连续-离散随机动态系统中贝叶斯平滑的高斯滤波和变分逼近
Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems
摘要：
对于由非线性随机微分方程和离散时间测量描述的系统，贝叶斯平滑方程通常是难以处理的。高斯近似是近似真实平滑分布的计算有效方式。在这项工作中，我们提出了两个高斯近似方法之间的比较。基于高斯滤波的高斯平滑器使用滤波分布的高斯近似来形成平滑分布的近似。变分高斯平滑器基于最小化近似平滑分布相对于真实分布的Kullback-Leibler发散。结果表明，对于高度非线性系统，变分高斯平滑器可以用来迭代改进高斯滤波平滑解。我们还提出了线性化和西格玛点的方法来近似的棘手的高斯期望的变分高斯平滑方程。此外，我们还将变分高斯光滑器推广到一类具有奇异扩散矩阵的系统。
英文摘要：
The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the true smoothing distribution. In this work, we present a comparison between two Gaussian approximation methods. The Gaussian filtering based Gaussian smoother uses a Gaussian approximation for the filtering distribution to form an approximation for the smoothing distribution. The variational Gaussian smoother is based on minimizing the Kullback-Leibler divergence of the approximate smoothing distribution with respect to the true distribution. The results suggest that for highly nonlinear systems, the variational Gaussian smoother can be used to iteratively improve the Gaussian filtering based smoothing solution. We also present linearization and sigma-point methods to approximate the intractable Gaussian expectations in the Variational Gaussian smoothing equations. In addition, we extend the variational Gaussian smoother for certain class of systems with singular diffusion matrix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
