ConclusionsTranslate the Gaussian distribution in signal space
to log-Gaussian distribution in distance space in order to model
the distribution of distance measurement.Use a probabilistic
approach to model location estimation.For location tracking
requirement, propose a error model to evaluate the performance of
the sensor deployment.Combine error model with awake/sleep protocol
to control network topology.
My name is ShengPo Kuo.Today, I will present our work about the
deployment issue in the wireless sensor networks. The title is A
Probabilistic Signal-Strength-Based Evaluation Methodology for
SensorNetwork Deployment.This is the outline of this
presentation.First, I will give a brief introduction of the
wireless sensor networks and mention our motivation and goal of
this paper.Then, I will explain the problem statement and the
assumptions.Third, we propose an error estimate model to evaluate
the location positioning or location tracking capability of a
specific sensor network.Then, I will present some
applications.Finally, I will draw a conclusion.
Introduction:workmotivation & overviewProblem statement and
assumptions:assumptionError estimate model and algorithm:algorithm
& modelApplications and experimental Results: demo &
modelWireless ad hoc sensor network has a collection of sensor
nodes.Each sensor node is a tiny device. These sensors can sense,
compute, and communicate with each other.So, it is usually to use a
number of sensors to perform particular tasks, such as target
detection, location tracking, environment monitoring and
controlling.In this paper, we focus on the location tracking
application.
Wireless ad hoc sensor network overviewsensor
nodesensorSensinge.g, ComputationCommunication:wireless
linkneighborad hoc sensor network,
sensor,trackingdetectionmonitor
So, for a location tracking application, given us a sensor
deployment, we can ask:How to find the location of the object in
the environment? andHow to evaluate the performance or error degree
of the sensor deployment? AndWhere to add more sensors to improve
the performance of the sensor deployment?
To answer these questions, we introduce a probabilistic location
estimation model and then propose an error model to evaluate the
performance of the sensor deployment, and then try to reduce the
error degree.
*deploymentmotivation:sensor
deployment1.2.deploymentperformance3.sensorsperformanceOur Approach
:1.location estimation model2.Error modelsensor
deploymentperformanceerror degreeHere, I will define the problem
and describe the assumptions.
assumptionTaking received signal strength indicator to perform
positioning task is usually inaccurate.This is because of
interference, fading, and multipath effect.We can see this figure.
If there are three sensors and one object located here.Each sensor
measure the distance to the object.So, we can expect to get three
circles to locate objects position.However, because of the
unreliable RSSI, the estimation may be incorrect.For example, if
the sensor s_3 measure a smaller signal strength value, then the
positioning result will be wrong.
RSSI():ex:1.2.interference3.signal
propagationmultipathfading1.triangulation2.3.Sensor
s1d14.s2s335.s36.algorithmtrackingerror7.8.error9.Informallysensor
deploymenttracking OBerror degree (sensor)In this paper, we use a
probabilistic location estimation model to illustrate the
inaccuracy caused by the unstable RSSI.So, based on the
probabilistic location estimation model, we want to evaluate the
positioning capability of a sensor network.Formally, we can define
as follows:Given a sensor network deployment S, we want to use an
error degree Es of o to express the positioning performance when
the object is at location o.So, if the error degree of any location
o within an area A is smaller than a predefined threshold Et, then
we call region A is sound.On the contrary, we call this region
unsound region.
1.Location estimation modelRSSI2.sensor deployment SSperformance
formallysensor deployment performancebreak points/regions.sound
regionregion Aerror degreethreshold Etregion Asound
regionregionlocation trackingerror degreethresholdbreak
points/regions3.error degree Es(o)This is our assumption:There are
many sensor nodes and their location are known.These location
information can be obtained from manually input or GPS devices.
nsensor ad hoc sensor networksensor node(sensorGPS) Then, I will
use a simple path loss model to introduce the decay of signal
strength over distance.Also I will mention how to model the
unstable signal strength.Then, I will transform the unstable
phenomenon from signal space to distance space.Based on this model,
we can derive we can derive the location estimation model and error
model.
Algorithm & modelPath loss modelpath loss modelDistance
estimation modelsignal spacedistance spaceLocation estimation
modelError modelerror
In general, the decay of signal strength over distance can be
modeled as this equation.Path loss of distance d equals to the path
loss of a reference distance d_0 plus 10 times a path loss decay
exponent n times log d over d_0 and finally plus a Gaussian random
variable.When we only consider the first two parts. The signal
strength decays from a reference distance d_0. d_0 is closed to the
transmitter, such as 1 meter. One example of the first two part is
shown in this figure. The signal strength decays as a log
function.The final part is our concern. We usually uses a gaussian
distribution to model the unstable signal strength.This unstable
fact can be illustrated in this figure.When an object is fixed at
this location. We collect all signal strength. And, in theory, we
can get a distribution like this figure.
path loss()1.transmitterreceiverdfadingfollowlog() 2.sensor
30ms,s(d=30,dB) ()mean PL(d) followGaussian normal
distribution()transmitterd0log()d=30sensorPL(70)70m sensor70m
signal spacedistance spaceThe previous slide shows the unstable
effect is modeled by a gaussian distribution.Now, we transform the
gaussian distribution from signal space to distance space.Using the
path loss equation, we can derive a log-Normal distribution.This
figure shows an example. We can see the x-coordinate is
distance.
