论文标题
Pearson Chi^2-Divergence方法可减少高斯混合物及其在高斯 - 及过滤器中的应用
Pearson chi^2-divergence Approach to Gaussian Mixture Reduction and its Application to Gaussian-sum Filter and Smoother
论文作者
论文摘要
高斯混合物分布在各种统计问题中很重要。特别是，它用于高斯 - 滤波器中，用于具有非高斯噪声输入的线性状态空间模型。但是，对于这种方法，必须有效地减少高斯组件数量的有效方法。在本文中，我们表明可以获得Pearson Chi^2差异的封闭形式表达，并且可以在连续降低高斯组件中的两个高斯组件的测定中测定。通过数值示例，对于一维和二维分布模型，将表明，在大多数情况下，所提出的标准几乎同样作为kullback-libler差异进行，为此，计算成本昂贵的数值集成是必要的。还显示了用于高斯 - 和平滑的应用。
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.
