Sigma-Point Kalman Filters

Sigma-Point Kalman Filters represents a major advance over traditional Extended Kalman Filtering.  SPKFs represent a family of derivative-free recursive Bayesian estimation filters.  These include:

• Unscented Kalman filter (UKF) 
• Central difference Kalman filter (CDKF) 
• Square-root SPKFs 
• Sigma-point particle filter 
• Gaussian mixture sigma-point particle filter
  

Our research focus is on the development of the SPKF for machine learning, including state-estimation, parameter estimation, and dual estimation frameworks.  

For additional information contact Rudolph van der Merwe or E. A. Wan .

General Presentations: 

• Sigma-Point Kalman Filters - Overview.
• Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models   (talk given at Workshop on Advances in Machine Learning, Monteal, June 2003)
• Probabilistic Inference using Sigma-Point Kalman Filters   (Ph.D. Thesis Defense - Rudolph van der Merwe, 2004)

• Sigma-Point Kalman Filter based Integrated Navigation Systems (Overview).
• See publications [1] and [2].
  

• Dual Estimation
• Human Head/Face Tracking
• Countour Tracking for HCI
• Mobile Robot Localization

We have developed a Matlab toolkit called ReBEL that contains the above mentioned and other related algorithms. See the ReBEL homepage for more detail.

1. R. van der Merwe, E. A. Wan, and Simon Julier, "Sigma-Point Kalman Filters Nonlinear Estimation and Sensor Fusion - Applications in Integrated Navigation", in AIAA Guidance Navigation and Controls Conference, March, 2004, pdf.

2. R. van der Merwe and E. A. Wan, "Sigma-Point Kalman Filters for Integrated Navigation", in Proceedings of the 60th Annual Meeting of The Institute of Navigation (ION), Dayton, OH, Jun, 2004, pdf.

3. R. van der Merwe and E. Wan, "Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models", in Proceedings of the Workshop on Advances in Machine Learning, Montreal, Canada., Jun, 2003, pdf , DjVu , postscript .

4. R. van der Merwe and E. Wan, "Gaussian Mixture Sigma-Point Particle Filters for Sequential Probabilistic Inference in Dynamic State-Space Models", in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Hong Kong, Apr, 2003, pdf , DjVu , postscript .

5. E. A. Wan and R. van der Merwe, "Kalman Filtering and Neural Networks", chap. Chapter 7 : The Unscented Kalman Filter, (50 pages), Wiley Publishing, Eds. S. Haykin, 2001, pdf , postscript .

6. R. van der Merwe and E. A. Wan, "The Square-Root Unscented Kalman Filter for State and Parameter-Estimation", in International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, Utah, May, 2001, pdf , DjVu , postscript .

7. R. van der Merwe and E. A. Wan, "Efficient Derivative-Free Kalman Filters for Online Learning", in European Symposium on Artificial Neural Networks (ESANN), Bruges, Belgium, Apr, 2001, pdf , DjVu , postscript .

8. Eric A. Wan and Rudolph van der Merwe, "The Unscented Kalman Filter for Nonlinear Estimation", in Proceedings of Symposium 2000 on Adaptive Systems for Signal Processing, Communication and Control (AS-SPCC) , IEEE, Lake Louise, Alberta, Canada, Oct, 2000, DjVu , postscript .

9. R. van der Merwe, A. Doucet, N. de Freitas and E. Wan, "The Unscented Particle Filter", in Advances in Neural Information Processing Systems (NIPS13), MIT Press, Eds. T. K. Leen, T. G. Dietterich and V. Tresp, Dec, 2000, pdf , DjVu , postscript

10. R. van der Merwe, N. de Freitas, A. Doucet and E. Wan, "The Unscented Particle Filter", num. CUED/F-INFENG/TR 380, Cambridge University Engineering Department, Cambridge, England, Aug, 2000, pdf , DjVu , postscript .

11. Eric Wan and Rudolph van der Merwe, "Noise-Regularized Adaptive Filtering for Speech Enhancement", in Proceedings of EUROSPEECH, Budapest, Hungary, Sep, 1999, ericwan@ece.ogi.edu , pdf , postscript .

12. Eric A. Wan and Rudolph van der Merwe and Alex T. Nelson, "Dual Estimation and the Unscented Transformation", in Advances in Neural Information Processing Systems 12, pp. 666-672, MIT Press, Eds. S.A. Solla and T.K. Leen and K.-R. Muller, Nov, 2000, pdf , DjVu , postscript .

Supported in part by the NSF and ONR: