Information Quality Management in Sensor Networks based on the Dynamic Bayesian Network model

Abstract

To satisfy application information quality (IQ) constraints in a sensor network, the efficient way is to choose the most appropriate sensor nodes and sensor modalities which would provide a required IQ for the current state of the system. In this paper, two formulations of an activity recognition application are considered - the first based on static Bayesian network (BN), and the second on dynamic Bayesian network (DBN) which allows temporal changes to the conditional probabilities of the system states. It is shown that for similar results, in the certainty of state estimation, the formulation based on DBN uses much less resources, because it relies significantly on the readings obtained in the past. Also DBN model is more robust since it greatly reduces the likelihood of selecting unnaturally drastic state changes.

Full text

Page 1

Information Quality Management in Sensor
Networks based on the Dynamic Bayesian Network
model
Andrei Tolstikov1, Wendong Xiao2, Jit Biswas2and Chen-Khong Tham1
1Dept of Electrical & Computer Engineering, National University of Singapore
3 Engineering Drive 3, Singapore 117576, {eletag, eletck}@nus.edu.sg
2Institute for Infocomm Research
21 Heng Mui Keng Terrace, Singapore 119613, {wxiao, biswas}@i2r.a-star.edu.sg
Abstract
To satisfy application Information Quality (IQ) constraints in
a sensor network, the efficient way is to choose the most
appropriate sensor nodes and sensor modalities which would
provide a required IQ for the current state of the system. In this
paper, two formulations of an activity recognition application
are considered - the first based on static Bayesian Network
(BN), and the second on Dynamic Bayesian Network (DBN)
which allows temporal changes to the conditional probabilities
of the system states. It is shown that for similar results, in the
certainty of state estimation, the formulation based on DBN
uses much less resources, because it relies significantly on the
readings obtained in the past. Also DBN model is more robust
since it greatly reduces the likelihood of selecting unnaturally
drastic state changes.
1. INTRODUCTION
Multi-modal sensor networks are expected to become an
important part of the future ubiquitous intelligent comput-
ing. They are capable of obtaining information and deriving
complex characteristics of the phenomena taking place in the
environment being monitored. However, since the processing
of information from sensors of different modalities is com-
plex, and applications, built in such environments, are highly
dependent on the particular content of the information, the de-
ployed sensor network applications are mainly custom-made.
However, for sensor networks to become widely used there
have to be a way to separate the complexity of information
processing from the application development.
One of the approaches to obtain such separation is to use
an architecture where a layer which processes information
supplies the applications with the processed high-level in-
formation. The additional advantage of such separation is
that the high level information can be reused by different
applications, enabling more complex environment intelligence
and saving resources for data acquisition. The diagram of such
an architecture is shown in Fig. 1. However, in this case we
need to introduce some metrics which characterize the quality
of the supplied information and ensure applications that the
X1
X2
X3
X4
XN
Application
Application
Application
Sensor Network
Fig. 1:
Each application deals only with collective information obtained by the
sensor network. The information values are represented by the boxes. This
information is already high-level and therefore has to be characterized by the
description of the quality of information (IQ)
The diagram of the application interaction with sensor network.
data supplied is suitable for application needs. The efficient
way to satisfy these application requirements is to choose the
most appropriate sensor nodes and sensor modalities which
would provide a required IQ for the current state of the system.
It is important to notice that the quality of obtained information
in general depends on the state of the system (phenomena)
being monitored. Therefore if we want to provide efficiently
information about a phenomena observed, we have to consider
its state in our decision which resources to use.
A. Relevant work
There are a few architectures which use a notion of quality
of obtained information and do sensor management with
the aim to satisfy certain IQ bounds. MiLAN [1] addresses
the question of how to guarantee IQ in the presence of
resource constraints. However, MilAN uses very rough and
non-transparent notion of quality. In QUASAR [2], the IQ
notion of application error tolerance is introduced and ad-

