Digital Signal Processing 34 (2014) 29–38
Contents lists available at ScienceDirect
Digital Signal Processing
www.elsevier.com/locate/dsp
Multi-sensor distributed fusion filtering for networked systems with
different delay and loss rates
Na Li, Shuli Sun
∗
, Jing Ma
School of Electronics Engineering, Heilongjiang University, Harbin 150080, China
a r t i c l e i n f o a b s t r a c t
Article history:
Available
online 4 August 2014
Keywords:
Multi-sensor
Packet
loss
Random
delay
Distributed
fusion filter
Networked
system
This paper mainly focuses on the multi-sensor distributed fusion estimation problem for networked
systems with time delays and packet losses. Measurements of individual sensors are transmitted to
local processors over different communication channels with different random delay and packet loss
rates. Several groups of Bernoulli distributed random variables are employed to depict the phenomena of
different time delays and packet losses. Based on received measurements of individual sensors, local
processors produce local estimates that have been developed in a new recent literature. Then local
estimates are transmitted to the fusion center over a perfect connection, where a distributed fusion filter
is obtained by using the well-known matrix-weighted fusion estimation algorithm in the linear minimum
variance sense. The filtering error cross-covariance matrices between any two local filters are derived. The
steady-state property of the proposed distributed fusion filter is analyzed. A simulation example verifies
the effectiveness of the algorithm.
© 2014 Elsevier Inc. All rights reserved.
1. Introduction
During the past decades, the research on networked systems
and sensor networks has attracted much attention since they make
resources convenient for sharing and have broad applications in-
cluding
target tracking, signal processing, multiple robots, and so
on [1–3]. The random delays and packet losses are usually in-
duced
by the network congestions during data transmissions of
networked systems [4]. Therefore, the design on estimators and
controllers for networked systems is challenging [5,6].
Several
literatures have focused on single sensor systems with
packets losses or/and time delays [7–14]. However, the research
on multi-sensor systems subject to time delays and losses are not
fully reported in the literatures. Multi-sensor information fusion
has broad applications in target tracking, navigation and detec-
tion
since they can fully make use of information from all sensors
and overcome the defect of single sensor lying in the limitation
of time and space. Thus, the study on multi-sensor information
fusion is significant. Distributed fusion estimation plays an im-
portant
role in information processing for multi-sensor systems.
In [15], distributed consensus filters are designed for sensor net-
works,
where each sensor implements the estimate based on the
data from neighboring sensors. However, the communication time
*
Corresponding author.
E-mail
address: sunsl@hlju.edu.cn (S. Sun).
delays are not taken into account. Since the distributed fusion has
better robust and flexibility than the centralized fusion, many re-
sults
on the distributed fusion estimation have been reported in
recent years, including the decentralized filter with the parallel
structure [16], the federal Kalman filter [17], the Maximum Likeli-
hood
fusion filter [18], the unified optimal linear estimation fusion
[19] and distributed fusion weighted by matrices [20]. Several fu-
sion
estimation algorithms have been designed for multi-sensor
systems with the transmission delays or packet losses in [21–24],
where, however, the delays and packet losses are not taken into
account simultaneously. In [25–27], distributed and centralized fu-
sion
estimators have been respectively designed for packet losses
and one-step random delays or variable delays. However, multi-
step
random delays are not taken into account. Distributed track-
to-track
fusion on Kalman-type filtering and retrodiction at arbi-
trary
communication rates is also addressed for target tracking in
[28,29], where the correlation among local filters is ignored.
Recently,
a new model to depict the phenomena of multi-step
random delays and packet losses during data transmissions in net-
worked
systems has been developed and an optimal linear filter
has been presented in [30]. In this paper, we will generalize the
results for single sensor in [30] to the case of multiple sensors. We
will investigate the distributed fusion filtering problem as shown
in Fig. 1. Each sensor transmits its measurements to a local pro-
cessor
over imperfect networks which lead to random delays and
packet losses. Each local processor produces local estimate based
on received measurements from sensor itself and then transmits
http://dx.doi.org/10.1016/j.dsp.2014.07.016
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© 2014 Elsevier Inc. All rights reserved.