Wireless sensor networks typically gather data at a number of locations. However, it is desirable to be able to design applications and reason about the data in more abstract forms than points of data. This paper examines one way in which this can be done. By bestowing the ability to predict inter-node values upon the network, it is proposed that it will become possible to build applications that are unaware of the concrete reality of sparse data. This interpolation capability is realised as a service of the network. We present an implementation of this service and discuss its merits and shortcomings. Additionally, we present an initial application of the service in the form of isopleth generation. That is, the delineation of contours of constant parameter value. Finally, we discuss the improvements required to create more sophisticated applications and services and examine the benefits these improvements would bring.

1. Experimental Applications of Mapping Services in
Wireless Sensor Networks
James Shuttleworth, Mohammad Hammoudeh, Elena Gaura, Robert Newman
Cogent Computing Applied Research Centre
Department of Creative Computing
Coventry University, Coventry, UK. CV1 5FB
{j.shuttleworth, aa2792, e.gaura, r.m.newman}@coventry.ac.uk
be processed, aggregated, distilled and acted upon within the
network, possibly with only selected data being reported back
to a monitoring user. The wireless sensor nodes are usually
more than capable of performing these tasks, as long as the ap-
plication developer creates the required software, constructing
specific functions from what has become increasingly generic
hardware.
There has been a consistent effort to change the mechanism
of use of certain capabilities in wireless sensor networks,
to simplify and abstract them, turning them into services of
the network rather than being the result of coordinating the
services of individual nodes. TinyDB’s retrieval of data [1],
for example, uses the abstraction of SQL to effectively hide
the details of data collection, buffering, and transmission.
Following on from such work and moving to a slightly
higher level of abstraction, we propose a new network service:
map generation. The primary purpose of wireless sensor
networks is to collect and transmit data, but other capabilities
have arisen to support this goal. Just as clustering, routing and
aggregation allow for more sophisticated and efficient use of
Fig. 1. Height map from USGS data covering the Grand Canyon
the network resources, a mapping service would support other
network services and make many more applications possible
with little extra effort.
Abstract— Wireless sensor networks typically gather data at a
number of locations. However, it is desirable to be able to design In this paper, we present our first steps towards a general
applications and reason about the data in more abstract forms mapping service. We define a simple service, discuss our
than points of data. This paper examines one way in which this simulation of networks that implement it and present an
can be done. example application built on the service.
By bestowing the ability to predict inter-node values upon
the network, it is proposed that it will become possible to build
applications that are unaware of the concrete reality of sparse II. B ENEFITS OF AN IN -N ETWORK M APPING S ERVICE
data. This interpolation capability is realised as a service of
the network. We present an implementation of this service and We predict many benefits to result from the development of
discuss its merits and shortcomings. an efficient and flexible in-network mapping service.
Additionally, we present an initial application of the service Networks of nodes are built to solve problems and many
in the form of isopleth generation. That is, the delineation of
problems are essentially problems of interpolation between
contours of constant parameter value.
Finally, we discuss the improvements required to create more points and it is this set of problems that we intend to address
sophisticated applications and services and examine the benefits with a mapping service. Defining lines of constant height or
these improvements would bring. pressure, contours and isobars, for example, requires knowl-
edge not just of measurements at a few scattered locations,
I. I NTRODUCTION but also the likely values between them. Contours and isobars
The purpose of any wireless sensor network is to gather are, in fact, specific types of isopleth and a very simple early
data. In the most simple systems, the collected data might implementation of isopleth determination is presented later in
be instantly reported. In more complex systems, the data will this paper.