Page 2

dressed by using approximation for the cases when data is
lost or unavailable due to resource limitations. However, the
described approach is only applicable to rather simple in-
network processing.
Midfusion architecture[3], similar to our approach, separates
information fusion into two levels - sensor and application,
each of them represented by Bayesian network (BN). For the
complete processing in the particular environment the BNs
are combined in such a way that the results given by the
combined BN satisfy certain requirement. However, in making
decision which set of sensors to choose Midfusion middleware
only considers the available applications, their structure and
available sensors. The state of the observed phenomena is not
taken into account and sensor allocation is changed only when
the applications or available sensors are changed.
In [4] Feng Zhao et. al. described the framework of
information-directed approach to signal and information pro-
cessing. As an example of an application of their framework
they consider fixed application - target tracking. For this fixed
application the algorithm for choosing the best sensors for a
given state of the observed phenomenon is proposed. However,
the choice of applications in their framework is limited to
the target tracking and therefore may be of limited use for
observing arbitrary phenomena.
In [6] was proposed a framework which made dynamic
resource allocations according to the current observed phe-
nomena state. The goal of the framework was to choose
optimal set of sensors to monitor a system while maintaining a
certain level of the quality of information obtained. As a model
for fusion authors proposed to use the Dynamic Bayesian
Network (DBN) [7] model. However, despite the fact that the
framework used DBN with the hypothesis being a temporal
node, it did not specifically address the issue of changing
phenomena state.
B. Paper plan
In this paper, we describe some implications of using BN or
DBN models for efficiently managing sensor resources for
monitoring of changing state of the observed phenomena.
We also discuss metrics for sensor selection algorithms and
propose two different approaches for sensor selection. For
simplicity, we do not consider the loss of the data in the
network, although we describe how it can be accounted for.
The motivating scenario for this paper is the application
for patient activity tracking and behavior analysis in the home
or hospital ward environment. This kind of scenario is very
interesting because of the two reasons. First, the sensors for
this system are essentially multi-modal, since the environment
may change drastically enough to make useless any particular
sensor modality, be it video, audio or position sensors. The
examples of such changes are changes in the lighting for
video, change in the noise level for sound, obstruction for
position sensors such as ultrasonic or absence of tags for
the tag-based positioning. Second, the set of applications may
also change drastically, as the changing number of people or
other changes in the environment invoke either new copies of
existing applications or applications which are idle most of the
time and only are supposed to respond to certain conditions.
In the next section we explain which particular metric
of information quality is addressed in this paper, introduce
terms and notations and formulate the optimization problem
addressed on this paper. In sections 3 and 4 we explain
how Bayesian network and Dynamic Bayesian model can
be used to provide adaptation to the resource use in the
sensor networks. In the end we present our comparison of
the performance of the schemes based on the BN and DBN.
2. NOTATIONS AND DEFINITIONS
A. Information quality metrics
There are two major classes of IQ metrics: information com-
pleteness and information uncertainty. The first class includes
such metrics as coverage, data completeness etc. The second
class includes tracking accuracy, false alarm rate or correct
recognition rate.
In the example of the patient tracking application the
main IQ metrics are tracking accuracy, activity or behavior
recognition false alarm rate, timeliness for notification of
critical situations and completeness of the activity tracking
in time (assuming coverage is full). In this paper we consider
mainly the application of activity recognition, and therefore the
main metric we address, is the certainty level in the activity
recognition. The choice of method is dictated in this case, by
the fact that the sources of information for activity recognition
are very heterogeneous. Bayesian networks are convenient
for this situation because they allow fusion of heterogeneous
multi-modal data.
B. Notations
Θ = {θ1,...,θK} - set of system state descriptions obtained
by the fusion system. In the terms of Bayesian networks, they
represent a set of hypotheses.
In some cases we are going to distinguish between the
estimated state Θ and the actual state of the system we denote
Ω = {ω1,...,ωK}
Total set of sensors S = {S1,...,Sn} and set of sensors
producing data at time t, St⊆ S
The measurement of sensor i at time t is z(t)
the measurements belonging to a finite set of possible values
Fi= {fi
feature extracted by a complex sensor modality such as video
or audio, or an area of possible values for a continuous sensor
modality such as position. By Z(t)we denote a vector of
measurements z(t)
i, each of
1,...,fi
L}. The meaning of each fi
jis either a particular
i.
C. Optimization problem formulation
In this paper we only consider resource optimization for a
single application. The goal is to provide certain level of IQ.
If the IQ is better than what is required, then the resources
should be saved. If the IQ is worse, then resource cost is
ignored. Effectively it is a minimization problem
Minimize CIQ(IQreq− IQ(R))++ CT
where cost of IQ violation greatly dominates the cost of
resources.
resR

