Splitting-up Spectral Method for Nonlinear Filtering Problems with Correlation Noises

被引：1

作者：

Zhang, Fengshan ^{[1
]}

Zou, Yongkui ^{[1
]}

Chai, Shimin ^{[1
]}

Zhang, Ran ^{[1
]}

Cao, Yanzhao ^{[2
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

[2] Auburn Univ, Dept Math & Stat, Auburn, AL 36840 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2022年 / 93卷 / 01期

关键词：

Nonlinear filtering problem; Zakai equation; Splitting-up technique; Error analysis; ZAKAI EQUATION; DATA ASSIMILATION; ERROR ANALYSIS; APPROXIMATION; SYSTEMS; CONVERGENCE; SUBJECT; MODEL;

D O I：

10.1007/s10915-022-01994-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：24

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