Distributed Kalman Consensus Filtering Algorithm
Based on Event-driven
*
Ning Wu, Li Guo and Chunxi Yang
Faulty of Chemical Engineering
Kunming University of Science and Technology
Kunming, Yunnan, China
ycx@kmust.edu.cn
*
This work is partially supported by CNSF Grant 61364002, 51465024 and the Science Foundation of Yunnan Province Grant 2013Z128.
Abstract –Considering the fact that each wireless senor node
owns limited power in wireless sensor networks, a new type of
distributed Kalman-consensus filtering algorithm based on
event-driven is proposed for reducing energy consumption. This
event-driven scheme is triggered by the updated covariance
which is commonly used to describe errors between the true
value and the estimated one. In this scheme, each sensor node
communicates with its neighbour nodes when the updated
covariance exceeds a given threshold for ensuring the filtering
accuracy, otherwise not communicates for saving energy.
Moreover, this scheme has self-adaptive function to adjust times
of connection among nodes according to different given filtering
accuracies. Consequently, this algorithm can save energy of
nodes effectively and thus prolong the life of wireless sensor
networks under the condition of guaranteeing enough filtering
accuracy.
Keywords: - wireless sensor networks; event-driven; energy
consumption; distributed consensus; Kalman filtering.
I. INTRODUCTION
Recent decades, wireless sensor networks (WSNs) has
been studied and applied in many fields due to its low cost,
small size, multi-function, high flexibility and simple
installation [1-4]. WSNs are often arranged in remote areas or
hard-to-reach areas for monitoring and detecting interested
field. As a result, it is difficult to charge or change the power
supply. So it makes energy consumption and energy
management of wireless sensor network becomes a very
important issue. Many researchers focus on how to reduce the
data transmission rate in order to reduce the energy
consumption.
Reference [5] proposes a self-adaptive sampling strategy,
namely SOD, which has been widely used in the field of
control and estimation. The event-driven scheme which can
significantly reduce the amount of data transmission was
shown in [7-8]. In [9], a relevant sampling protocol was
presented for the event-driven state estimation on the basis of
the Kullback-Leibler (KL) divergence. The KL divergence can
reflect the stochastic characteristic of the filter variables by
estimation error and error covariance.
However, the aforesaid algorithms are centralized
algorithms, which increase the energy consumption of the
sensor nodes by transmitting all the data to the fusion centre.
Distributed Kalman consensus filtering algorithm has been
widely used in information fusion technology of wireless
sensor networks for its obvious advantages, such as low
calculation difficulty, faster convergence speed and high
accuracy [11-13]. It can reduce the transmission load of a
single sensor to prolong the lifetime of the network. Besides,
in real applications of sensor networks, we need to adjust the
filtering accuracy adaptively according to the external
environment, such as different time, weather or temperature.
Based on these considerations, we propose a distributed
consensus Kalman filtering method on the basis of the updated
covariance driven. The algorithm is relatively simple, which
can effectively reduce the times of communications and
prolong the life of wireless sensor networks. At last, the
algorithm can be verified by numerical simulation and
compared with a classical distributed Kalman consensus
filtering algorithm from filtering performances and power
consumption.
II.
FILTERING ALGORITHM
A. System Model
It is assumption that a wireless sensor networks, which n
sensor nodes are uniformly deployed on a unit square
detection area (the simple random geometric graph with
n = 50
nodes is shown in Fig.1), and the transmission radius of nodes
satisfy
() (2log )/rn n n≥ . Consider the following linear
system:
1000
;(,)
kkk
xAxBwxNxP
+
=+ ∈ (1)
1, 2, ,
iiii
kkk
Hx v i n=+=…, (2)
Where
1m
k
x
×
∈ℜ and
1im
k
z
×
∈ℜ are the state vector and sensor
measurement of sensor
i , respectively.
mm
A
×
∈ℜ denotes
state transition matrix and
imm
H
×
∈ℜ denotes observation
matrix.
m
k
w ∈ℜ is input noise of the process
with (0, )
k
wNQ∈ ,
1im
k
v
×
∈ℜ is measurement noise with
(0, )
ii
k
vN∈ℜ. Assume that
k
w and
i
k
v are zero-mean white
Gaussian noise with the following statistics respectively:
[] ;[] ()()
ij i
kl kl kl
ww Q Evv R i j k l
δδδ
==−− (3)
Where,
1, 0
()
00
τ
δτ
τ
=
⎧
=
⎨
≠
⎩
,
。
978-1-4673-9104-7/15/$31.00 ©2015 IEEE
Proceeding of the 2015 IEEE
International Conference on Information and Automation
Lijiang, China, August 2015