Page 3

Fig. 2:
recognition of eating in the kitchen. The top node represent the activity we
want to detect. Blue nodes represent the features provided by different sensor
modalities. Actions node has three possible values: Nobody present, Person
in the kitchen and Person eating
The Bayesian Network for estimation of the quality of action
D. Sensor model
In this case we assume that every sensor is actually com-
plex device which performs some feature extraction and then
provide us with processed information. Since it is processed
data, depending on the acquisition method and type of data
processing, sensors may have different costs even if they share
the same physical sensor modality. For example considering
video modality, some features may be produced with satis-
factory quality using low frame rate and low computational
power. Others may require much better video quality and
therefore more computational power. We assume that modality
can provide the model of measurement Mi = Pr(xi|fi
which we can use to construct the Bayesian Network.
j),
3. SENSOR SELECTION USING BAYESIAN NETWORK
One of the ways to find the required set of sensors which
would satisfy the IQ requirements is to use a Bayesian network
model. Bayesian network [5] is a graphical representation of
the dependency between random variables. Because of the
hierarchical dependency between variables the joint proba-
bility distribution can be expressed in terms of conditional
probabilities of variables depending only on the variables
immediately above the variable in the hierarchy, called parents
and denoted by a set π(Xi). The joint probability is given by
P(X) =
n
?
i=1
P(Xi|π(Xi))
The example of the Bayesian network is presented on the
Figure 2.
Usually, the top node of the Bayesian network model
describes the system state Θ, called hypothesis, which we want
to estimate. The leaf nodes of the network represent measured
values zi(in the case of sensor network - sensor readings or
features). Given the joint probability, we can use it to estimate
the state of the system based on the sensor data measured. It is
done by computing the marginal distribution Pr(Θ = θk|Z).
However, for several reasons, Bayesian network model is
not very suitable for the dynamic phenomena-aware resource
management. First, since there is no notion of time in the
Bayesian network, the estimation of the state Θ is only valid
for the moment when the sensor readings were taken. Second,
many sensor readings has to be taken at the same time to
provide satisfactory IQ because sensor readings from the
previous time moments cannot be reused. Third, Bayesian
network does not provide a way to estimate system state in
the future time moment and therefore does not allow predictive
sensor selection.
Therefore the dynamic adaptation of the selected sensors
which can be done using Bayesian network include reaction
to the changes in application IQ requirements and the change
in the set of avaiable sensor modalities. Such an adaptation
was realized in the Midfusion [3].
Below, we describe the sensor selection based on the
Dynamic Bayesian network model and explain how it can
address the limitations stated above.
4. SENSOR SELECTION USING DYNAMIC BAYESIAN
NETWORK
A. Dynamic Bayesian network model
Dynamic Bayesian network [11] is a Bayesian network con-
structed from above Bayesian network with addition of the
temporal behavior of some of the system variables. There is
a copy of the static BN for every time moment, describing
the dependency between random variables at the particular
moment. Besides, the nodes of BN which describe the random
variables which evolve in time become temporal nodes. These
variables are assumed to have first-order Markov dependency
on their values at the previous time moment and therefore each
temporal node has an additional parent - a copy of the same
node from the previous time slice.
The joint probability distribution is therefore has time
component and is given by
P(X1:T) =
T?
t=1
n
?
i=1
P(Xt
i|π(Xt
i))
Since the first order Markov process is assumed for the
state of the temporal nodes, it is sufficient to keep only two
time slices of the DBN to describe the system. First time
slice describes the past, the second describes the future. If
there was any data taken at the last moment, it is added as
evidence nodes to the first copy of the BN. Note, that although
the first copy of the BN is built on the basis of the original
static BN, the conditional probability distributions (CPD) for
the temporal nodes are different, because they depend on all
the past observations. On the other hand, the CPDs for the
temporal nodes in the second copy of the BN are equal to the
original CPDs. This change in CPDs of the temporal nodes
represents all the dynamics of the system. On the other hand,
the fact that the CPD for the temporal nodes is changing every

