GP-BayesFilters: Gaussian Process Bayes Filters for
Dynamical Systems
The goal of this project is to integrate Gaussian process prediction
and observation models into Bayes filters. These GP-BayesFilters are
more accurate than standard Bayes filters using parametric models. In
addition, GP models naturally supply the process and observation noise
necessary for Bayesian filters.
Project Contributors
Jonathan Ko, Dieter Fox, Dan Klein, Dirk Haehnel
Main publications
GP-BayesFilters
GP models for GPBF can be learned given enough training data. The
resultant models have advantages over standard parametric models.
They are more accurate, can can naturally provide the process and
observation uncertainty used in Bayesian filters. This uncertainty
considers both system noise as well as uncertainty from training data
distribution. In addition, approximate parametric models can be
combined with GP models which yields further improvements.
We will illustrate GPBF by tracking a small robotic blimp using
two cameras mounted in an indoor environment. The ground truth
position and velocity of the blimp is given by a VICON motion tracking
system. The observation is the shape of the ellipse that is extracted
from the camera image. The GP models are learned offline and are
integrated into an unscented Kalman filter. The blue ellipses show
the observations for the various sigma points. The green ellipse
shows the actual observation. An animation of the GP-UKF in action can
be found here or clicking the image above.
Learning Prediction and Observation Models for GPBFs
The standard formulation of GPBF is limited by its need for ground
truth system states. However, we develop a technique where these
ground truth states can be estimated along with GP hyperparameters in
a unified framework. Our approach called GPBF-Learning extends
Gaussian Process Latent Variable Models to the setting of dynamical
robotics systems. In addition to learning the latent state space with
no ground truth information at all, GPBF-Learning can use weak labels
to learn the latent states in cases where only sparse and/or imprecise
labels are available.
The images above show GPBF-Learning applied to a toy slotcar problem.
An inertial measurement unit (IMU) is mounted on the car which
provides gyro and accelerometer data. We use GPBF-Learn to find the
ground truth states given the IMU measurements. The top-most image is
the raw camera frame of the slotcar on the track. The top right graph
in the lower image indicates the position of the slotcar in the 3d
latent space found by GPBF-Learn. Bottom left and right graphs show
the current observation values and control input, respectively.
Videos of the raw frames and slotcar moving through the latent space
can be found here
and here, or by clicking on the images above.