REDG in Sensor Networks for Environment Reconstruction 3
2.1. Environment reconstruction
The objective of environment reconstruction [1] is to rebuild
the accurate environment in cyberspace based on the gathered
sensory data, which is commonly realized by WSNs. Several
real applications can be found in [3, 4, 6]. However, such
applications are restricted by the energy and storage resources.
The energy constraint is a classic problem in WSNs.
According to [2], battery capacity only doubled in the past 35
years. Moreover, the hazardous sensing environment precludes
manual battery replacement. Energy constraint is unlikely to be
solved in the near future on account of the size limitation of
sensor nodes.
In recent years, the data deluge issue becomes a serious
bottleneck of WSNs. A recent report [10] found that the total
amount of world data storage is growing 31% slower than
the amount of data generated worldwide (dominated by sensor
networks). This expanding gap indicates that storage efficiency
will be a critical issue in WSNs.
2.2. Existing resource-efficient methods
This work is related to energy-efficient and storage-efficient
methods. However, we find that existing approaches cannot
satisfy the joint problem of energy constraint and data deluge
for environment reconstruction.
In WSNs, the energy-efficient methods are investigated from
physical layer [12], link layer [11, 14], network layer [13]to
application layer [2]. Particularly, scheduling the duty cycle of
every sensor node is the widely employed approach for energy-
saving data gathering [15–17, 32]. Although these solutions
are highly diverse, none of them considers an adaptive energy-
efficient mechanism according to the change of environment.
There are also plenty of data compression and data aggre-
gation approaches, which are studied to reduce the storage
consumption in WSNs, e.g. [18–20]. However, we observe that
these approaches operate at the sink or relay nodes. In another
word,theenvironmentaldataactually have been sensedand then
be processed. In this case, some storage and energy resources
have been used. Hence, in this paper, we study the storage-
efficient problem by reducing the amount of data gathering at
the source nodes.
2.3. Compressive sensing
CS [23–25] is a generic method to recover the whole condition
with only a few sampled data [33–36]. Several effective
CS-based applications have been developed in data recovery
field. For instance, network traffic estimation [28], road traffic
interpolation [26] and localization in mobile networks [27].
CS-based methods have the potential to reconstruct the
environment in WSN applications. It has been proved that the
environment can be near-optimally recovered even there are
more than 70% sensory data are missing [30], which motivates
us to exploit CS to reduce the amount of data gathering. Until
now, there is no CS-based method having been studied to
optimize the data gathering for environment reconstruction.
3. PRELIMINARIES
3.1. System model and notation
In environment reconstruction system, sensor nodes are
distributed in the given area to sense and gather data to the
sink during a given period of time. Suppose there are totally n
sensor nodes. The period of monitoring time is evenly divided
into t time slots, any sensor node can periodically (once per
time slot) sense the environmental data.
Definition 1. Environment condition (EC): EC is the real
environmental data sensed by sensor node i at the time slot
j denoted by x(i,j), where i = 1, 2
...,nand j = 1, 2...,t.
Definition 2. En
vironment matrix (EM): EM is the matrix of
all real environmental data, which is a mathematical way to
describe the dynamic environment. All ECs x(i,j) form a EM:
X = (x(i, j))
n×t
. (1)
Thereby, this is a matrix constituting of n rows and t columns.
A complete EM presents that all ECs are gathered, which
indicates the 100% accurate environment reconstruction.
Definition 3. Binary index matrix (BIM): BIM is a n × t
matrix, which indicates whether the sensor node i at time slot
j senses the EC or not. BIM is defined by
B = (b(i, j))
n×t
=
1ifx(i, j) is gathered,
0 otherwise.
(2)
Definition4. Gatheredmatrix (GM): GM isthe matrix ofonly
gathered data by a WSN. Since some ECs may not be gathered,
elements of GM are either EC (x(i, j)) gathered by sensor node
or zero (b(i, j) = 0). Thereby, GM is an incomplete EM. GM
is denoted by G and can be presented by
G = X · B. (3)
Definition 5. Estimated environment matrix (E2M): E2M is
the result of environment reconstruction, which is generated by
interpolating the missing values in GM to approximate EM.
E2M is denoted by
ˆ
X = ( ˆx(i, j))
n×t
. (4)
3.2. Problem statement
In this paper, we focus on the data gathering problem for saving
the resource consumption and acquiring accurate environment
reconstruction.
Section B: Computer and Communications Networks and Systems
The Computer Journal
, 2014
at Beihang University on December 23, 2014http://comjnl.oxfordjournals.org/Downloaded from