无线传感器网络中分布式推理的序列粒子束积算法

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"Sequential Particle-Based Sum-Product Algorithm for Distributed Inference in Wireless Sensor Networks" 这篇研究论文主要探讨了在无线传感器网络（WSNs）中利用顺序粒子基的乘积和算法（Sequential Particle-Based Sum-Product Algorithm, SPSPA）进行分布式推断的问题。无线传感器网络通常由大量部署的小型设备组成，这些设备通过无线通信进行协作，用于数据采集和处理。在这样的环境中，分布式推断是解决复杂问题的关键技术，例如目标跟踪、环境监测等。论文中，作者采用因子图（Factor Graph, FG）作为建模工具来表述分布式推断问题。因子图是一种有效的概率模型，它将复杂的概率分布分解为局部函数，使得推理过程更为简化。针对包含连续变量和非线性局部函数的因子图，论文提出了SPSPA算法。该算法基于粒子滤波方法，这是一种统计估计技术，常用于处理随机过程和非线性问题。 SPSPA的核心在于使用重要性采样方法从消息乘积中进行采样。重要性采样允许在高维空间中有效地近似难以直接采样的分布，而其计算复杂度与粒子数量呈线性关系，这大大提高了算法的效率。由于无线传感器网络的资源限制，低复杂度的算法对于实际应用至关重要。论文将SPSPA应用于分布式跟踪问题，通过对粒子数量和测量噪声的影响进行评估，验证了算法的性能。这种评估有助于理解算法在不同条件下的表现，从而优化参数设置和提高系统整体的可靠性。关键词：分布式推断，因子图，粒子滤波，乘积和算法，目标跟踪。该论文的贡献在于提出了一种适用于无线传感器网络的高效分布式推断算法，其创新点在于结合了粒子滤波和因子图理论，解决了非线性和连续变量的挑战，为WSN中的分布式问题求解提供了一个实用的解决方案。此外，通过实验验证，该算法在资源有限的传感器节点上表现出良好的性能和适应性。

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 1, JANUARY 2013 341

Sequential Particle-Based Sum-Product Algorithm

for Distributed Inference in Wireless

Sensor Networks

Wei Li, Zhen Yang, and Haifeng Hu

Abstract—Graphical models have been widely applied in solv-

ing distributed inference problems in wireless sensor networks

(WSNs). In this paper, the factor graph (FG) is employed to model

a distributed inference problem. Using particle ﬁltering methods, a

sequential particle-based sum-product algorithm (SPSPA) is pro-

posed for distributed inference in FGs with continuous variables

and nonlinear local functions. Importance sampling methods are

used to sample from message products, and the computational

complexity of SPSPA is thus linear in the number of particles.

The SPSPA is applied to a distributed tracking problem, and its

performance is evaluated based on the number of particles and

the measurement noise.

Index Terms—Distributed inference, factor graph (FG), particle

ﬁltering, sum-product algorithm (SPA), target tracking.

I. INTRODUCTION

T IS widely recognized that distributed inference methods

developed for graphical models comprise a principled ap-

proach to information fusion in wireless sensor networks

(WSNs) [1]. With graphical inference tools, the s imilarity

between WSNs and graphical models compels researchers to

model sensor network problems using graphical models so that

the graph-based inference algorithms, including belief propaga-

tion (BP) [2], sum-product algorithm (SPA) [3], and variational

algorithms [4], can be applied to WSNs.

Manuscript received February 3, 2012; revised May 16, 2012, August 15,

2012 and September 19, 2012; accepted September 20, 2012. Date of publi-

cation October 2, 2012; date of current version January 14, 2013. This work

was supported in part by the National Basic Research Program of China

(973 Program) under Grant 2011CB302903; by the National Natural Science

Foundation of China under Grant 60971129, Grant 61271335, and Grant

61071092; by the Fundamental Research Funds for the Central Universities

under Grant 2009B31714; by the Scientiﬁc Innovation Research Program of

College Graduate in Jiangsu Province under Grant CXZZ12_0473 and Grant

CXLX11_0408; by the China Postdoctoral Science Foundation under Grant

2012M511309; by the Postdoctoral Science Foundation of Jiangsu Province

under Grant 1101125C; by the Open Research Fund of National Mobile

Communications Research Laboratory of Southeast University under Grant

2011D04; and by a project from the Priority Academic Program Development

of Jiangsu Higher Education Institutions. The review of this paper was coordi-

nated by Dr. G. Mao.

W. Li is with the Key Laboratory of Broadband Wireless Communication

and Sensor Network Technology, Ministry of Education, Nanjing University of

Posts and Telecommunications, Nanjing 210003, China, and also with the Col-

lege of Computer and Information Engineering, Hohai University, Changzhou

213022, China (e-mail: liw@hhuc.edu.cn).

Z. Yang and H. Hu are with the Key Laboratory of Broadband Wireless Com-

munication and Sensor Network Technology, Ministry of Education, Nanjing

University of Posts and Telecommunications, Nanjing 210003, China (e-mail:

yangz@njupt.edu.cn; huhf@njupt.edu.cn).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TVT.2012.2221484

A wide range of distributed inference problems has been

reformulated with graphical models, including self-localization

[5], multitarget tracking [6], and nonlinear distributed estima-

tion [7]. However, in many distributed inference problems,

graphical models often involve continuous variables and non-

linear relations between the variables. The corresponding in-

ference algorithms usually involve integral equations that are

analytically intractable.

Particle ﬁlters (PFs) [8], [9] have proven to be an effective

solution to nonlinear/non-Gaussian problems. They form the

basis for many Bayesian tracking algorithms [10]. PFs use

Monte Carlo methods [11] to represent the posterior probability

density function (pdf) by a set of random samples with associ-

ated weight and compute estimates based on these samples and

weights. Although PFs are often effective, they are specialized

to temporal inference problems whose corresponding graphs

are Markov chains. For most of the distributed inference prob-

lems in WSNs, which are modeled by more complex graphical

models, PFs appear to be not suitable to these problems.

The nonparametric BP (NBP) algorithm [12] effectively

extends PFs to general graphs by combining the information

from the neighboring nodes in graphical models. NBP asso-

ciates a regularizing kernel with each particle and computes the

message products using a local Gibbs sampling procedure. This

algorithm has been widely used in many distributed inference

problems [13], [14]. However, the use of NBP is restricted to

graphical models with pairwise local functions.

Factor graphs (FGs) [3] provide a powerful general frame-

work for developing statistical models of distributed inference

problems. Once the stochastic dependence between the vari-

ables is modeled by an FG, the SPA can be used to infer or

estimate knowledge about the unknown variables. Based on

the FG and the SPA, [15] developed a nonparametric solution

for the general nonlinear and non-Gaussian inference problems

using the Monte Carlo method. The message-passing algorithm

(MPA) proposed in [15] is superior to the NBP in the sense

that it assumes no limitations on the type of relations between

the variables. Nevertheless, similar to NBP, the Gibbs sampler

used in [15] leads to high computational complexity, which is

quadratic in the number of particles.

This paper presents a generic framework for performing

distributed inference in WSNs. An FG is employed to model

the distributed inference problems. Based on PFs, a sequen-

tial particle-based SPA (SPSPA) is proposed for the general

nonlinear/non-Gaussian inference problems in FGs. In the pro-

posed algorithm, the importance sampling methods are used to

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