Automatica 89 (2018) 358–363
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Automatica
journal homepage: www.elsevier.com/locate/automatica
Brief paper
Sequential fusion estimation for clustered sensor networks
✩
Wen-An Zhang
a,
*, Ling Shi
b
a
Department of Automation, Zhejiang University of Technology, and the Zhejiang Provincial United Key Laboratory of Embedded Systems,
Hangzhou 310023, China
b
Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
a r t i c l e i n f o
Article history:
Received 13 December 2016
Received in revised form 14 July 2017
Accepted 20 November 2017
Available online 9 January 2018
Keywords:
Multi-sensor information fusion
Optimal estimation
Sensor networks
Networked systems
a b s t r a c t
We consider multi-sensor fusion estimation for clustered sensor networks. Both sequential measurement
fusion and state fusion estimation methods are presented. It is shown that the proposed sequential fusion
estimation methods achieve the same performance as the batch fusion one, but are more convenient
to deal with asynchronous or delayed data since they are able to handle the data that are available
sequentially. Moreover, the sequential measurement fusion method has lower computational complexity
than the conventional sequential Kalman estimation and the measurement augmentation methods, while
the sequential state fusion method is shown to have lower computational complexity than the batch state
fusion one. Simulations of a target tracking system are presented to demonstrate the effectiveness of the
proposed results.
© 2018 Elsevier Ltd. All rights reserved.
1. Introduction
Fusion estimation for sensor networks has attracted much re-
search interest during the last decade, and has found applications
in a variety of areas (Cao et al., 2014; Chen, Li, & Lai, 2013; He,
Wang, Ji, & Zhou, 2011; Ilic, Xie, Khan, & Moura, 2010; Oka & Lampe,
2010). Compared with the centralized structure, the distributed
structure is more preferable for sensor networks because of its
reliability, robustness and low requirement on network bandwidth
(Dong, Wang, & Gao, 2012; Duan & Li, 2011; He et al., 2011; Millan
et al., 2013; Yan, Xiao, Xia, & Fu, 2013). When the number of sensors
is large, it is wasteful to embed in each sensor an estimator and
the communication burden is high. Moreover, for long-distance
deployed sensors, it may not be possible to allocate communication
channels for all sensors. An improvement is to adopt the hierarchi-
cal structure for distributed estimation (Song, Zhang, & Yu, 2014;
Zhang, Qi, & Deng, 2014), by which all the sensors in the network
are divided into several clusters and the sensors within the same
cluster are connected to a cluster head (CH) which acts as a local
estimator. Then, the distributed estimation is carried out in two
stages. In the first stage, the local estimator in each cluster fuses the
✩
The work was supported by the National Natural Science Foundation of China
under Grant No.61573319, the Zhejiang Provincial Natural Science Foundation
of China under Grant No. LR16F030005, and the HKUST KTH Partnership FP804.
The material in this paper was not presented at any conference. This paper was
recommended for publication in revised form by Associate Editor Bert Tanner under
the direction of Editor Christos G. Cassandras.
*
Corresponding author.
E-mail addresses: wazhang@zjut.edu.cn (W.-A. Zhang), eesling@ust.hk (L. Shi).
measurements from its cluster to generate a local estimate. Then,
the local estimators exchange and fuse local estimates to produce a
fused estimate to eliminate any disagreements among themselves.
Various results on multi-sensor fusion estimation for sensor
networks have been available in the literature, including central-
ized fusion and distributed fusion, as well as measurement fusion
and state fusion (Bar-Shalom & Li, 1995; Deng, 2006; Hu, Duan, &
Zhou, 2010; Julier & Uhlman, 2009; Ran & Deng, 2009; Roecker
& McGillem, 1988; Song, Zhu, Zhou, & You, 2007; Sun & Deng,
2004; Xia, Shang, Chen, & Liu, 2009; Xing & Xia, 2016; Zhang,
Chen Michael, Liu, & Liu, 2017; Zhang, Liu, & Yu, 2014). However,
most of the results are based on the idea of batch fusion, that is,
measurements or local estimates are fused all at a time at the
fusion instant until all of them are available at the estimator, as
illustrated in Fig. 1(a). Such a batch fusion estimation may induce
long computation delay, thus it is not appropriate for real-time
applications. A possible improvement is to adopt the idea of se-
quential fusion (Aran, Burger, Caplier, & Akarun, 2009; Shen, Luo,
Zhu, & Song, 2012), by which the measurements or local estimates
are fused one by one according to the time order of the data
arriving at the estimator, as illustrated in Fig. 1(b). In this way, the
fusion and the state estimation could be carried out over the entire
estimation interval, which help reduce computation burdens at the
estimation instant and ultimately reduce the computation delay.
Some relevant results on sequential fusion estimation have been
presented in Deng, Zhang, Qi, Liu, and Gao (2012), Huang and Qin
(2010) and Yan, Li, Xia, and Fu (2013, 2015). The results in Yan, Li et
al. (2013) and Yan et al. (2015) provide an efficient measurement
fusion estimation approach to deal with asynchronous or delayed
https://doi.org/10.1016/j.automatica.2017.12.038
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