| 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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