2. Another problem that is at heart simply a problem of inter- of geometric parameter interpolation has been shown to work
polation is surface reconstruction. While mesh-based models well for reconstructing underlying geography when the entire
are feasible and useful for specific applications int he con- network has been queried [2]. However, It does not extend
text of WSNs [2], an interpolation-based model of surface well to variable surfaces or overlapping local mapping, since
reconstruction offers benefits such as being locally applicable, it requires a complete data set to define the surface.
of arbitrary detail and easily subjected to image processing A more general method is interpolation by inverse distance
techniques. and, specifically, Shepard [4] interpolation which improves on
Other aspects of wireless sensor networks that would benefit it.
from such a service include clustering, in which geographical The simple inverse distance algorithm, used in WSN appli-
context might be useful; deployment, for which the mapping cations before [5], is defined as:
service could provide information on network density related  N
to terrain or phenomenon complexity, and so on. d−u zi


 i=1 i


As well as these easy to identify benefits, it is likely that

if d = 0 for all Di


 N
having such a service would make new applications obvious,
f (P ) = −u
di
just as there has been as recent increase in new Internet 

 i=1
applications combining existing services to produce new and 


until now unthought-of “mashups”.



Of course, the efficacy and efficiency of applications based zi if di = 0 for some Di
on such a service are tied to how well the service is imple- Where, P is the point at which the interpolated value is
mented. required, di is the distance from P to the point numbered i
The implementation of the mapping service presented in in the N known points and zi is the known value at point
this paper, and the example application built upon it, are not i. The exponent, u, is used to control the smoothness of the
optimal. In short, they are inefficient and na¨ve. However,
ı interpolation. High values lead to sharp edges between regions
while more sophisticated implementations of the algorithm while low values lead to soft edges.
are being devised and tested, this simple approach gives us Shepard [4] devised a number of improvements to this basic
an opportunity to investigate the usefulness and validity of its algorithm to limit the effect of distant points, make use of the
application. direction of the relationship between known points and the
point to be interpolated and to incorporate information on the
III. A LGORITHMS FOR M AP G ENERATION slope between known points. The algorithm, including the first
Map generation is essentially a problem of interpolation two of these refinements, has been implemented to interpolate
from sparse and irregular points. Given a set of known data between sensor readings and is discussed further here.
points representing the nodes’ perception of a given measur-
IV. S IMULATION WITH S EN S OR
able parameter of the phenomenon, what is the most likely
complete and continuous map of that parameter? In order to implement our mapping approach and study
In the field of computer graphics, this problem is known as its properties, we have extended an in-house sensor network
an unorganised points problem, or a cloud of points problem. simulator called “SenSor” [6]. SenSor is a realistic and
That is, since we assume that the position of the points in xy scalable Python based simulator, in which each sensor node
is known, the third parameter can be thought of as height and runs in its own thread and communicates using the same
surface reconstruction algorithms can be applied. protocols as its physical counterpart. Sensors have a fixed API,
Simple algorithms use the point cloud as vertices in the with customisable internals. This enables us to experiment
reconstructed surface. These are not difficult to calculate, but with different algorithms for managing the network topology,
can be inefficient if the point cloud is not evenly distributed, simulating fault management strategies and so on, within the
or is dense in areas of little geometric variation. same simulation. Sensors are modelled as a pool of concurrent,
Approximation, or iterative fitting algorithms define a new communicating threads. Individual sensors are able to:
surface that is iteratively shaped to fit the point cloud. Al- 1) Gather and process data from a model environment
though approximation algorithms can be more complex, the 2) Locate and communicate with their (geographically or
positions of vertices are not bound to the positions of points otherwise) nearest neighbours
from the cloud. For applications in WSNs, this means that we 3) Determine whether they are operating ”correctly” and
can define a mesh density different to the number of sensor act accordingly to alter the network topology
nodes, and produce a mesh that makes more efficient use of Separate interfaces gather information from the network
the vertices. Self organising maps are one of the algorithms and display it. This partitioning allows us to experiment with
that can be used for surface reconstruction [3]. This method different ways of processing individual node data into infor-
uses a fixed number of vertices that move towards the known mation. Using this simulation framework, we implement our
data. mapping services. For our experiments, we provided SenSor
Note that surface reconstruction on typical non-overlapping with interpolation capabilities and developed a plug-in to do
terrains is equivalent to sparse-data interpolation. This kind draw the isopleths.

