A new probability distribution for simultaneous representation of uncertain position and orientation
A new probability distribution for simultaneous representation of uncertain position and orientation
复制标题
一种同时表示不确定位置和方向的新概率分布
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
U. Hanebeck
中科院分区：
文献类型：
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作者：
Igor Gilitschenski;G. Kurz;S. Julier;U. Hanebeck
这项工作提出了一种新颖的方法来表示平面中刚体运动李群的不确定性。这是通过使用对偶四元数来表示平面刚体运动并提出指数分布族中的概率分布来实现的，该分布本质上尊重表示的基础结构。这在涉及强测量噪声的场景中特别有用。讨论了新提出的分布模型和宾厄姆分布之间的关系。所提出的结果涉及归一化常数、模式、参数估计技术和封闭式贝叶斯测量融合的计算公式。
This work proposes a novel way to represent uncertainty on the Lie group of rigid-body motions in the plane. This is achieved by using dual quaternions for representation of a planar rigid-body motion and proposing a probability distribution from the exponential family of distributions that inherently respects the underlying structure of the representation. This is particularly beneficial in scenarios involving strong measurement noise. A relationship between the newly proposed distributional model and the Bingham distribution is discussed. The presented results involve formulas for computation of the normalization constant, the mode, parameter estimation techniques, and a closed-form Bayesian measurement fusion.