Graduate Exam Abstract

Nicholas Klausner

Ph.D. Final
May 20, 2014, 10:00 am
Dean's Conference Room (B214 Engineering)
Detection of Multiple Correlated Time Series and its Application in Synthetic Aperture Sonar Imagery

Abstract: Detecting the presence of a common but unknown
signal among two or more data channels is a
problem that finds its uses in many applications,
including collaborative sensor networks,
geological monitoring of seismic activity, radar,
and sonar. The Generalized Likelihood Ratio Test
tests the null hypothesis that the composite
covariance matrix of the channels is block-
diagonal, using a generalized Hadamard ratio.
Using the theory of Gram determinants, it is shown
that this Hadamard ratio is stochastically
equivalent to a product of scalars which are
independently drawn from a beta distribution under
the null hypothesis. This result may then be used
to derive approximate characterizations of the
null distribution of this test statistic including
an asymptotic chi-squared distribution and as well
as saddlepoint approximations, both of which may
be used to determine an appropriate detection

These results are then extended to the problem of
detecting the presence of spatially correlated
time series when each observer employs an array of
sensors. Assuming wide-sense stationary processes
in both time and space, the likelihood ratio is
shown to involve a Hadamard ratio of an estimated
cross-spectral matrix at every
frequency/wavenumber pair, a test statistic
referred to as broadband coherence. Although an
asymptotic result, simulations of several
applications show that even finite dimensional
implementations of the broadband coherence
statistic can provide a significant improvement in
detection performance.

These methods are then applied to the detection of
underwater targets in pairs of high frequency and
broadband sonar images coregistered over the
seafloor. A comprehensive study of these methods
is conducted using several sonar imagery datasets
collected at different geographical locations with
the environments from each presenting unique
challenges. These datasets will be used to
demonstrate the usefulness of results pertaining
to the null distribution of the generalized
Hadamard ratio and to study the effects different
clutter environments can have on its
applicability. They will also be used to compare
the performance of the broadband coherence
detector to several alternative detection
techniques. The results presented here will show
that the fundamental principle of detecting
underwater targets using coherence-based
approaches is itself a very useful solution for
this problem and that the broadband coherence
statistic is adequately adept at achieving this.

Adviser: Mahmood Azimi
Co-Adviser: Louis Scharf
Non-ECE Member: Dan Cooley
Member 3: Ali Pezeshki
Addional Members: N/A

Klausner, N.; Azimi-Sadjadi, M.R., "Multi-sonar adaptive target detection using the Sphericity Test," Oceans - San Diego, 2013 , pp. 1-5, 23-27 Sept. 2013

Klausner, N.; Azimi-Sadjadi, M.; Scharf, L.; Cochran, D., "Space-time coherence and its exact null distribution," Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on , pp. 3919-3923, 26-31 May 2013

Klausner, N.; Azimi-Sadjadi, M.; Scharf, L., "Detection of correlated time series in a network of sensor arrays," Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on , to appear

Klausner, N.; Azimi-Sadjadi, M.R.; Scharf, L.L., "Detection of Spatially Correlated Time Series From a Network of Sensor Arrays," Signal Processing, IEEE Transactions on , vol. 62, no. 6, pp. 1396-1407, March, 2014

Klausner, N.; Azimi-Sadjadi, M.R.;, "Non-Gaussian target detection in sonar imagery using the multivariate Laplace distribution," Oceanic Engineering, IEEE Journal of, accepted

Program of Study:
ECE 652
ECE 752
ECE 795
STAT 520
MATH 532
MATH 618