3. For the purposes of the experiment reported here, nodes
are designated into logical groups called clusters where each
cluster is managed by a master node called cluster-head,
as in LEACH [7]. The use of clusters improves network
performance and reliability by localising network traffic. Also,
cluster-head nodes run a time aggregation function to reduce
redundancy and minimise energy consumption by decreasing
the number of transmissions. In this algorithm, robustness is
achieved by storing multipath and electing backup node(s) that
can substitute for the cluster-head when the current cluster
round ends or in some failures. During the set-up phase nodes
will select to belong to the nearest cluster-head using the
number-of-hops metric. The use of this metric will result in
a more fair distribution of nodes among clusters and establish
shorter paths, hence reducing the energy expenditure since
bridging the distance between the node and its cluster-head Fig. 2. SenSor, the WSN simulator, showing information transmission
will be less expensive. Because of the random transmission between nodes and a visualisation of the interpolated surface
delays and synchronisation errors, we use a back-off waiting
scheme, similar to one used in [8], to lessen these effects.
When a node receives an advertisement message it waits for
a constant time to gather more set-up messages; when the timer
expired it rebroadcasts the message with the best metric and
resets the back-off timer. The number-of-hops metric together
with the back-off time will help to reduce the set-up messages
and create more uniform clusters. During the transmission
phase, sensing nodes transmit data to their cluster-head which
retransmit messages to the querying node. All nodes were
given a virtually infinite supply of energy and the protocol was
allowed to run until it converged. Since the energy is unlimited
we have used other metrics to measure energy consumption
like the number of messages sent. For our experiments, we
created an 600-node network in such a way that nodes are
scattered randomly in area of 256 × 256 m2 . Figure 2 shows a
random topology of 600 nodes scattered over a terrain where
the edges represent communication neighbours.
The power of the sensor radio transmitter is set to cover all
nodes within a 50m radius. The processing delay for transmit- Fig. 3. Interpolated field generated from 600 simulated nodes randomly
ting a message is randomly chosen between 0 and 5 seconds, distributed on the surface from Figure 1
simulating real-world characteristics of low-power radio trans-
mission. Using this network configuration we gathered the data
to interpolate the landscape and draw the isopleths from the V. E XPERIMENTAL A PPLICATION
interpolated output. The determination of isopleths or contours is useful in a
The landscape image is fed to the simulator and sensors number of applications and the ability to find the “edges”
will “perceive” the colour intensity at the xy position of of a phenomenon has been put forward before as a useful
the landscape image corresponding to their coordinates as operation [9]. Such an ability would enable the systematic
gathered sense data. After cluster-heads are selected and paths finding and delineation of the borders of phenomena such
are established, an external observer can choose to query any as gaseous emissions or freezing conditions, creating height
node to collect the information necessary to interpolate the contour maps, calculating lines of sight, and so on.
surface from the network. Every node responds to the query To highlight this potential use of an in-network mapping
message by sending its sense value and position through the service, we present an implementation of isopleth generation.
cluster head. This collected information could then be used to This is a simple implementation, with little regard for effi-
build the network surface using the interpolation algorithm. ciency, but nevertheless provides a genuinely useful output for
the purposes of visualisation or phenomenon edge delineation.
With this framework in place, we were able to experiment With no optimisation or refinement to reduce communica-
with isopleth generation.

