Gradient flows in uncertainty propagation and filtering of linear Gaussian systems
Gradient flows in uncertainty propagation and filtering of linear Gaussian systems
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线性高斯系统不确定性传播和滤波中的梯度流
DOI：
10.1109/cdc.2017.8264109
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
T. Georgiou
中科院分区：
文献类型：
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作者：
A. Halder;T. Georgiou
这项工作的目的主要是暂时的，目的是阐明约旦-Kinderlehrer-奥托（JKO）计划的不确定性传播，和一个变种，Laugesen-Mehta-Meyn-Raginsky（LMMR）计划过滤。我们指出，这些变分方案可以被理解为近似的运营商在空间的密度函数，实现梯度流。这些计划持有的承诺，导致有效的方法来解决福克-普朗克方程以及非线性滤波方程。我们在本文中的目的是详细开发的基本思想设置的线性随机系统的高斯噪声和恢复已知的结果。
The purpose of this work is mostly expository and aims to elucidate the Jordan-Kinderlehrer-Otto (JKO) scheme for uncertainty propagation, and a variant, the Laugesen-Mehta-Meyn-Raginsky (LMMR) scheme for filtering. We point out that these variational schemes can be understood as proximal operators in the space of density functions, realizing gradient flows. These schemes hold the promise of leading to efficient ways for solving the Fokker-Planck equation as well as the equations of non-linear filtering. Our aim in this paper is to develop in detail the underlying ideas in the setting of linear stochastic systems with Gaussian noise and recover known results.