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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAC.2015.2498701, IEEE
Transactions on Automatic Control
JOURNAL OF L
A
T
E
X CLASS FILES, VOL. 6, NO. 1, NOVEMBER 2015 1
Hierarchical Fusion Estimation for Clustered
Asynchronous Sensor Networks
Wen-An Zhang, Member, IEEE, Bo Chen, and Michael Z. Q. Chen, Member, IEEE
Abstract—In this note, a hierarchical fusion estimation method
is presented for clustered sensor networks with a very general
setup where sensors (sensor nodes) and estimators (cluster heads)
are allowed to work asynchronously with aperiodic sampling and
estimation rates. A sequential measurement fusion (SMF) method
is presented to design local estimators, and it is shown that the
SMF estimator is equivalent to the measurement augmentation
(MA) estimator in precision but with much lower computational
complexity. Two types of sequential covariance intersection (CI)
fusion estimators are presented for the fusion estimation. The
proposed SCI fusion estimators provide a satisfactory estimation
precision that is close to the centralized batch CI (BCI) estimator
while requiring smaller computational burden as compared
with the BCI estimator. Therefore, the proposed hierarchical
fusion estimation method is suitable for real-time applications in
asynchronous sensor networks with energy constraints. Moreover,
the method is applicable to the case with packet delays and losses.
Index Terms—Sensor networks, networked systems, optimal
estimation, sensor fusion, multi-rate estimation.
I. INTRODUCTION
Fusion estimation for sensor networks has attracted much
research interest during the last decade, and has found ap-
plications in a variety of areas [1]-[3]. Compared with the
centralized structure, the distributed structure, in which each
sensor acts also as an estimator, is more preferable for sen-
sor networks because of its reliability, robustness and low
requirement on network bandwidth [3]. When the number
of sensors is large, it is wasteful to embed in each sensor
an estimator and the communication burden increases as
many sensors communicate with each other in a short time.
Moreover, for long-distance deployed sensors, it may not be
possible to allocate communication channels for all sensors.
An improvement is to divide the sensors into several clusters
and the sensors within the same cluster are connected to a
cluster head (CH) acting as a local estimator [4]. In such a
clustered sensor network, each local estimate is not optimal in
the sense that not all measurements in the sensor network are
used in a cluster. Moreover, there exist disagreements among
local estimates obtained at different clusters, and such a form
of group disagreement regarding the signal estimation may be
undesirable for a peer-to-peer sensor network. A simple yet
efficient improvement is to adopt a hierarchical fusion strategy,
This work was supported by the National Natural Science Foundation of
China (Grant Nos. 61573319 and 61403345) and the Research Grants Council,
Hong Kong, through the General Research Fund under Grant 106140120.
Wen-An Zhang and Bo Chen are with the Department of Automation,
Zhejiang University of Technology, Hangzhou 310023, P.R.China; Michael Z.
Q. Chen is with the Department of Mechanical Engineering, The University
of Hong Kong, Hong Kong. (email:wazhang@zjut.edu.cn).
that is, each CH first collects measurements from its cluster to
generate a local estimate and then collects local estimates from
the other clusters to produce a fused one. Some similar ideas
on the hierarchical fusion estimation have been presented, for
example, in [5] and [6].
Existing results on hierarchical fusion usually assume that
all sensors and estimators are synchronized, which adds com-
plexity to the estimator design since time-synchronization
techniques should be used. Actually, it is not easy to realize
strict time synchronization of the entire network, and thus it
is of practical significance to develop an estimation method
that is able to work with asynchronous sensors and estimators
[7]. On the other hand, in many situations, it is not necessary
for sensors to transmit measurements and generate estimates
at every sampling from the energy-efficiency perspective, and
the sensors may work with multiple rates according to their
power status [8]. Consider a situation where a sensor network
is deployed to observe a dynamical process, but the process is
not changing too rapidly over a certain time interval. Then it
is wasteful from an energy-saving perspective for sensors to
transmit every measurement and generate every estimate over
this interval, and this waste is amplified by packet losses which
are usually unavoidable in sensor networks [8]-[10]. Therefore,
aperiodic sampling and estimation may be a more preferable
strategy for sensor networks with energy constraints. Then, it
is necessary to develop fusion estimation methods for asyn-
chronous sensors and estimators due to the aperiodic sampling
and estimation. As shown in Fig. 1(a), various measurements
generated at different time scales may be available for esti-
mating over an estimation interval, where T
r
k
and t
r,l
k
denote
the estimation instant and the sampling instants, respectively,
while s and e denote the sensors and estimators, respectively.
How to make full use of the measurements is a main challenge
in the asynchronous estimation. Some approaches, including
the measurement augmentation and the distributed state fu-
sion, have been presented in existing results to solve the
problem [11], [12]. The approaches are somewhat complex
since pseudo-measurements whose noises are correlated to
the process noise were used [12], or correlations between
local estimates were considered [11]. For sensor networks, an
estimation algorithm of practical significance should first be of
low computation complexity since the computation capability
of a sensor node is quite limited.
In this note, a sequential estimation approach is proposed to
solve the hierarchical fusion estimation problem for clustered
asynchronous sensor networks with delays and packet losses.
The main contributions of the note are as follows: First, a
sequential measurement fusion (SMF) estimation method is
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