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 threshold. 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