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Due to the differences in the inherent properties of digital
and analog systems, synchronization of mixed signal systems
is an important step in obtaining network consensus. The
network of nodes will be mobile and the environment will be
changing, which results in a dynamic network topology. Thus,
stability of ubiquitous sensing will become an important
issue. Sensor bias, measurement noises, communication delay
and interference will inevitably cause system deviation.
Since the sensor network uses a common communication channel
to share analog and digital information, a unified framework
to assess its capacity is required. In order to achieve the
theoretical performance bound, many factors, such as sensor
bias and measurement-to-object association, should be
considered. In addition, these algorithms should be
sequential for the real-time implementation. Hence, an
adaptive network architecture that can learn and evolve its
monitoring and inference capabilities over time to deal with
unknown faults or failures would be desirable. We have built
a strong collaboration of expertise in information theory,
complex network, signal processing and dynamic systems
theory to address these problems. We will work with our
industrial partners¾PPIC,
CRC Canada, Dr. Robot, DRDC, AUG signals, and Precarn for
practical applications of our research results. In the
following subsections, we detail the individual subprojects.
1. Dynamics of
Networked Information Processing Systems
Based on our previous work , we will continue the
theoretical development for a rigorous analysis of the
multi-stability exhibited by simple delayed inhibitory loops
of neurons. This important multi-stability enables a simple
network acting as analog memories. In the current model for
the recurrent inhibitory loop, the effect of the inhibitory
postsynaptic potential from the inhibitory neuron to the
excitatory neuron is simplified as a delayed self-feedback
of the membrane potential of the excitatory neuron. However,
a realistic model should account for the coupling between
the inhibitory and excitatory neurons. This results in a
model with two nonlinear coupled delay differential
equations which link the dynamics of these two neurons. A
novel approach linking the symbolic dynamics will be
developed for the analysis of asymptotic stability of equilibria and periodic orbits and their domains of
attraction of nonlinear coupled delay differential
equations. We will study the relationship between the number
of fixed points of the phase-resetting map and the number of
distinct periods of stable patterns rather than the number
of stable patterns for all the value of delay.
To reflect inevitable delay in communication as well as the
interference in communication channel, we will model the
network of heterogeneous dynamic systems using coupled
delay-differential/difference equations and analyze the
effect of additive and multiplicative noise on its
stability. We will use the Ito and Stratonovic
interpretation of the stochastic integral to generate
solutions to the coupled differential equation. Using the
stochastic variant of Liapunov's second method, the effects
of additive noise in both delayed and non-delayed systems
will be analyzed. It was shown by Dr. Mackey in his previous
work that with respect to mean square stability, depending
on the parameters, additive white noise may lead to a
destabilization of differential delay equations. We will
further look at the dynamics of sensor network from the
entropy evolution view point. Here we compare and contrast
the temporal evolution of the conditional and Gibbs’
entropies in a variety of dynamical settings. One of the
advantages of this approach is that it will result in a
complete Bayesian method by combining dynamics and signal
processing to estimate the parameters. Dr. Milton has
analyzed the effect of delay and noise in unstable dynamics.
We will extend this study to a network of coupled delay
differential equations and analyze stable and unstable fixed
points. We will further assess the sensitivity of the system
on its parameters using bifurcation analysis.
We will use graph theory to analyze consensus
in sensor network. We will work on synchronized regions,
synchronization conditions, and the relationships between
the graphical network topology and the dynamical network
synchronizability.
Some new criteria and methods for enhancing the network
synchronizability will be established, and
information-feedback-based stabilization methods as well as
synchronized-region enlargement issues will be addressed.
Dr. Guanrong Chen has used the
non-identical oscillators based on the both state-space and
Kuramoto models which are represented by coupled
differential equations to analyze the synchronization
properties of complex networks. This work will be extended
to heterogeneous networks with analog and digital data. We
will develop synchronization schemes for sensor networks
based on the Lyapunov functional method and Kronecker
product properties which ensure that the dynamical coupled
array will achieve global exponential synchronization. This
will be accomplished by a suitable design of the coupling
matrices, the inner linking matrices, and/or some free
parameters to express the relationships among the network
components. The important issue of how the topology affects
the synchronizability in a network will be addressed,
thereby finding a way to improve network synchronizability
by a suitable slight change of its topology.
Another
important issue needs to be addressed is the identification
of dynamic systems. In the past, Dr. Leung’s work on chaotic
sequence for estimating parameters of linear and nonlinear
systems which resulted in semi-blind estimation scheme that
has comparable performance with non-blind statistical
identification methods. Our recent work shows that by using
chaotic symbolic sequence, even with very short sequence,
one can achieve theoretical performance bound. It was Dr.
Mackey’s proof that, every symbolic itinerary can be
represented with the corresponding chaotic trajectory opens
up new ways to do blind system identification. Using this
one to one relationship, we will build a generalized
framework for the identification of systems when the input
is analog or digital or a mixture of both. When sequences
from multiple sources need to be aligned, we use the
information theoretic techniques developed by Dr.
Garssberger.
2.
Information processing in networked dynamic systems
When a sensor
network is composed of digital and analog information
simultaneously, there raises a fundamental problem: what is
the optimal performance that the sensing system can achieve.
