Advertisement

Autonomous Robots

, Volume 27, Issue 1, pp 75–90 | Cite as

GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models

Article

Abstract

Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Key components of each Bayes filter are probabilistic prediction and observation models. This paper shows how non-parametric Gaussian process (GP) regression can be used for learning such models from training data. We also show how Gaussian process models can be integrated into different versions of Bayes filters, namely particle filters and extended and unscented Kalman filters. The resulting GP-BayesFilters can have several advantages over standard (parametric) filters. Most importantly, GP-BayesFilters do not require an accurate, parametric model of the system. Given enough training data, they enable improved tracking accuracy compared to parametric models, and they degrade gracefully with increased model uncertainty. These advantages stem from the fact that GPs consider both the noise in the system and the uncertainty in the model. If an approximate parametric model is available, it can be incorporated into the GP, resulting in further performance improvements. In experiments, we show different properties of GP-BayesFilters using data collected with an autonomous micro-blimp as well as synthetic data.

Keywords

Gaussian process Bayesian filtering Dynamic modelling Machine learning Regression 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abbeel, P., Coates, A., Montemerlo, M., Ng, A., & Thrun, S. (2005). Discriminative training of Kalman filters. In Proceedings of robotics: science and systems (RSS). Google Scholar
  2. Bar-Shalom, Y., Li, X.-R., & Kirubarajan, T. (2001). Estimation with applications to tracking and navigation. New York: Wiley. CrossRefGoogle Scholar
  3. Brooks, A., Makarenko, A., & Upcroft, B. (2006). Gaussian process models for sensor-centric robot localisation. In Proceedings of the IEEE international conference on robotics & automation (ICRA) (pp. 56–61). Google Scholar
  4. Csató, L., & Opper, M. (2002). Sparse on-line Gaussian processes. Neural Computation, 14(3), 641–668. MATHCrossRefGoogle Scholar
  5. Deshpande, A. D., Ko, J., & Matsuoka, Y. (2009). Anatomically correct testbed hand control: muscle and joint control strategies. In Proceedings of the IEEE international conference on robotics & automation (ICRA). Google Scholar
  6. Doucet, A., de Freitas, J. F. G., Murphy, K., & Russell, S. (2000). Rao-Blackwellised particle filtering for dynamic Bayesian networks. In Proceedings of the conference on uncertainty in artificial intelligence (UAI). Google Scholar
  7. Edakunni, N., Schaal, S., & Vijayakumar, S. (2007). Kernel carpentry for online regression using randomly varying coefficient model. In Proceedings of the international joint conference on artificial intelligence (IJCAI). Google Scholar
  8. Engel, Y., Szabo, P., & Volkinshtein, D. (2006). Learning to control an octopus arm with Gaussian process temporal difference methods. In Y. Weiss, B. Schölkopf, & J. Platt (Eds.), Advances in neural information processing systems 18 (NIPS) (pp. 347–354). Cambridge: MIT Press. Google Scholar
  9. Ferris, B., Hähnel, D., & Fox, D. (2006). Gaussian processes for signal strength-based location estimation. In Proceedings of robotics: science and systems (RSS). Google Scholar
  10. Ferris, B., Fox, D., & Lawrence, N. (2007). WiFi-SLAM using Gaussian process latent variable models. In Proceedings of the international joint conference on artificial intelligence (IJCAI). Google Scholar
  11. Girard, A., Rasmussen, C., Quin̈onero Candela, J., & Murray-Smith, R. (2005). Gaussian process priors with uncertain inputs—application to multiple-step ahead time series forecasting. In Advances in neural information processing systems 15 (NIPS). Cambridge: MIT Press. Google Scholar
  12. Goldberg, P., Williams, C. K. I., & Bishop, C. (1998). Regression with input-dependent noise: A Gaussian process treatment. In Advances in neural information processing systems 10 (NIPS) (pp. 493–499). Cambridge: MIT Press. Google Scholar
  13. Gomes, S. B. V., & Ramos, J. G. Jr. (1998). Airship dynamic modeling for autonomous operation. Proceedings of the IEEE international conference on robotics & automation (ICRA) (p. 4). Google Scholar
  14. Grimes, D., Chalodhorn, R., & Rao, R. (2006). Dynamic imitation in a humanoid robot through nonparametric probabilistic inference. In Proceedings of robotics: science and systems (RSS). Google Scholar
  15. Julier, S., & Uhlmann, J. (1997). A new extension of the Kalman filter to nonlinear systems. In International symposium on aerospace/defense sensing, simulation and controls. Google Scholar
  16. Kersting, K., Plagemann, C., Pfaff, P., & Burgard, W. (2007). Most likely heteroscedastic Gaussian process regression. In Proceedings of the international conference on machine learning (ICML), Corvallis, Oregon, USA, March 2007. Google Scholar
