A deterministic method for sequential estimation of 3-D rotations is presented. The Bingham distribution is used to represent uncertainty directly on the unit quaternion hypersphere. Quaternions avoid the degeneracies of other 3-D orientation representations, while the Bingham distribution allows tracking of large-error (high-entropy) rotational distributions. Experimental comparison to a leading EKF-based filtering approach on both synthetic signals and a ball-tracking dataset shows that the Quaternion Bingham Filter (QBF) has lower tracking error than the EKF, particularly when the state is highly dynamic. We present two versions of the QBF- suitable for tracking the state of first- and second-order rotating dynamical systems.

A new system for object detection in cluttered RGB-D images is presented. Our main contribution is a new method called Bingham Procrustean Alignment (BPA) to align models with the scene. BPA uses point correspondences between oriented features to derive a probability distribution over possible model poses. The orientation component of this distribution, conditioned on the position, is shown to be a Bingham distribution. This result also applies to the classic problem of least-squares alignment of point sets, when point features are orientation-less, and gives a principled, probabilistic way to measure pose uncertainty in the rigid alignment problem. Our detection system leverages BPA to achieve more reliable object detections in clutter.

We present a robotic walking aid capable of learning models of users' walking-related activities. Our walker is instrumented to provide guidance to elderly people when navigating their environments; however, such guidance is difficult to provide without knowing what activity a person is engaged in (e.g., where a person wants to go). The main contribution of this paper is an algorithm for learning models of users of the walker. These models are defined at multiple levels of abstractions, and learned from actual usage data using statistical techniques. We demonstrate that our approach succeeds in determining the specific activity in which a user engages when using the walker. One of our proto-type walkers was tested in an assisted living facility near Pittsburgh, PA; a more recent model was extensively evaluated in a university environment.