JACIII Vol.15 No.7 pp. 860-868
doi: 10.20965/jaciii.2011.p0860


An Unscented Rauch-Tung-Striebel Smoother for a Vehicle Localization Problem

Saifudin Razali*, Keigo Watanabe*, Shoichi Maeyama*,
and Kiyotaka Izumi**

*Department of Intelligent Mechanical Systems, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530, Japan

**Department of Mechanical Engineering, Saga University, 1 Honjomachi, Saga 840-8502, Japan

March 5, 2011
May 9, 2011
September 20, 2011
unscented transformation, Rauch-Tung-Striebel smoother, vehicle localization
The Unscented Kalman Filter (UKF) has become relatively a new technique used in a number of nonlinear estimation problems to overcome the limitation of Taylor series linearization. It uses a deterministic sampling approach known as sigma points to propagate nonlinear systems and has been discussed in many literature. However, a nonlinear smoothing problem has received less attention than the filtering problem. Therefore, in this article an unscented smoother based on Rauch-Tung-Striebel formis examined for discretetime dynamic systems. It has advantages available in unscented transformation over approximation by Taylor expansion as well as its benefit in derivative free. To show the effectiveness of the proposed method, the unscented smoother is implemented and evaluated through a vehicle localization problem.
Cite this article as:
S. Razali, K. Watanabe, S. Maeyama, and K. Izumi, “An Unscented Rauch-Tung-Striebel Smoother for a Vehicle Localization Problem,” J. Adv. Comput. Intell. Intell. Inform., Vol.15 No.7, pp. 860-868, 2011.
Data files:
  1. [1] R. van der Merwe, “Sigma point Kalman filter for probabilistic inference in dynamic state-space models,” Ph.D. Thesis, Oregon Health Science University, Portland, 2004.
  2. [2] G. Evensen, “The ensemble Kalman filter: Theoretical formulation and practical implementation,” Ocean Dynamics, Vol.53, pp. 343-367, 2003.
  3. [3] M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. on Signal Processing, Vol.50, No.2, pp. 174-188, 2002.
  4. [4] S. J. Julier and J. K. Uhlmann, “Unscented filtering and nonlinear estimation,” Proc. of the IEEE, Vol.92, No.3, pp. 401-422, 2004.
  5. [5] E. Wan and R. van der Merwe, “The Unscented Kalman Filter,” New York: Wiley, 2004.
  6. [6] H. E. Rauch, F. Tung, and C. T. Striebel, “Maximum likelihood estimates of linear dynamic systems,” AIAA Journal, Vol.3, No.8, pp. 1445-1450, 1965.
  7. [7] H. E. Rauch, “Solutions to linear smoothing problem,” IEEE Trans. on Automatic Control, Vol.8, No.4, pp. 371-372, 1963.
  8. [8] S. Särkkä, “Unscented Rauch-Tung-Striebel smoother,” IEEE Trans. on Automatic Control, Vol.AC-53, No.3, pp. 845-849, 2008.
  9. [9] S. Razali, K. Watanabe, S. Maeyama, and K. Izumi, “An unscented Rauch-Tung-Striebel smoother for a bearing only tracking problem,” Int. Conf. on Control, Automation and Systems 2010, Gyeonggi-do, Korea, 2010.
  10. [10] S. Razali, K. Watanabe, S. Maeyama, and K. Izumi, “An unscented Rauch-Tung-Striebel smoother for a vehicle tracking problem,” Int. Conf. on Soft Computing and Intelligent Systems and Int. Symposium on Advanced Intelligent Systems 2010, Okayama, Japan, 2010.
  11. [11] S. J. Julier and J. K. Uhlmann, “A new approach for filtering nonlinear transformations,” Proc. of the 1995 American Control, Conference, Seattle, Washington, pp. 1628-1632, 1995.
