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 3 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Scientific Computing Pub Date : 2024-07-26 DOI:10.1137/23m1600505

Ajay Jasra, Kengo Kamatani, Mohamed Maama

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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

SIAM Journal on Scientific Computing 数学-应用数学

CiteScore

5.50

自引率

3.20%

发文量

209

审稿时长

1 months

期刊介绍： The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.