department of Electrical Engineering, University of Washington) ;
  • Amindavar, Hamidreza (Department of Electrical Engineering, Amirkabir University of Technology)
  • 투고 : 2013.01.27
  • 심사 : 2013.04.18
  • 발행 : 2013.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we propose a new adaptive single model to track a maneuvering target with abrupt accelerations. We utilize the stochastic differential equation to model acceleration of a maneuvering target with stochastic volatility (SV). We assume the generalized autoregressive conditional heteroscedasticity (GARCH) process as the model for the tracking procedure of the SV. In the proposed scheme, to track a high maneuvering target, we modify the Kalman filtering by introducing a new GARCH model for estimating SV. The proposed tracking algorithm operates in both the non-maneuvering and maneuvering modes, and, unlike the traditional decision-based model, the maneuver detection procedure is eliminated. Furthermore, we stress that the improved performance using the GARCH acceleration model is due to properties inherent in GARCH modeling itself that comply with maneuvering target trajectory. Moreover, the computational complexity of this model is more efficient than that of traditional methods. Finally, the effectiveness and capabilities of our proposed strategy are demonstrated and validated through Monte Carlo simulation studies.

키워드

참고문헌

  1. J.A. Cho et al., "Moving-Target Tracking Based on Particle Filter with TDOA/FDOA Measurements," ETRI J., vol. 34, no. 2, Apr. 2012, pp. 260-263. https://doi.org/10.4218/etrij.12.0211.0218
  2. R. Singer, "Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets," IEEE Trans. Aerospace Electron. Syst., vol. AES-6, no. 4, 1970, pp. 473-483. https://doi.org/10.1109/TAES.1970.310128
  3. H. Zhou and K.S.P. Kumar, "A 'Current' Statistical Model and Adaptive Algorithm for Estimating Maneuvering Targets," AIAA J. Guidance, Control, Dynamics, vol. 7, 1984, pp. 596-602. https://doi.org/10.2514/3.19900
  4. X.R. Li and V.P. Jilkov, "Survey of Maneuvering Target Tracking Part I: Dynamic Models," IEEE Trans. Aerospace Electron. Syst., vol. 39, no. 4, 2003, pp. 1333-1364. https://doi.org/10.1109/TAES.2003.1261132
  5. I.H. Whang, J.G. Lee, and T.K. Sung, "Modified Input Estimation Technique Using Pseudoresiduals," IEEE Trans. Aerospace Electron. Syst., vol. 30, no. 1, 1994, pp. 220-228. https://doi.org/10.1109/7.250422
  6. H. Lee and M.J. Tahk, "Generalized Input-Estimation Technique for Tracking Maneuvering Targets," IEEE Trans. Aerospace Electron. Syst., vol. 35, no. 4, 1999, pp. 1388-1402. https://doi.org/10.1109/7.805455
  7. H. Khaloozadeh and A. Karsaz, "Modified Input Estimation Technique for Tracking Manoeuvring Targets," IET Radar, Sonar & Navigation, vol. 3, no. 1, 2009, pp. 30-41. https://doi.org/10.1049/iet-rsn:20080028
  8. T.C. Wang and P.K. Varshney, "A Tracking Algorithm for Maneuvering Targets," IEEE Trans. Aerospace Electron. Syst., vol. 29, no. 3, 1993, pp. 910-925. https://doi.org/10.1109/7.220939
  9. Y. Bar-Shalom and K. Birmiwal, "Variable Dimension Filter for Maneuvering Target Tracking," IEEE Trans. Aerospace Electron. Syst., vol. AES-18, no. 5, 1982, pp. 621-629. https://doi.org/10.1109/TAES.1982.309274
  10. A.T. Alouani et al., "A Two-Stage Kalman Estimator for State Estimation in the Presence of Random Bias and for Tracking Maneuvering Targets," Proc. 30th Conf. Decision Control., 1991, pp. 2059-2062.
  11. L. Jing and P. Vadakkepat, "Interacting MCMC Particle Filter for Tracking Maneuvering Target," Digital Signal Process., vol. 20, no. 2, 2010, pp. 561-574. https://doi.org/10.1016/j.dsp.2009.08.011
