Multiple-step prediction using a two stage Gaussian Process model

A two stage probabilistic prediction model is presented that uses nonparametric Gaussian Process (GP) regression to model continuous complex actions combined with a parametric model for known system dynamics. This two stage model is applied to the case of anticipating driver behavior and vehicle motion. The cross covariances between the initial state distribution and the control action distributions given by the GP regression model are computed analytically, allowing for a closed form evaluation of the joint distribution over the initial state and the GP outputs. Computing these cross covariances is necessary to capture important state dependent behavior in the GP data such as lane keeping for road vehicles. The proposed prediction model is evaluated using driving data collected from three human subjects navigating a standard four-way intersection in a driving simulation.

[1]  Matthias Althoff,et al.  Model-Based Probabilistic Collision Detection in Autonomous Driving , 2009, IEEE Transactions on Intelligent Transportation Systems.

[2]  Agathe Girard,et al.  Propagation of uncertainty in Bayesian kernel models - application to multiple-step ahead forecasting , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

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

[4]  Albert S. Huang,et al.  A Bayesian nonparametric approach to modeling motion patterns , 2011, Auton. Robots.

[5]  Christos Dimitrakakis,et al.  TORCS, The Open Racing Car Simulator , 2005 .

[6]  S. Kolski,et al.  Detection, prediction, and avoidance of dynamic obstacles in urban environments , 2008, 2008 IEEE Intelligent Vehicles Symposium.

[7]  Yoshiaki Shirai,et al.  Probabilistic Uncertainty Modeling of Obstacle Motion for Robot Motion Planning , 2002, J. Robotics Mechatronics.

[8]  Inseok Hwang,et al.  Intent-Based Probabilistic Conflict Detection for the Next Generation Air Transportation System , 2008, Proceedings of the IEEE.

[9]  Irfan A. Essa,et al.  Gaussian process regression flow for analysis of motion trajectories , 2011, 2011 International Conference on Computer Vision.

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

[11]  Agathe Girard,et al.  Prediction at an Uncertain Input for Gaussian Processes and Relevance Vector Machines Application to Multiple-Step Ahead Time-Series Forecasting , 2002 .

[12]  Amaury Nègre,et al.  Probabilistic Analysis of Dynamic Scenes and Collision Risks Assessment to Improve Driving Safety , 2011, IEEE Intelligent Transportation Systems Magazine.

[13]  Marcus Obst,et al.  Empirical evaluation of vehicular models for ego motion estimation , 2011, 2011 IEEE Intelligent Vehicles Symposium (IV).

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

[15]  S. Julier,et al.  A General Method for Approximating Nonlinear Transformations of Probability Distributions , 1996 .

[16]  David J. Fleet,et al.  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE Gaussian Process Dynamical Model , 2007 .

[17]  Peter J. F. Lucas,et al.  Multiple-step Time Series Forecasting with Sparse Gaussian Processes , 2011 .