Generalised particle filters with Gaussian mixtures

被引：12

作者：

Crisan, D. ^{[1
]}

Li, K. ^{[2
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 07期

基金：

英国工程与自然科学研究理事会;

关键词：

Stochastic partial differential equation; Nonlinear filtering; Zakai equation; Particle filters; Gaussian mixtures; L-2-convergence; TARGET TRACKING;

D O I：

10.1016/j.spa.2015.01.008

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Stochastic filtering is defined as the estimation of a partially observed dynamical system. Approximating the solution of the filtering problem with Gaussian mixtures has been a very popular method since the 1970s. Despite nearly fifty years of development, the existing work is based on the success of the numerical implementation and is not theoretically justified. This paper fills this gap and contains a rigorous analysis of a new Gaussian mixture approximation to the solution of the filtering problem. We deduce the L-2-convergence rate for the approximating system and show some numerical examples to test the new algorithm. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：2643 / 2673

页数：31

共 36 条

[1] NONLINEAR BAYESIAN ESTIMATION USING GAUSSIAN SUM APPROXIMATIONS [J].

ALSPACH, DL ;

SORENSON, HW .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1972, AC17 (04) :439-&

[2]

Anderson B., 1979, Optimal Filtering

[3] Particle filtering for partially observed Gaussian state space models [J].

Andrieu, C ;

Doucet, A .

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2002, 64 :827-836

[4]

[Anonymous], 2000, Proceedings of the 16th Annual Conference on Uncertainty in Artificial Intelligence (UAI-00)

[5]

Bain A, 2009, STOCH MOD APPL PROBA, V60, P1, DOI 10.1007/978-0-387-76896-0_1

[6]

Carmi A, 2009, FUSION: 2009 12TH INTERNATIONAL CONFERENCE ON INFORMATION FUSION, VOLS 1-4, P1179

[7] Mixture Kalman filters [J].

Chen, R ;

Liu, JS .

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2000, 62 :493-508

[8] Particle filters with random resampling times [J].

Crisan, D. ;

Obanubi, O. .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2012, 122 (04) :1332-1368

[9]

Crisan D., 2014, ARXIV14016592

[10]

Crisan D., 2013, P R SOC LOND A, V469

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