针对一类部分观测的片断确定性马尔可夫过程的多级粒子过滤器

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

ACS Applied Electronic Materials Pub Date : 2024-07-26 DOI:10.1137/23m1600505

Ajay Jasra, Kengo Kamatani, Mohamed Maama

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引用次数: 0

摘要

SIAM 科学计算期刊》，第 46 卷第 4 期，第 A2475-A2502 页，2024 年 8 月。摘要本文考虑了一类部分观测的片断确定性马尔可夫过程的滤波问题。特别是，我们假设一个常微分方程（ODE）驱动着确定性元素，并且只能通过时间离散化进行数值求解。我们根据 Lemaire、Thieullen 和 Thomas [Adv. Appl. Probab.，52 (2020)，pp. 138-172] 中的方法，开发了一种新的粒子和多级粒子滤波器 (MLPF)，以近似与离散化 ODE 相关的滤波器。我们提供了与 MLPF 相关的均方误差约束，这为算法模拟参数的设置提供了指导，并意味着与使用粒子滤波器相比，可以获得显著的计算收益。我们的理论主张在几个数值示例中得到了证实。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Multilevel Particle Filters for a Class of Partially Observed Piecewise Deterministic Markov Processes

SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page A2475-A2502, August 2024.
Abstract. In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes. In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in Lemaire, Thieullen, and Thomas [Adv. Appl. Probab., 52 (2020), pp. 138–172], a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameters of the algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples.

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来源期刊

ACS Applied Electronic Materials Multiple-

CiteScore

7.20

自引率

4.30%

发文量

567