A Novel Forgetting Factor Recursive Least Square Algorithm Applied to the Human Motion Analysis
This paper is concerned with studying the forgetting factor of the recursive least square (RLS). A new dynamic forgetting factor (DFF) for RLS algorithm is presented. The proposed DFF-RLS is compared to other methods. Better performance at convergence and tracking of noisy chirp sinusoid is achieved. The control of the forgetting factor at DFF-RLS is based on the gradient of inverse correlation matrix. Compared with the gradient of mean square error algorithm, the proposed approach provides faster tracking and smaller mean square error. In low signal-to-noise ratios, the performance of the proposed method is superior to other approaches.
[1] S.Haykin, Adaptive Filter Theory, 3rd-ed, Printice Hall,1996.
[2] S.Haykin, A.H.Sayed, J.Zeidler, P.Yee, P.Wei, "Tracking of linear
Time-Variant Systems," Proc. MILCOM, pp.602-606, San Diego, Nov.
1995.
[3] H.Sadoghi Yazdi, M.Lotfizad, E.Kabir , M.Fathi "Application of
trajectory learning in tracking vehicles in the traffic scene" 9th Iranian
computer conference vol.1, pp.180-187, Feb 2004. (In Persian)
[4] H.Sadoghi Yazdi, M.Lotfizad "A new approach for tracking objects
using combination of RLS and MAP algorithms, 11th,Iranian Electronic
Eng. Conference vol.3, pp.258-266, 2003. (In Persian)
[5] J. Jiang, R. Cook, "Fast Parameter Tracking RLS Algorithm with High
Noise Immunity," Electronic Letters 28, pp. 2043-2045, October 1992.
[6] D.J. Park, B.E. Jun, "Self-Perturbing RLS Algorithm with Fast Tracking
Capability," Electronics Letters 28, pp. 558-559, March 1992.
[7] J.M. Cio, T. Kailath, "Fast Fixed-Order, Least Squares Algorithms for
Adaptive Filtering," ICASSP 83, Boston, 1983.
[8] C.F. So, S.C. Ng, S.H. Leung, "Gradient Based Variable Forgetting
Factor RLS Algorithm," Signal Processing 83, pp. 1163 - 1175, 2003.
[9] T.R. Fortescue, L.S. Kershenbaum, B.E. Ydstie, Implementation of
Self-Tuning Regulators with Variable Forgetting Factors," Automatica
17, pp. 831-835, 1981.
[10] D.J. Park, et al., "Fast Tracking RLS Algorithm Using Novel
Variable Forgetting Factor with Unity Zone, Electron. Letters 27, pp.
2150-2151, November 1991.
[11] S. Song, et al., "Gauss Newton Variable Forgetting Factor
Recursive Least Squares for Time Varying Parameter Tracking,"
Electron. Letters 36, pp. 988-990, May 2000.
[12] D. T. M. Slock and T. Kailath, "Fast transversal filters with data
sequence weighting," IEEE Trans. Acoust., Speech, Signal Process., vol.
33, no. 3, pp. 346-359, Mar. 1989.
[13] B. Toplis and S. Pasupathy, "Tracking improvements in fast RLS
algorithms using a variable forgetting factor," IEEE Trans. Acoust.,
Speech, Signal Process., vol. 36, no. 2, pp. 206-227, Feb. 1988.
[14] Shu-Hung Leung, C. F. So, "Gradient-Based Variable Forgetting
Factor RLS Algorithm in Time-Varying Environments," IEEE Trans. On
Signal Processing, vol. 53, no. 8, pp.3141-3150, Aug. 2005.
[15] D.M. Gavrila, "The Visual Analysis of Human Movement: A
Survey," Computer Vision and Image Understanding, vol. 73, no. 1, pp.
82-98, 1999.
[16] T.B. Moeslund and E. Granum, "A Survey of Computer Vision-
Based Human Motion Capture," Computer Vision and Image
Understanding, vol. 81, no. 3, pp. 231-268, Mar. 2001.
[17] Y. Wang, G. Baciu, "Human Motion Estimation from Monocular
Image Sequence Based on Cross-Entropy Regularization," Pattern
Recognition Letters, vol.24, pp.315-325, 2003.
[18] L. Wang, W. Hu, T. Tan, "Recent Developments in Human Motion
Analysis," Pattern Recognition, vol. 36, pp. 585-601, 2003.N. Kawasaki,
"Parametric study of thermal and chemical nonequilibrium nozzle flow,"
M.S. thesis, Dept. Electron. Eng., Osaka Univ., Osaka, Japan, 1993.