distance spacetransmitterreceiverdX(d)sensord X(d)Using the
derived distance estimation model, we can proceed to derive the
location estimation model in theory.I declare some notation
first.
signal mappingnotationSnsensor(xi, yi)o(xo, yo)disensor si
lilsensor si AregionOk, now I introduce how to derive the location
estimation model.The first equation is the distance estimation
model mentioned before.For positioning, each sensor will give its
distance estimation result.So, for each location, we product all
probability from each sensor and finally do a normalization.We note
it Go(l).I use an example to let this location estimation model
clearer.
osensor si l si l g_o^i(l)()sensor
s1nsensorsaccumulatenormalizedGo(l)() Go(l)sensor deploymentl In
this figure, we place the object at (20,35). And the first sensor
S1 is located at (15,25).Then, we use the G_o(l) to compute the
probability of each location.The result is shown in the figure.We
can see the cross-section from sensor s_1 to object is similar to
the figure of the distance estimation model.
50*50n=2 free space, variance=11(2035)Sensor(1525)Then, we can
use the same way to compute the probability of each location when
there are two, three or more sensors.Intuitively, if there are
three or more sensors, we can estimate an unique location.
2sensor2Sensor3Until now, given us a sensor network deployment,
we can derive G_o(l) to represent the probability of each location
in theory.Then, we focus on the error estimation model.We use
Es(o,l) to express a kind of expected value for error
meaning.Es(o,l) is defined as Go(l) times d(l,o).This means the
error expected value of location l when the object is at location
o.So, we can define another notation Es(o) by the summation of all
locations within the area A to express the error degree of the
object placed at location o when performing location tracking by
sensor set S. Like the following equation.
error modelsensor deploymentperformance1.()osensor set S l
=()*()()o l Es (o,l)2.sensor deployment Stracking ooerror degree
Es(o)=location l 1.4181Finally, we can define Es hat to express the
overall performance of the sensor deployment S for location
tracking.It sums up the Es(o) of all possible object location
within the area A.
sensor deployment Sperformanceerror degree=Es^Examplesensor
deployment s1s2s3performance=31.6117This is an example of the error
estimation model.We can see the location near by the sensors has
smaller error degree.
1.()Example1deploymentlocation trackingerror
degree2.deploymentlocation trackingoverall performance5.7316104In
the following presentation, I will introduce two applications using
the derived error estimation model.
1.Demo2.error modelperformanceThe first application is a
deployment strategy. Its purpose is to deploy more sensors for a
given deployment.We can see initially there are only one
sensor.Based on the error estimation model, we can see the
surrounding of this environment has higher error degree.So, we
greedily deploy extra sensors at the weakest points for accuracy
improvement.This is the final result after we deploy ten
sensors.These figures show the improvement of this deployment
strategy.
error modeltrackingperformancemax error
degreesensor()sensorrandom(1010)sensorerror()max error
degreeaverage error degreesensorThe second application is a
power-saving protocol.This power saving protocol let sensors change
to sleep mode when there are enough sensors for the location
tracking application and let sensor change to active mode when
there are not enough sensors for the location tracking application.
Here we use the derived error estimation to determine whether the
sensors can satisfy the accuracy requirement or not.First, I will
introduce the awake protocol.This protocol is based on the Voronoi
diagram.Voronoi diagram is a graph. This graph algorithm can
partition the sensor network into several polygons and all points
in a polygon are closest to only one sensor in this polygon.
Error model performanceawake protocolawakesensorVoronoi
diagram()sensorsensoractive sensorVoronoiregionregionsensorsiAwake
protocol1.Vtnetwork configurationsensor set Stopologybackoff
timer2.Etthreshold3.active sensoruniquebackoff timer ti4.backoff
timer0si2Sensormonitorperformance Ei (epsilon
i)Location_maxregionerror degree5.performance Ei (epsilon i)
threshold Et siawakeLocation_maxsensorWe can see this figure. The
network is partitioned by the active sensors.We use black node to
represent active sensors and the other gray nodes are inactive
sensors.So, each active sensor calculate the error degree of each
location in its polygon.If it detect that any location has error
degree higher than the threshold, it will find one closest inactive
and awake it.For example, if the red node in this figure has too
high error degree, the sensor Si will find the closest sensor Sj
and then awake it to improve the accuracy.
performance Ei (epsilon i) threshold Et
siawakeLocation_maxsensor sj
On the other hand, if all location in a polygon satisfies the
error threshold, the active sensor in that polygon should try to
change to sleep mode.
error modelredundant sensorawake protocoltimer=0performance
threshold Etsleep_request messageneoghborNeighborsleep_request
messagesisleepmonitor okoksleep_accept message sisi
sleepsleep_reject messageSi neighborsleep_accept messagesleepWe use
this example to illustrate this protocol directly.If sensor Si
detects that all locations in its polygon are sound, it will try to
go to sleep mode.Why not directly go to sleep mode?This is because
this sleep decision may make some location cannot satisfy the error
threshold.So, the sensor Si needs to send a sleep_request message
to its neighbors to make sure its decision will not make some
location unsound.
()Sisleep_request
messageneighborsleep()neighborsisleepchecktopologyokoksi
sleep_accept message.si neighborsleep_accept messagenetwork
configuration Vt broadcastOk, this slide shows some
conclusions.
distance space2.model3.error modelsensor deployment
performance4.error modelprotocolcontrol network topology