4. Fig. 4. A contour at 116 units drawn over Figure 1 Fig. 5. A contour at 116 units drawn on the interpolated field in Figure 3
tion costs, the algorithm is very simple. A request is made to In a more advanced implementation, this algorithm would
any node, giving the value of the required isopleth. A height of be replaced by one that begins with an efficient search for the
120 metres, for example, if contours of height were needed. first matching value and then a process of extending the search
This node is then responsible for collecting the information along the isopleth as it is discovered.
needed to produce the result. A threshold figure is also given,
VI. N EXT S TEPS
t, so that values ±t are included.
The simple algorithm presented here causes this node to We have presented, above, our very early research into
then query every other node in the network for their value mapping and the applications of mapping in wireless sensor
of the parameter in question. Once all data is collected, the networks. Leading directly from the work in this paper, there
interpolation is performed as described in Section III, and are a number of avenues that need to be followed.
every value matching the required isopleth is recorded as being The na¨ve approach above collects all of the data in a central
ı
part of that isopleth. location and processes it there. In networks of a few nodes,
This algorithm has been implemented using the simulation this might even be the most sensible solution. However, in
software SenSor and the simple API described in Section IV. networks of nodes large enough to be useful, the number of
Figure 1 shows a height map of a section of the Grand Canyon, transmissions needed to accomplish the task would become so
taken from data recorded by the US Geological Survey [10]. If large as to require a more intelligent solution.
we apply the isopleth generation algorithm to this data directly, The cost of communication in this initial system is very
we are left with a result such as that shown in Figure 4. This high because the interpolation step, the mapping service, is
contour was generated for a height of 116 units and a threshold fairly simple and requires that all data is collected to a point.
of 1. For the most simple case, in which the node collecting data is
To present the result of generating isopleths on interpolated in direct communication with all other nodes in the network,
fields as described above, Figure 5 shows the result of gener- the number of hops is simply N − 1, for N nodes. However,
ating an isopleth with the same parameters as in Figure 4, on this is an unlikely situation in any real world application. The
the interpolated field shown in Figure 3. likelihood is exponential growth with N .
Clearly the interpolated terrain is similar to the real surface. Although the cost, in terms of power of transmission of data
Determining exactly how close the similarity is, and what the in wireless sensor networks far outweighs the usual processing
algorithmic limits to the accuracy of the representation, is a load, the nodes are most often power-limited devices with,
problem we are currently investigating. Consider, though, that at best, a fixed schedule of battery replacement, and so
the information used to reconstruct the surface in Figures 3 computational drain on this resource cannot be completely
and 5 is just 600 points, while the original is recorded as overlooked. For small collections of data of around 50 nodes
65,536. Taking the position of the nodes into account as extra interpolating 65,536 points (a square field 256 × 256) takes
information, the reconstruction is built using less than 3% of very little time, just a few seconds, on a desktop computer
the original data. and would take just a little more on modern sensor nodes.

5. In a real deployment, the number of sensor nodes might We feel that this area of research is pertinent to modern
easily exceed 1,000, depending upon the required density, wireless sensor networks, and in this paper we have taken
drastically increasing computational expense. The acceptabil- initial steps towards exploring it. We have identified appli-
ity of such a computational load in a wireless sensor network cations, such as isopleth generation, that the service would
is debatable, but in this case would probably be unacceptable make simple to develop, and challenges that need to be met
for most deployments. before such a service is feasible. Challenges such as local
The simplest improvement is to develop a complete imple- interpolation, required to make the service efficient enough to
mentation of Shepard’s refinements and assess how this affects be deployed.
the accuracy of the interpolated field when compared to a This paper is not the result of a completed project, but the
known real surface or phenomenon. Although the algorithm exposition of the start of one. The problems and limitations
presented by Shepard [4] is decades old, it is often only described above are the opportunities we intend to take and
implemented in its most simple form and it would be of the lines we intend to follow.
great benefit to have empirical evidence of the performance of The work presented above has been useful in a number
the various improvements to this suggested by Shepard, when of ways. Firstly, it allowed us to extend SenSor so that it
applied to data likely to be perceived by sensor networks. is capable of simulating networks with complex predefined
A particularly interesting feature of the refinements is that variations of parameters over space. This is a useful advance,
they deal with limiting the data included in the weighted since it allows for precise control over the parameters of the
average, or adjusting weights based on context. These im- virtual deployment.
provements might be instantly applicable as ways to reduce Secondly, it gave us an opportunity to examine the appli-
communication costs as well as improve the quality of the cability of Shepard interpolation in the reconstruction of a
interpolation. That is, if local information is required, then parameter map from sparsely sampled data. The experience
only local nodes need be queried. gained here is proving to be invaluable in developing more
Taking this idea further, we arrive at the idea of a mapping sophisticated implementations of the service and its applica-
service that allows for local querying. Our proposed solution, tions.
currently being developed, is an application of the more Finally, we have been able to identify limitations and
advanced mapping service outlined above. problems as well as potential extensions and solutions that
An isopleth for a given parameter at a given value can be would otherwise have been missed until later iterations.
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