  12. J.K. Tugnait, "Detection and Estimation for Abruptly Changing Systems," Automatica, vol. 18, 1982, pp. 607-615. https://doi.org/10.1016/0005-1098(82)90012-7
  13. H.A.P. Blom and Y. Bar-Shalom, "The Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients," IEEE Trans. Automatic Control, vol. 33, no. 8, 1988, pp. 780-783. https://doi.org/10.1109/9.1299
  14. U. Hammes and A.M. Zoubir, "Robust MT Tracking Based on M-Estimation and Interacting Multiple Model Algorithm," IEEE Trans. Signal Process., vol. 59, no. 7, 2011, pp. 3398-3409. https://doi.org/10.1109/TSP.2011.2138702
  15. X. Fu et al., "New Interacting Multiple Model Algorithms for the Tracking of the Manoeuvring Target," IET Control Theory Appl., vol. 4, no. 10, 2010, pp. 2184-2194. https://doi.org/10.1049/iet-cta.2009.0583
  16. L.A. Johnston and V. Krishnamurthy, "An Improvement to the Interacting Multiple Model (IMM) Algorithm," IEEE Trans. Signal Process., vol. 49, no. 12, 2001, pp. 2909-2923. https://doi.org/10.1109/78.969500
  17. A. Munir and D.P. Atrherton, "Adaptive Interacting Multiple Model Algorithm for Tracking a Manoeuvring Target," IEE Proc. Radar, Sonar, Nav., vol. 142, no. 1, 1995, pp. 11-17. https://doi.org/10.1049/ip-rsn:19951528
  18. J. Liu and R. Li, "Hierarchical Adaptive Interacting Multiple Model Algorithm," IET Control Theory Appl., vol. 2, no. 6, 2008, pp. 479-487. https://doi.org/10.1049/iet-cta:20070340
  19. A. Munir and D.P. Atherton, "Maneuvering Target Tracking Using an Adaptive Interacting Multiple Model Algorithm," Ame. Control Conf., vol. 2, 1994, pp. 1324-1328.
  20. M. Hajiramezanali and H. Amindavar, "Maneuvering Target Tracking Based on SDE Driven by GARCH Volatility" IEEE Statistical Signal Process. Workshop, Ann Arbor, MI, USA, 2012, pp. 764-767.
  21. M. Hajiramezanali and H. Amindavar, "Maneuvering Target Tracking Based on Combined Stochastic Differential Equations and GARCH Process," 11th Int. Conf. Inf. Sci., Signal Process. Appl., Montreal, Quebec, Canada, 2012, pp. 1293-1297.
  22. R.F. Engle, "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, vol. 50, 1982, pp. 987-1007. https://doi.org/10.2307/1912773
  23. T. Bollerslev, "Generalized Autoregressive Conditional Heteroskedasticity," J. Econometrics, vol. 31, 1986, pp. 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  24. M. Amirmazlaghani, H. Amindavar, and A. Moghaddamjoo, "Speckle Suppression in SAR Images Using the 2-D GARCH Model," IEEE Trans. Image Process., vol. 18, no. 2, Feb. 2009, pp. 250-259. https://doi.org/10.1109/TIP.2008.2009857
  25. S.H. Fouladi and H. Amindavar, "Blind Separation of Dependent Sources Using Multiwavelet Based on M-GARCH Model," 11th Int. Conf. Inf. Sci., Signal Process. Appl., Montreal, Québec, Canada, 2012, pp. 49-53.
  26. T. Bollerslev, R.Y. Chou, and K.F. Kroner, "ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence," J. Econometrics, vol. 52, no. 1-2, 1992, pp. 5-59. https://doi.org/10.1016/0304-4076(92)90064-X
  27. B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 6th ed., New York: Springer, 2003.
  28. Z. Schuss, Theory and Applications of Stochastic Processes, New York: Springer, 2010.
  29. M. Hochbruck and A. Ostermann, "Exponential Integrators," Acta Numerica, vol. 19, 2010, pp. 209-286. https://doi.org/10.1017/S0962492910000048
  30. Y. Bar-Shalom, X.R. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation: Theory, Algorithm and Software, 1st ed., Wiley-Interscience, 2001.
  31. S. Sarkka, "On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems," IEEE Trans. Autom. Control, vol. 52, no. 9, 2007, pp. 1631-1641. https://doi.org/10.1109/TAC.2007.904453