Integrating generic sensor fusion algorithms with sound state representations through encapsulation of manifolds
Author(s): Hertzberg C, Wagner R, Frese U, Schröder L
Publication year: 2013
Journal issue: 1
Pages range: 57-77
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.
FAU Authors / FAU Editors How to cite
APA: Hertzberg, C., Wagner, R., Frese, U., & Schröder, L. (2013). Integrating generic sensor fusion algorithms with sound state representations through encapsulation of manifolds. Information Fusion, 14(1), 57-77. https://dx.doi.org/10.1016/j.inffus.2011.08.003
MLA: Hertzberg, Christoph, et al. "Integrating generic sensor fusion algorithms with sound state representations through encapsulation of manifolds." Information Fusion 14.1 (2013): 57-77.