  12. [12] S. J. Julier, J. K. Uhlmann, and H. F. Durrant-Whyte, “A new method for nonlinear transformations of means and covariances in filters and estimators,” IEEE Trans. on Automatic Control, Vol.45, No.3, pp. 477-482, 2000.
  13. [13] Y. C. Ho and R. C. K. Lee, “A Bayesian approach to problems in stochastic estimation and control,” IEEE Trans. on Automatics Control, Vol.9, No.4, pp. 333-339, 1964.
  14. [14] S. Särkkä, “Recursive Bayesian Inference on Stochastic Differential Equations,” Ph.D. Thesis, Helsinki University of Technology, 2006.
  15. [15] Y. Wu, D. Hu, M. Wu, and X. Hu, “Unscented kalman filtering for additive noise case: Augmented versus nonaugmented.” IEEE Signal Processing Letters, Vol.12, No.5, pp. 357-360, 2005.
  16. [16] E. A. Wan, and R. v. d. Merwe, “The unscented Kalman filter,” S. Haykin (Ed.), Kalman Filtering and Neural Networks, Ch.7, Wiley, 2001.
  17. [17] M. Klaas, M. Briers, N. de Freitas, A. Doucet, S. Maskell, and D. Lang, “Fast particle smoothing: If I had a million particles,” Proc. of ICML 2006, 2006.
  18. [18] B. Barshan and H. F. Durrant-Whyte, “Inertial navigation systems for mobile robots,” IEEE Trans. on Robotics and Automation, Vol.11, No.3, pp. 328-342, 1995.
  19. [19] R. E. Kalman, “A new approach to linear filtering and prediction problems,” ASME J. of Basic Engineering, Vol.86, pp. 35-45, 1960.
  20. [20] S. I. Roumeliotis, G. S. Sukhatme, and G. A. Bekey, “Smoother based 3D attitude estimation for mobile robot localization,” Technical report, University of Southern California, 1998.
  21. [21] J. J. Leonard and H. F. Durrant-Whyte, “Mobile robot localization by tracking geometric beacons,” IEEE Trans. on Robotics and Automation, Vol.7, No.3, pp. 376-382, 1991.
  22. [22] R. Negenborn, “Robot localization and kalman filter,” M.S. thesis, Utrecht University, 2003.
  23. [23] S. Thrun, “Bayesian landmark learning for mobile robot localization,” Machine Learning, Vol.33, No.1, 1998.
  24. [24] A. Elfes, “Sonar-based real world mapping and navigation,” IEEE J. of Robotics and Automation (RA), Vol.3, No.3, pp. 249-265, 1987.
  25. [25] S. Thrun. “Learning maps for indoor mobile robot navigation,” Artificial Intelligence, 1999.
  26. [26] T. Bailey, “Mobile Robot Localization and Mapping in Extensive Outdoor Environments,” Ph.D. thesis, University of Sydney, Australian Center for Field Robotics, 2002.
  27. [27] T. Bailey, “Localization in large-scale environment,” Robotics and Autonomous System, Vol.37, No.4, pp. 261-281, 2001.
  28. [28] J. Nieto, T. Bailey, and E. Nebot, “Recursive scan-matching SLAM,” Robotics and Autonomous System, Vol.55, No.5, pp. 39-49, 2007.
  29. [29] H. Durrant-Whyte and T. Bailey, “Simultaneous localisation and mapping (SLAM): Part I The essential algorithms,” IEEE Robotics & Automation Magazine, Vol.13, Issue 2, pp. 99-110, 2006.
  30. [30] T. Bailey, “Constrained initialization for bearing only SLAM,” IEEE Int. Conf. on Robotics and Automation, No.2, pp. 1966-1977, 2003.
  31. [31] A. Costa, G. Kantor, and H. Choset, “Bearing-only landmark initialization with unknown data association,” Proc. IEEE Int. Conf. on Robotics and Automation, Vol.2, pp. 1764-1770, 2004.

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