Approximations of the Optimal Importance Density Using Gaussian Particle Flow Importance Sampling

被引:42
作者
Bunch, Pete [1 ]
Godsill, Simon [1 ]
机构
[1] Univ Cambridge, Dept Engn, Trumpington St, Cambridge CB2 1PZ, England
基金
英国工程与自然科学研究理事会;
关键词
Algorithms; Bayesian methods; Sampling; Signal processing; Time series; SEQUENTIAL MONTE-CARLO; FILTERS;
D O I
10.1080/01621459.2015.1038387
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
Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn from the prior and then moved according to some dynamics over an interval of pseudo-time such that their final values are distributed according to the desired posterior. In practice, implementing a particle flow, sampler requires multiple layers of approximation, with the result that the final samples do not in general have the correct posterior distribution. In this article we consider using an approximate Gaussian flow for sampling with a class of nonlinear Gaussian models. We use the particle flow within an importance sampler, correcting for the discrepancy between the target and actual densities with importance weights. We present a suitable numerical integration procedure for use with this flow and an accompanying step-size control algorithm. In a filtering context, we use the particle flow to sample from the optimal importance density, rather than the filtering density itself, avoiding the need to make analytical or numerical approximations of the predictive density. Simulations using particle flow importance sampling within a particle filter demoristrate significant improvement over standard approximations of the optimal importance density, and the algorithm falls within the standard sequential Monte Carlo framework.
引用
收藏
页码:748 / 762
页数:15
相关论文
共 36 条
[1]   Particle Markov chain Monte Carlo methods [J].
Andrieu, Christophe ;
Doucet, Arnaud ;
Holenstein, Roman .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2010, 72 :269-342
[2]  
[Anonymous], 1995, Multitarget-Multisensor Tracking:Principles and Techniques
[3]  
[Anonymous], PROC CVPR IEEE, DOI DOI 10.1109/CVPR.2000.854758
[4]   ALGORITHM - SOLUTION OF MATRIX EQUATION AX+XB = C [J].
BARTELS, RH ;
STEWART, GW .
COMMUNICATIONS OF THE ACM, 1972, 15 (09) :820-&
[5]  
Bunch P, 2013, 2013 IEEE 5TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP 2013), P360, DOI 10.1109/CAMSAP.2013.6714082
[6]   An overview of existing methods and recent advances in sequential Monte Carlo [J].
Cappe, Olivier ;
Godsill, Simon J. ;
Moulines, Eric .
PROCEEDINGS OF THE IEEE, 2007, 95 (05) :899-924
[7]  
Daum F., 2011, P SOC PHOTO-OPT INS, V8050
[8]  
Daum F., 2013, P SPIE SIGNAL PROCES, V8745
[9]  
Daum F., 2008, P SOC PHOTO-OPT INS, V6969
[10]  
Daum F., 2009, P SOC PHOTO-OPT INS