Page 4

Fig. 3: The Dynamic version of the Bayesian Network from the previous
figure. Yellow nodes are temporal nodes. In this case, the timed nodes are
Activity, Something on the table, Position and Sitting.
time step actually represent the memory of the past sensor
readings embedded in the model. Even if one of the sensors
give a new information at the next time step, it will not affect
the distribution of the hypothesis state much, unless it comes
from a very reliable sensor or correlates with other data.
Similar to the Bayesian network, usually the top nodes
of the both copies of the BN represent a hypothesis Θ and
leaf nodes represent sensor readings or features zi. The only
difference is that both Θ and zihave different time indices in
the two copies of the BN, e.g. z(t−1)
of the state in the past is done using evidence readings Z(t−1)
and prediction of the system state at the next time moment
Θ(t)is done by obtaining the distribution Pr(Θ(t)= θk).
Since distribution at the time t − 1 together with obtained
evidence defines the distribution at the time moment t, we
can use joint distribution Pr(Θ = θk,z1= f1
to find which set of sensors would likely to give satisfactory
information quality.
Figure 3 shows an example of the Dynamic Bayesian
network corresponding to the Bayesian network from the
Figure 2.
i
and z(t)
i. The estimation
j1,...,zn= fn
jn)
B. Phenomena tracking using DBN
The phenomena tracking is done in the following way. Be-
low we present one cycle of the acquisition, estimation and
selection process. In this process we assume that the data is
acquired from all the sensors in parallel.
1 Acquire sensor readings according to
the set St−1
2 Update hypothesis distribution using
acquired data Pr(Θ|Z(t−1))
3 Update joint distribution for the next
step Pr(Θ(t),s1,...,sn)
4 Select subset of sensors St for the
next step so that entropy H(t)(Θ) < threshold
5 Update joint distribution for temporal
nodes for the next step Pr(θ(t),Xτ1,...,Xτm)
Similar to [6], we estimate the expected entropy of the
hypothesis at the next time moment as
H(t)(Θ|S) =
=
?
Θ
?
Z(t)∈F1...Fn
Pt(θ,z(t)
1,...z(t)
n)logP(θ|z(t)
1,...z(t)
n) (1)
Depending on the algorithm implementation, either total
entropy H, or normalized entropy H can be used, where
H(Θ) = H(Θ)/log(|θ|), |θ| is the number of hypothesis
states.
Primary objective of the sensor selection algorithm is there-
fore to choose sensors which would give the expected entropy
of the state hypothesis below certain threshold. Please note,
that, unlike the case of the static Bayesian network, in the
dynamic case the data obtained previously is still useful,
because it affects the joint probability distribution Pr(Θ =
θk,z1 = f1
sensors required to satisfy the application requirements can
be low or even no sensor readings may be required.
j1,...,zn = fn
jn). Because of this, the number of
C. Sensor Selection in the case of high certainty
However, the memory effect of the DBN model has a draw-
back, too. If the entropy obtained during previous time step is
already quite low, then, depending on the transition probabili-
ties between hypothesis states, it may stay low for several time
steps even if no new data is obtained. Although it does allow
to save on the resource use, this effect carries a risk that we
may miss the change in the system state. Since, in this case,
the certainty is already high, we do not need to improve it by
selecting sensors which would give low expected entropy for
all the system states. Instead, we would like to focus on the
possibility of the change in the state.
In this case, we can use the metric which expresses expected
entropy of the result for the actual phenomena states different
from the current most likely state. We propose to use expected
entropy conditional on the actual system state.
It is computed similar to the expected entropy for the sensor
set in the Equation 1, except that the probability of a particular
sensor reading set is conditional on the actual system state.
H(t)(Θ|S,ωi) =
?
Z(t)
Pr(z(t)
1,...z(t)
n|ωi)×
×
?
Θ∈F1...Fn
Prt(θ|z(t)
1,...z(t)
n)logPr(θ|z(t)
1,...z(t)
n)
(2)
The distribution Pr(z(t)
static Bayesian network. This is because in particular static
network correctly describes distribution of the readings for
a particular actual state, whereas Dynamic Bayesian network
describes our belief about the readings distribution based on
the current estimated system state.
1,...z(t)
n |ωi) is computed using the