[19] F. Marzani, E. Calais, L. Legrand, "A 3-D Marker-Free System for
the analysis of Movement Disabilities-An Application to the Legs,"
IEEE Trans. On Information Technology in Biomedicine, Vol. 5, No.1,
March 2001.
[20] W. Lu, Y-P. Tan, "A Vision-Based Approach to Early Detection of
Drowning Incidents in Swimming Pools," IEEE Trans. On Circuits and
Systems for Video Technology, Vol. 14, No.2, pp. 159-178, Feb. 2004.
[21] L.Zhao, C.Thorpe, " Qualitative and Quantitative Car Tracking
from a Range Image Sequence," Proc. CVPR, Santa Barbara, CA, June
23-25, pp. 496-501,1998.
[22] A. K. Roy-Chowdhury, "A measure of deformability of shapes,
with applications to human motion analysis," IEEE Computer Society
Conference on Computer Vision and Pattern Recognition, CVPR 2005,
Vol.1, pp.398-404, June 2005.
[23] S-E. Kim, C-J. Park, I-H. Lee, "A Tracking Method of End-
Effectors in a Vision-Based Marker-Free Motion Capture System,"
Proceedings of the 2004 IEEE conf. on Cybernetics and Intelligent
Systems, pp. 129-134, Dec. 2004.
[24] Q. Xian-Jie, W. Zhao-Qi, X. Shi-Hong, W. Yong-Dong, "A Virtual-
Real Comparison Technique Used on Sport Simulation and Analysis,"
IEEE
[25] L. Molina-Tanco, J. P. Bandera, R. Marfil, F. Sandoval, "Real-time
Human Motion Analysis for Human-Robot Interaction," IEEE/RSJ
International Conf. on Intelligent Robots and Systems, IROS 2005, pp.
1808-1813, Aug. 2005.
[26] B. Dariush, H. Hemami, M. Parnianpour, "Analysis and Synthesis
of Human Motion From External Measurements," IEEE Int. Conf. on
Robotics & Automation, pp. 4015-4020, April 2000.
[1] S.Haykin, Adaptive Filter Theory, 3rd-ed, Printice Hall,1996.
[2] S.Haykin, A.H.Sayed, J.Zeidler, P.Yee, P.Wei, "Tracking of linear
Time-Variant Systems," Proc. MILCOM, pp.602-606, San Diego, Nov.
1995.
[3] H.Sadoghi Yazdi, M.Lotfizad, E.Kabir , M.Fathi "Application of
trajectory learning in tracking vehicles in the traffic scene" 9th Iranian
computer conference vol.1, pp.180-187, Feb 2004. (In Persian)
[4] H.Sadoghi Yazdi, M.Lotfizad "A new approach for tracking objects
using combination of RLS and MAP algorithms, 11th,Iranian Electronic
Eng. Conference vol.3, pp.258-266, 2003. (In Persian)
[5] J. Jiang, R. Cook, "Fast Parameter Tracking RLS Algorithm with High
Noise Immunity," Electronic Letters 28, pp. 2043-2045, October 1992.
[6] D.J. Park, B.E. Jun, "Self-Perturbing RLS Algorithm with Fast Tracking
Capability," Electronics Letters 28, pp. 558-559, March 1992.
[7] J.M. Cio, T. Kailath, "Fast Fixed-Order, Least Squares Algorithms for
Adaptive Filtering," ICASSP 83, Boston, 1983.
[8] C.F. So, S.C. Ng, S.H. Leung, "Gradient Based Variable Forgetting
Factor RLS Algorithm," Signal Processing 83, pp. 1163 - 1175, 2003.
[9] T.R. Fortescue, L.S. Kershenbaum, B.E. Ydstie, Implementation of
Self-Tuning Regulators with Variable Forgetting Factors," Automatica
17, pp. 831-835, 1981.
[10] D.J. Park, et al., "Fast Tracking RLS Algorithm Using Novel
Variable Forgetting Factor with Unity Zone, Electron. Letters 27, pp.
2150-2151, November 1991.
[11] S. Song, et al., "Gauss Newton Variable Forgetting Factor
Recursive Least Squares for Time Varying Parameter Tracking,"
Electron. Letters 36, pp. 988-990, May 2000.
[12] D. T. M. Slock and T. Kailath, "Fast transversal filters with data
sequence weighting," IEEE Trans. Acoust., Speech, Signal Process., vol.
33, no. 3, pp. 346-359, Mar. 1989.
