Splitting-up Spectral Method for Nonlinear Filtering Problems with Correlation Noises
Splitting-up Spectral Method for Nonlinear Filtering Problems with Correlation Noises
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DOI：
10.1007/s10915-022-01994-6
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发表时间：
2022-09
影响因子：
2.5
通讯作者：
Fengshan Zhang;Yongkui Zou;Shimin Chai;Ran Zhang;Yanzhao Cao
中科院分区：
文献类型：
--
作者：
Fengshan Zhang;Yongkui Zou;Shimin Chai;Ran Zhang;Yanzhao Cao
本文通过求解相应的Zakai方程来研究非线性滤波问题。利用分裂技术，我们用一阶随机偏微分方程和确定性二阶偏微分方程组成的两个方程来逼近Zakai方程.对于分裂方程，我们使用谱Galerkin方法的空间离散和有限差分格式的时间离散。主要结果是误差估计的半离散化计划的空间变量，和误差估计的全离散化计划。为了提高数值性能，我们采用了自适应技术，以准确地定位在每次迭代的解决方案的支持域。最后，我们提出了数值实验来证明我们的理论分析。
In this paper, we study nonlinear filtering problems via solving their corresponding Zakai equations. Using the splitting-up technique, we approximate the Zakai equation with two equations consisting of a first-order stochastic partial differential equation and a deterministic second-order partial differential equation. For the splitting-up equations, we use a spectral Galerkin method for the spatial discretization and a finite difference scheme for the temporal discretization. The main results are an error estimate for the semi-discretized scheme with respect to the spatial variable, and an error estimate for the full discretized scheme. To improve the numerical performance, we apply an adaptive technique to accurately locate the support domain of the solution in each time iteration. Finally, we present numerical experiments to demonstrate our theoretical analysis.