Publication type: 
Article 
Author: 
Christoph Hertzberg, René Wagner, Udo Frese, Lutz Schröder 
Title: 
Integrating Generic Sensor Fusion Algorithms with Sound State Representations through Encapsulation of Manifolds 
Volume: 
14 
Page(s): 
57 – 77 
Journal: 
Information Fusion 
Number: 
1 
Year published: 
2013 
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. 
ISSN: 
15662535 
Internet: 
http://www.sciencedirect.com/science/article/pii/S1566253511000571 
PDF Version: 
http://arxiv.org/pdf/1107.1119v1 
Keywords: 
Sensor fusion manifold state representation orientation 
Note / Comment: 
Available online 14 September 2011 
Status: 
Reviewed 
Last updated: 
17. 06. 2014 

