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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 real-valued vector. However, for many quantities, most notably orientations in 3D, S is not a vector space, but a so-called manifold, i.e. it behaves like a vector space locally but has a more complex global topological structure. For integrating these quantities, several ad-hoc 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 vector-space 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 least-squares 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 "flat-vector" view for the generic algorithm and a "named-members" view for the problem specific functions.
ISSN: 1566-2535
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

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