[13] B. Toplis and S. Pasupathy, "Tracking improvements in fast RLS
algorithms using a variable forgetting factor," IEEE Trans. Acoust.,
Speech, Signal Process., vol. 36, no. 2, pp. 206-227, Feb. 1988.
[14] Shu-Hung Leung, C. F. So, "Gradient-Based Variable Forgetting
Factor RLS Algorithm in Time-Varying Environments," IEEE Trans. On
Signal Processing, vol. 53, no. 8, pp.3141-3150, Aug. 2005.
[15] D.M. Gavrila, "The Visual Analysis of Human Movement: A
Survey," Computer Vision and Image Understanding, vol. 73, no. 1, pp.
82-98, 1999.
[16] T.B. Moeslund and E. Granum, "A Survey of Computer Vision-
Based Human Motion Capture," Computer Vision and Image
Understanding, vol. 81, no. 3, pp. 231-268, Mar. 2001.
[17] Y. Wang, G. Baciu, "Human Motion Estimation from Monocular
Image Sequence Based on Cross-Entropy Regularization," Pattern
Recognition Letters, vol.24, pp.315-325, 2003.
[18] L. Wang, W. Hu, T. Tan, "Recent Developments in Human Motion
Analysis," Pattern Recognition, vol. 36, pp. 585-601, 2003.N. Kawasaki,
"Parametric study of thermal and chemical nonequilibrium nozzle flow,"
M.S. thesis, Dept. Electron. Eng., Osaka Univ., Osaka, Japan, 1993.
[19] F. Marzani, E. Calais, L. Legrand, "A 3-D Marker-Free System for
the analysis of Movement Disabilities-An Application to the Legs,"
IEEE Trans. On Information Technology in Biomedicine, Vol. 5, No.1,
March 2001.
[20] W. Lu, Y-P. Tan, "A Vision-Based Approach to Early Detection of
Drowning Incidents in Swimming Pools," IEEE Trans. On Circuits and
Systems for Video Technology, Vol. 14, No.2, pp. 159-178, Feb. 2004.
[21] L.Zhao, C.Thorpe, " Qualitative and Quantitative Car Tracking
from a Range Image Sequence," Proc. CVPR, Santa Barbara, CA, June
23-25, pp. 496-501,1998.
[22] A. K. Roy-Chowdhury, "A measure of deformability of shapes,
with applications to human motion analysis," IEEE Computer Society
Conference on Computer Vision and Pattern Recognition, CVPR 2005,
Vol.1, pp.398-404, June 2005.
[23] S-E. Kim, C-J. Park, I-H. Lee, "A Tracking Method of End-
Effectors in a Vision-Based Marker-Free Motion Capture System,"
Proceedings of the 2004 IEEE conf. on Cybernetics and Intelligent
Systems, pp. 129-134, Dec. 2004.
[24] Q. Xian-Jie, W. Zhao-Qi, X. Shi-Hong, W. Yong-Dong, "A Virtual-
Real Comparison Technique Used on Sport Simulation and Analysis,"
IEEE
[25] L. Molina-Tanco, J. P. Bandera, R. Marfil, F. Sandoval, "Real-time
Human Motion Analysis for Human-Robot Interaction," IEEE/RSJ
International Conf. on Intelligent Robots and Systems, IROS 2005, pp.
1808-1813, Aug. 2005.
[26] B. Dariush, H. Hemami, M. Parnianpour, "Analysis and Synthesis
of Human Motion From External Measurements," IEEE Int. Conf. on
Robotics & Automation, pp. 4015-4020, April 2000.
@article{"International Journal of Information, Control and Computer Sciences:54936", author = "Hadi Sadoghi Yazdi and Mehri Sadoghi Yazdi and Mohammad Reza Mohammadi", title = "A Novel Forgetting Factor Recursive Least Square Algorithm Applied to the Human Motion Analysis", abstract = "This paper is concerned with studying the forgetting factor of the recursive least square (RLS). A new dynamic forgetting factor (DFF) for RLS algorithm is presented. The proposed DFF-RLS is compared to other methods. Better performance at convergence and tracking of noisy chirp sinusoid is achieved. The control of the forgetting factor at DFF-RLS is based on the gradient of inverse correlation matrix. Compared with the gradient of mean square error algorithm, the proposed approach provides faster tracking and smaller mean square error. In low signal-to-noise ratios, the performance of the proposed method is superior to other approaches.
", keywords = "Forgetting factor, RLS, Inverse correlation matrix, human motion analysis.", volume = "3", number = "9", pages = "2236-8", }