In this project, we will investigate the capacity of a
sensing system by taking the geo-distribution, the
uncertainty of sensor measurements and the communication
constraints (power, bandwidth) into account. The method of
graph entropy will be used to model the interchange
semantics between digital and analog systems. A
generalization of Kolmogorov-Chaitin complexity will be
developed to provide sufficient conditions under which the
asymptotic equipartition property of interchange systems
holds. We will derive scaling laws for the growth of the
number of sensor nodes and the number of events to be
monitored. Mutual information (MI) will be used to measure
the similarity and dissimilarity of the information from
multiple sources. Compared to the conventional algorithms
that use heuristic scoring and expert knowledge, MI-based
methods are able to provide a more objective and model
independent solution. Based on the MI estimator from Dr.
Grassberger, we will develop a nearest neighbor based MI
estimator by constraining the search window within the K-nearest
neighbors. The search of the nearest neighbors will be
carried out by the box-assisted, the k-D trie, and the
projection algorithm. We will compare their performances
starting from the scenario of fixed-mass and fixed-radius
neighborhoods in high dimensional systems.
An effective
processing technique for ubiquitous sensing needs to combine
the dissimilar information from multiple sources so that a
global picture of the sensing area can be obtained. Before
combining information from multiple sensors, the problems of
sensor alignment and association of sensor measurements to
the objects have to be resolved. Conventionally, these three
processes, i.e., registration, association and fusion, are
investigated separately. But in practice, they have mutual
effects on each other. Recently, we have formulated
registration, association and fusion of discrete dynamical
sensory data as a joint optimization problem, and proposed a
solution based on maximum likelihood estimation. We will
extend this method to nonlinear dynamical systems by using
our recently developed nonlinear filter. Compared to the
extended Kalman filter (EKF), this new nonlinear filter
provides optimal state and parameter estimates without using
any approximation of the nonlinear modal. We also plan to
extend this method to continuous dynamic systems. We will
use the exact finite-dimensional filter (EFT) developed by
Dr. Elliott to test the performance of our joint method at
the continuous domain. The convergence of these algorithms
will be analyzed using the discrete and continuous time
Kronecker’s lemma.
In order to
process dissimilar sensory data, a unified representation is
proposed based on information theoretic entropy. The entropy
will be first estimated by using the non-sequential
recursive pair substitution (NSRPS) algorithm, which was
developed by Dr. Grassberger. Instead of using states
estimates and the corresponding covariance, such information
theoretic entropy is then feed into our joint method to do
information fusion effectively. One of the disadvantages of
NSRPS is that it has high computation complexity thus can
only work offline. For the purpose of sequential processing,
we will model the entropy estimation problem as hidden
Markov chains, and develop a recursive version of NSRPS
based on Dr. Elliott’s work. A duality between a forward and
a backward un-normalized probability process will be
exploited so that the entropy estimates are updated with new
observations, without complete recalculation from the start.
We will compare the performance of this recursive NSRPS
approach with the conventional NSRPS in terms of estimation
accuracy and computation complexity. The estimation accuracy
will be evaluated by comparing with the performance bound
that is derived using MI.
3 Applications
Theoretical
findings of this project will be promptly translated to
solve many problems in Engineering. We collaborate with PPIC,
Dr Robot, DRDC, CRC, and Neocific to solve different
problems in sensor network. Details of individual projects
will be discussed next.
(a) Pipeline Monitoring
 Problem:
PPIC has installed several pipeline monitoring stations for
the City of Calgary (the figure on the left shows its setup
at 54 Ave NE, Calgary). The collected acoustic data is
stored in a 128 Mbits PC card. Due to the limited memory,
the data has to be manually downloaded to a laptop every
day.
Solutions: We will work with PPIC to provide a
wireless data transmission solution based on our software
radio technology. It will be installed at the site and used
for data transmission through a distance of 20 km.
Collaboration:
PPIC will provide two MITACS internships through this
project.
 (b)
Home Surveillance Robots
Problem:
The wireless module used by Dr. Robot is based on WiFi (IEEE
802.11g). Although its bandwidth is supposed to be
sufficient for wireless video transmission at 30 frames per
second, it is found that frame delay of 1 to 2 seconds
occurs frequently even when the robot is only 0.8 meters
away.
Solutions:
We will work with Dr. Robot to improve the efficiency of the
media access control (MAC) layer. An adaptive coding scheme
will be integrated into the current MAC, so that under a
harsh channel condition, video can be transmitted at a low
data rate instead of being dropped.
Collaboration:
Dr. Robot will provide two MITACS internship through this
project.
 (c)
Water monitoring
Problem: We are currently
working with AUG and Precarn to develop an intelligent
drinking water monitoring software (IDWMS). The water
sensors, as shown on left, include sensors for turbidity,
chlorine residual, pH, etc. The non-sensor information
includes customer complaints, maintenance schedules and
public health syndromic surveillance data. Due to the
different formats of sensory data and non-sensor
information, the current fusion technology cannot provide a
satisfactory solution to combine them effectively.
Solutions: We will develop a
unified fusion framework based on the information theoretic
filters. Both sensory data and non-sensory data will be
combined at decision level to provide early warning of
drinking water contamination.
Collaboration: AUG will
provide two internships to integrate our fusion techniques
to IDWMS.
 (d)
Information Processing in Sensor Network
Problem:
We are currently working with DRDC to develop an integrated
approach for wide area coastal surveillance. Providing
seamless coverage using multiple sensors is not possible in
this application.
Solutions: We intend to
develop a sparse information based assessment and planning
technique. Potential resource planning and allocation
controls and additional action sequences will be encoded
into utility functions which can then be simultaneously
evaluated along with situation assessment.
Collaboration: DRDC will
provide in-kind contribution for our research in situation
assessment and resource management. Further, they will also
provide two internships to integrate our work into their
systems
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