Integrating Generic Sensor Fusion Algorithms with Sound State Representations through Encapsulation of Manifolds
Abstract
Common estimation algorithms, such as least squares estimation or the Kalman filter, operate on a state in a state space S that is represented as a realvalued vector. However, for many quantities, most notably orientations in 3D, S is not a vector space, but a socalled manifold, i.e. it behaves like a vector space locally but has a more complex global topological structure. For integrating these quantities, several adhoc approaches have been proposed. Here, we present a principled solution to this problem where the structure of the manifold S is encapsulated by two operators, state displacement [+]:S x R^n > S and its inverse []: S x S > R^n. These operators provide a local vectorspace view \delta; > x [+] \delta; around a given state x. Generic estimation algorithms can then work on the manifold S mainly by replacing +/ with [+]/[] where appropriate. We analyze these operators axiomatically, and demonstrate their use in leastsquares estimation and the Unscented Kalman Filter. Moreover, we exploit the idea of encapsulation from a software engineering perspective in the Manifold Toolkit, where the [+]/[] operators mediate between a "flatvector" view for the generic algorithm and a "namedmembers" view for the problem specific functions.
 Publication:

arXiv eprints
 Pub Date:
 July 2011
 DOI:
 10.48550/arXiv.1107.1119
 arXiv:
 arXiv:1107.1119
 Bibcode:
 2011arXiv1107.1119H
 Keywords:

 Computer Science  Robotics;
 Computer Science  Computer Vision and Pattern Recognition;
 Computer Science  Mathematical Software