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

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.

[1]  Jean-Jacques E. Slotine,et al.  Stable adaptive control and recursive identification using radial Gaussian networks , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[2]  Frank L. Lewis,et al.  Aircraft Control and Simulation , 1992 .

[3]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[4]  Josué Jr. Guimarães Ramos,et al.  Airship dynamic modeling for autonomous operation , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[5]  Michael I. Jordan,et al.  Regression with input-dependent noise: A Gaussian process treatment , 1998 .

[6]  Klaus Obermayer,et al.  Gaussian process regression: active data selection and test point rejection , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

[7]  Bernhard Schölkopf,et al.  New Support Vector Algorithms , 2000, Neural Computation.

[8]  Alexander J. Smola,et al.  Sparse Greedy Gaussian Process Regression , 2000, NIPS.

[9]  Klaus Obermayer,et al.  Gaussian Process Regression: Active Data Selection and Test Point Rejection , 2000, DAGM-Symposium.

[10]  Nando de Freitas,et al.  Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks , 2000, UAI.

[11]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[12]  Nando de Freitas,et al.  Sequential Monte Carlo in Practice , 2001 .

[13]  Sebastian Thrun,et al.  Probabilistic robotics , 2002, CACM.

[14]  Lehel Csató,et al.  Sparse On-Line Gaussian Processes , 2002, Neural Computation.

[15]  C. Rasmussen,et al.  Gaussian Process Priors with Uncertain Inputs - Application to Multiple-Step Ahead Time Series Forecasting , 2002, NIPS.

[16]  Neil D. Lawrence,et al.  Fast Forward Selection to Speed Up Sparse Gaussian Process Regression , 2003, AISTATS.

[17]  Christopher J. Paciorek,et al.  Nonstationary Gaussian Processes for Regression and Spatial Modelling , 2003 .

[18]  Neil D. Lawrence,et al.  Gaussian Process Latent Variable Models for Visualisation of High Dimensional Data , 2003, NIPS.

[19]  Alexander J. Smola,et al.  Heteroscedastic Gaussian process regression , 2005, ICML.

[20]  C. Karen Liu,et al.  Learning physics-based motion style with nonlinear inverse optimization , 2005, ACM Trans. Graph..

[21]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[22]  Agathe Girard,et al.  Dynamic systems identification with Gaussian processes , 2005 .

[23]  David J. Fleet,et al.  Gaussian Process Dynamical Models , 2005, NIPS.

[24]  Neil D. Lawrence,et al.  Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models , 2005, J. Mach. Learn. Res..

[25]  Peter Szabó,et al.  Learning to Control an Octopus Arm with Gaussian Process Temporal Difference Methods , 2005, NIPS.

[26]  Zoubin Ghahramani,et al.  Sparse Gaussian Processes using Pseudo-inputs , 2005, NIPS.

[27]  Sebastian Thrun,et al.  Discriminative Training of Kalman Filters , 2005, Robotics: Science and Systems.

[28]  Dieter Fox,et al.  Gaussian Processes for Signal Strength-Based Location Estimation , 2006, Robotics: Science and Systems.

[29]  Rajesh P. N. Rao,et al.  Dynamic Imitation in a Humanoid Robot through Nonparametric Probabilistic Inference , 2006, Robotics: Science and Systems.

[30]  Alexei Makarenko,et al.  Gaussian process models for sensor-centric robot localisation , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[31]  David J. Nott,et al.  Semiparametric estimation of mean and variance functions for non-Gaussian data , 2006, Comput. Stat..

[32]  Dieter Fox,et al.  CRF-Filters: Discriminative Particle Filters for Sequential State Estimation , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[33]  Dieter Fox,et al.  GP-UKF: Unscented kalman filters with Gaussian process prediction and observation models , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[34]  Wolfram Burgard,et al.  Efficient Failure Detection on Mobile Robots Using Particle Filters with Gaussian Process Proposals , 2007, IJCAI.

[35]  Stefan Schaal,et al.  Kernel Carpentry for Online Regression Using Randomly Varying Coefficient Model , 2007, IJCAI.

[36]  Neil D. Lawrence,et al.  WiFi-SLAM Using Gaussian Process Latent Variable Models , 2007, IJCAI.

[37]  Dieter Fox,et al.  Gaussian Processes and Reinforcement Learning for Identification and Control of an Autonomous Blimp , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[38]  Wolfram Burgard,et al.  Most likely heteroscedastic Gaussian process regression , 2007, ICML '07.

[39]  Jan Peters,et al.  Local Gaussian process regression for real-time model-based robot control , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[40]  Dieter Fox,et al.  GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models , 2008, IROS.

[41]  Wolfram Burgard,et al.  Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness , 2008, ECML/PKDD.

[42]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[43]  Dieter Fox,et al.  Learning GP-BayesFilters via Gaussian process latent variable models , 2009, Auton. Robots.

[44]  Dieter Fox,et al.  Anatomically correct testbed hand control: Muscle and joint control strategies , 2009, 2009 IEEE International Conference on Robotics and Automation.