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@article{faucris.113624324,
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× ^{Rn}→S and its inverse:S×S→ ^{Rn}. These operators provide a local vector-space view δ x δ 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. © 2011 Elsevier B.V. All rights reserved.},
author = {Hertzberg, Christoph and Wagner, Rene and Frese, Udo and SchrÃ¶der, Lutz},
doi = {10.1016/j.inffus.2011.08.003},
faupublication = {yes},
journal = {Information Fusion},
keywords = {3D orientation; Boxplus-method; Estimation; Least squares; Manifold; Manifold toolkit; Unscented Kalman Filter},
note = {UnivIS-Import:2015-03-09:Pub.2013.tech.IMMD.profes{\_}1.integr},
pages = {57-77},
peerreviewed = {Yes},
title = {{Integrating} generic sensor fusion algorithms with sound state representations through encapsulation of manifolds},
volume = {14},
year = {2013}
}