Abstract: This paper addresses the problem of testing for the independence among multiple time series captured from different sensors. Implementing the Generalized Likelihood Ratio Test involves testing the null hypothesis that the composite covariance matrix of the channels is block-diagonal through the use of a generalized Hadamard ratio. Using the theory of Gram determinants, it is shown that this generalized Hadamard ratio can be written as a product of independent beta random variables under the null hypothesis. This result is then used to derive an asymptotic null distribution which can be used to identify an appropriate threshold when the sample support is large. Next, we turn 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. The proposed detection method is then demonstrated through simulation and compared to several similar techniques. The multichannel detection method is applied to Synthetic Aperture Sonar imagery of the seafloor. An alternative statistical model for this application will also be discussed.
Adviser: Dr. Mahmood Azimi Co-Adviser: Dr. Louis Scharf Non-ECE Member: Dr. Dan Cooley, Statistics Member 3: Dr. Ali Pezeshki, Electrical and Computer Engineering Addional Members: N/A
Publications: “Multi-Sonar Target Detection using Multi- Channel Coherence Analysis", Proceedings of IEEE/MTS Oceans, Seattle, September 2010.
“Detection in Multiple Disparate Systems using Multi-Channel Coherence Analysis", IEEE Transactions on Aerospace and Electronic Systems, accepted.
"Likelihood Updating for Gauss-Gauss Detection", European Signal Processing Conference 2012, Bucharest, Romania.
“Non-Gaussian Target Detection in Sonar Imagery using the Multivariate Laplace Distribution,” Proceedings of IEEE/MTS OCEANS 2011, Kona, Hawaii.
Program of Study: ECE412 ECE652 MATH532 MATH618 STAT520 ECE795 ECE516 ECE799