Integrating generic sensor fusion algorithms with sound state representations through encapsulation of manifolds
Integrating generic sensor fusion algorithms with sound state representations through encapsulation of manifolds
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DOI：
10.1016/j.inffus.2011.08.003
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发表时间：
2013-01-01
影响因子：
18.6
通讯作者：
Schroeder, Lutz
中科院分区：
文献类型：
--
作者：
Hertzberg, Christoph;Wagner, Rene;Schroeder, Lutz
常见的估计算法，如最小二乘估计或卡尔曼滤波，都是对状态空间S中的状态进行操作，状态空间S表示为实值向量。然而，对于许多量，尤其是3D中的方向，S不是一个向量空间，而是一个所谓的流形，即它在局部表现得像一个向量空间，但具有更复杂的全局拓扑结构。为了积分这些量，提出了几种特别的方法。在这里,我们提出一个原则解决这个问题在歧管的结构由两个运营商封装,状态位移盒装+:x r n - >年代及其逆盒装-:x年代——> r n这些运营商提供当地的向量空间视图栏右箭头x盒装+δx在给定状态通用估计算法可以在多方面的年代主要是用盒装取代+ / - + /盒装-在适当的地方。我们对这些算子进行了公理化分析，并证明了它们在最小二乘估计和无气味卡尔曼滤波器中的应用。此外，我们在Manifold Toolkit中从软件工程的角度利用了封装的思想，其中盒装的加减运算符在通用算法的“平面向量”视图和问题特定函数的“命名成员”视图之间进行调解。(C) 2011 Elsevier B.V.版权所有
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 boxed plus : S x R-n -> S and its inverse boxed minus : S x S -> R-n These operators provide a local vector-space view delta bar right arrow x boxed plus delta around a given state X. Generic estimation algorithms can then work on the manifold S mainly by replacing +/- with boxed plus/boxed minus 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 boxed plus/boxed minus operators mediate between a "flat-vector" view for the generic algorithm and a "named-members" view for the problem specific functions. (C) 2011 Elsevier B.V. All rights reserved.