Page 5

To combine entropies for the different actual states, we
propose to compute their weighted sum according to the
estimated state likelihood at the next time step.
? H(t)(Θ|S,Ω = θmax) =
1 − Pr(θ = θmax)H(t)(Θ|S,ωi)
Therefore the step 4 of the phenomena tracking is modified
4 If H(t)(Θ) > threshold, then Select subset
of sensors St for the next step so that
H(t)(Θ) < threshold
else Select subset of sensors St for the
next step so that ? H(t)(θmax) < threshold 2
The dynamics of the temporal nodes is described by a Markov
process. Since the state space of these nodes is limited, we
may assume that for the particular time interval the transition
probability table is a discrete time version of a more general
continuous time Markov chain, and the continuous Markov
chain is conservative and stable.
In this case we can obtain transition probability tables for
other time interval values using the following:
Pii(τ1) = Pii(τ0)
If we change the time interval between two time slices, we
have to modify the transition probability for the states of the
temporal nodes so that the system dynamics remain the same.
If instead of one time slot we make several time slots
which are shorter, we can distribute data acquisition between
these slots. Sequential acquisition may improve two aspects
of the data acquisition. First, compared to the case of parallel
acquisition, in sequential the obtained result may be used for
improving the choice of the next selection, thus further saving
sensor resources. Second, it may be useful in the case when
different time is required to request a data from the different
sensors, thus making very difficult simultaneous acquisition
without planning in advance.
=
?
ω?=θmax
Pr(θ = ωi)
(3)
D. Sequential acquisition
τ1
τ0 Pij(τ1) = Pij(τ0)1−Pii(τ1)
1−Pii(τ0)
E. Sensor selection with losses
If we have losses in the system, due to network or compu-
tational overload, then not all of the measured data will be
used in the final result. We can estimate the impact of the
losses on the expected entropy If we denote as σ the subset
of S, including the measurements which are not lost and are
actually used in the final result, then the expected information
gain in a system with losses is
J(t)(Θ|S) =
?
σ⊆S
H(t)(Θ|σ)Pr(σ)
where Pr(σ) is the probability that the set of readings not
lost is equal to the subset σ.
If we assume that the data from different sensors is lost
independently and loss probability of data from a sensor i is
qi, then, denoting
Qi(σ) =
?
1 − qi
qi
if
if
i ∈ σ
i ? σ
we get
J(t)(Θ|S) =
?
σ⊆S
H(t)(Θ|σ)
?
i
Qi(σ)
(4)
5. EXPERIMENTAL EVALUATION
We used Bayes Net toolbox [12] to evaluate the use of
the Bayesian Networks as well as Dynamic BN for the
phenomena-aware resource management. The scenario we
used was the observation of eating habits of a dementia patient
in the home environment. The task of the observation is
to track the time when the person is eating in the kitchen.
For both fusion and uncertainty estimation the we used the
networks shown correspondingly in Figures 2 and 3.
Both simulated examples used the same scenario: person
appears in the kitchen, wanders around for a while, coming
in, out, to the table etc. Then at some point he sits at the
table, starts eating after a while, then, after eating, removes
everything from the table and leaves the kitchen. Also, in both
cases we used the same set of sensor readings, which were
generated using our knowledge of scenario and static Bayesian
network model to represent imperfection in the sensing.
These sensor readings were used in the recognition of the
activity using full set of sensors or using reduced set chosen by
the phenomena-aware resource management. Here we present
four results - activity recognition using all the sensors with
BN model, all sensors with DBN model, reduced sensor set
with BN model and reduced set with DBN model.
In our simulation, each sensor modality had its own cost
reflecting relative resource use. For example, the cost of video
positioning was 10 times more than the cost of pressure sensor
on a chair. These costs we used to select more cost-efficient
sets of sensors.
Although we used both static and dynamic Bayesian net-
works, in fact the static BN was not properly used for the
sensor selection. This is because of the absence of the phenom-
ena state dynamics in the BN model as explained in section
3. Therefore we used post-factum sensor selection, when we
used the data from all the sensors to select a subset which
would give a good uncertainty bound for the phenomena state.
Although it is not realistic case, we still used it to compare
this ideal sensor selection using BN model with realistic sensor
selection using DBN model.
The compared results are presented on the Figures 4, 5 and
6.
As it can be seen, for similar results in the certainty of
state estimation, the phenomena-aware model based on the
DBN can use much less resources. This is mainly due to the
fact that the DBN model relies significantly on the readings
obtained in the past.
Another comment concerns the lack of memory in the BN
model. In our model, there are some states of the Action
and Position which prohibit immediate transitions from one
to another. For example, Action state Person Eating can