Integrating Generic Sensor Fusion Algorithms with Sound State Representation through Encapsulation of Manifolds
Type of publication:  Article 
Citation:  hertzbergIF10 
Journal:  Information Fusion 
Volume:  14 
Number:  1 
Year:  2013 
Pages:  5777 
Note:  Available online 14 September 2011 
ISSN:  15662535 
URL:  http://www.sciencedirect.com/s... 
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. 
Userfields:  bdskurl1={http://www.sciencedirect.com/science/article/pii/S1566253511000571}, pdfurl={http://arxiv.org/pdf/1107.1119v1}, project={A7FreePerspective}, status={Reviewed}, 
Keywords:  Sensor fusion manifold state representation orientation 
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