尺度无迹变换高斯和滤波器：理论与应用
Scaled unscented transform Gaussian sum filter: theory and application
摘要：
在这项工作中，我们考虑在非线性/非高斯系统的状态估计问题。我们引入了一个框架，称为缩放无迹变换高斯和滤波器（SUT-GSF），它结合了两个想法：缩放无迹卡尔曼滤波器（SUKF）的基础上的概念缩放无迹变换（SUT），和高斯混合模型（GMM）。SUT用于近似由非线性函数变换的高斯随机变量的均值和协方差，而GMM用于近似通过一组高斯分布的随机变量的概率密度函数（pdf）。有了这两个工具，可以建立一个框架，同化非线性系统的递归方式。在这个框架内，可以将非线性随机系统视为一组子系统的混合模型，其中每个子系统采用由已知高斯随机过程驱动的非线性系统的形式。然后，对于每个子系统，应用SUKF估计由子系统的非线性控制方程变换的潜在高斯随机变量的均值和协方差。将子系统的估计值转换为GMM给出了pdf的显式（近似）形式，这可以被视为状态估计问题的“完整”解决方案，因为所有感兴趣的统计信息都可以从pdf的显式形式中获得。本文研究了基于尺度无迹变换的高斯和滤波器的构造。
英文摘要：
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf ... This work is on the construction of the Gaussian sum filter based on the scaled unscented transform.
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