  17. Ko, J., & Fox, D. (2008). GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS). Google Scholar
  18. Ko, J., & Fox, D. (2009). Learning GP-BayesFilters via Gaussian process latent variable models. In Proceedings of robotics: science and systems (RSS). Google Scholar
  19. Ko, J., Klein, D., Fox, D., & Hähnel, D. (2007a). GP-UKF: unscented Kalman filters with Gaussian process prediction and observation models. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS). Google Scholar
  20. Ko, J., Klein, D. J., Fox, D., & Hähnel, D. (2007b). Gaussian processes and reinforcement learning for identification and control of an autonomous blimp. In Proceedings of the IEEE international conference on robotics & automation (ICRA). Google Scholar
  21. Kocijan, J., Girard, A., Banko, B., & Murray-Smith, R. (2003). Dynamic systems identification with Gaussian processes. In Proceedings of 4th IMACS symposium on mathematical modelling (MathMod) (pp. 776–784). Google Scholar
  22. Lawrence, N. (2004). Gaussian process latent variable models for visualisation of high dimensional data. In Advances in neural information processing systems 17 (NIPS) (p. 2004). Google Scholar
  23. Lawrence, N. (2005). Probabilistic non-linear principal component analysis with Gaussian process latent variable models. Journal of Machine Learning Research, 6. Google Scholar
  24. Limketkai, B., Fox, D., & Liao, L. (2007). CRF-filters: discriminative particle filters for sequential state estimation. In Proceedings of the IEEE international conference on robotics & automation (ICRA). Google Scholar
  25. Liu, K., Hertzmann, A., & Popovic, Z. (2005). Learning physics-based motion style with nonlinear inverse optimization. In ACM transactions on graphics (Proceedings of SIGGRAPH). Google Scholar
  26. Nguyen, D., & Peters, J. (2008). Local Gaussian processes regression for real-time model-based robot control. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS). Google Scholar
  27. Nott, D. (2006). Semiparametric estimation of mean and variance functions for non-Gaussian data. Computational Statistics, 21(3–4), 603–620. MATHCrossRefMathSciNetGoogle Scholar
  28. Paciorek, C. (2003). Nonstationary Gaussian processes for regression and spatial modelling. Google Scholar
  29. Plagemann, C., Fox, D., & Burgard, W. (2007). Efficient failure detection on mobile robots using Gaussian process proposals. In Proceedings of the international joint conference on artificial intelligence (IJCAI). Google Scholar
  30. Plagemann, C., Kersting, K., & Burgard, W. (2008). Nonstationary Gaussian process regression using point estimates of local smoothness. In ECML PKDD ’08: proceedings of the European conference on machine learning and knowledge discovery in databases, part II (pp. 204–219), Antwerp, Belgium. Berlin: Springer. ISBN:978-3-540-87480-5, doi: 10.1007/978-3-540-87481-2_14 CrossRefGoogle Scholar
  31. Quinonero-Candela, J., & Rasmussen, C. E. (2005). A unifying view of sparse approximate Gaussian process regression. Journal of Machine Learning Research, 6, 1939–1959. MathSciNetGoogle Scholar
  32. Rasmussen, C. E., & Williams, C. K. I. (2005). Gaussian processes for machine learning. Cambridge: MIT Press. Google Scholar
  33. Sanner, R., & Slotine, J. (1991). Stable adaptive control and recursive identification using radial Gaussian networks. In Proceedings of IEEE conference on decision and control (CDC). Google Scholar
  34. Schölkopf, B., Smola, A., Williamson, R., & Bartlett, P. (2000). Letter communicated by John Platt new support vector algorithms. Google Scholar
  35. Seeger, M., & Williams, C. (2003). Fast forward selection to speed up sparse Gaussian process regression. In Workshop on AI and Statistics 9. Google Scholar
  36. Seo, S., Wallat, M., Graepel, T., & Obermayer, K. (2000). Gaussian process regression: Active data selection and test point rejection. In German association for pattern recognition (DAGM) symposium (pp. 27–34). Google Scholar
  37. Smola, A., & Bartlett, P. (2001). Sparse greedy Gaussian process regression. In Advances in neural information processing systems (NIPS) (pp. 619–625). Cambridge: MIT Press. Google Scholar
  38. Snelson, E., & Ghahramani, Z. (2006). Sparse Gaussian processes using pseudo-inputs. In Advances in neural information processing systems (NIPS) (pp. 1257–1264). Cambridge: MIT Press. Google Scholar
  39. Stevens, B. L., & Lewis, F. L. (1992). Aircraft control and simulation. New York: Wiley. Google Scholar
  40. Thrun, S., Burgard, W., & Fox, D. (2005). Probabilistic robotics. Cambridge: MIT Press. ISBN: 0-262-20162-3. MATHGoogle Scholar
  41. Wang, J., Fleet, D., & Hertzmann, A. (2006). Gaussian process dynamical models. In Advances in neural information processing systems 18 (NIPS) (pp. 1441–1448). Cambridge: MIT Press. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dept. of Computer Science & EngineeringUniversity of WashingtonSeattleUSA

Personalised recommendations