Gaussian approximation of non-linear measurement models on Lie groups
Gaussian approximation of non-linear measurement models on Lie groups
复制标题
李群上非线性测量模型的高斯逼近
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Marin Kobilarov
中科院分区：
文献类型：
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作者：
G. Chirikjian;Marin Kobilarov
李群上的扩展卡尔曼滤波器自然地出现在姿态估计的背景下，在机器人定位和映射中更为普遍。在这种情况下，通常要处理通过线性化和线性化不确定性变换处理的非线性测量模型。为了避免典型的基于坐标的线性化导致的精度损失，本文提出了一种通过直接在李群构型空间上定义的分布的二阶近似来精确描述与非线性测量模型相关的概率密度的方法。我们表明，与线性化测量模型的情况一样，这种密度可以很好地描述为指数坐标中的高斯分布（尽管与线性化测量模型产生的平均值和协方差不同）。因此，以前发展的不确定度传播和测量融合的方法可以应用于这种广义公式，而不需要线性化测量的先验假设。以平面机器人定位中的距离方位模型为例，对该方法进行了验证。
Extended Kalman filters on Lie groups arise naturally in the context of pose estimation and more generally in robot localization and mapping. Typically in such settings one deals with nonlinear measurement models that are handled through linearization and linearized uncertainty transformation. To circumvent the loss of accuracy resulting from the typical coordinate-based linearization, this paper develops a method for accurately describing the probability density associated with nonlinear measurement models by a second-order approximation of a distribution defined directly on the Lie group configuration space. We show that, like the case of linearized measurement models, this density can be described well as a Gaussian distribution in exponential coordinates (though with different mean and covariance than those that result from linearized measurement models). And therefore previously developed methods for propagation of uncertainty and fusion of measurements can be applied to this generalized formulation without the a priori assumption of linearized measurement. A case study using a range-bearing model in planar robot localization is presented to demonstrate the method.