混合高斯约简的皮尔逊卡方散度方法及其在高斯和滤波和平滑中的应用
Pearson chi^2-divergence Approach to Gaussian Mixture Reduction and its Application to Gaussian-sum Filter and Smoother
摘要：
高斯混合分布在各种统计问题中是重要的。特别地，它被用于非高斯噪声输入的线性状态空间模型的高斯和滤波器和平滑器。然而，为了使这种方法实用，需要一种有效的方法来减少高斯分量的数量。本文给出了皮尔逊卡方散度的一个封闭表达式，它可以应用于高斯分量序贯约化中两个高斯分量对的确定.通过一维和二维分布模型的数值例子，将表明，在大多数情况下，所提出的标准几乎等同于Kullback-Libler发散，计算成本高的数值积分是必要的。应用高斯和滤波和平滑。
英文摘要：
The Gaussian mixture distribution is important in various statistical problems. In particular it is used in the Gaussian-sum filter and smoother for linear state-space model with non-Gaussian noise inputs. However, for this method to be practical, an efficient method of reducing the number of Gaussian components is necessary. In this paper, we show that a closed form expression of Pearson chi^2-divergence can be obtained and it can apply to the determination of the pair of two Gaussian components in sequential reduction of Gaussian components. By numerical examples for one dimensional and two dimensional distribution models, it will be shown that in most cases the proposed criterion performed almost equally as the Kullback-Libler divergence, for which computationally costly numerical integration is necessary. Application to Gaussian-sum filtering and smoothing is also shown.
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