Title

Detection of transient signals

Date of Completion

January 1999

Keywords

Statistics|Engineering, Electronics and Electrical

Degree

Ph.D.

Abstract

The topic of this dissertation is the quick detection of transient signals. The transients of particular interest are those mostly encountered in underwater acoustic systems. A sequential detection scheme, specifically Page's test, is given central attention in the detector design, due to its excellent performance, sample efficiency, and its simple and easy implementation. ^ In the first part of the thesis (chapters 2 and 3), we deal with transients that could be represented as a hidden Markov model (HMM). Extension of the standard Page's test to dependent case is first presented. The procedure is particularized to HMM transients via the use of the forward variables for a HMM. Several examples are investigated in detail to reveal the advantage of the detector and to provide some insight as to how to use an HMM as a modeling tool to capture the dependence structure of a transient signal. The above approach is further extended to the detection of multiple superimposed HMMs. Two schemes are presented. The first, employing model expansion of HMMs, has superior performance yet requires substantial computational effort. The second approach, built on a multiple target (state) tracking algorithm, is less computationally intensive and gives reasonably good detection performance. ^ In the second part (chapters 3 and 4), the detection of transients with unknown location, structure, extent and strength is addressed. A homogeneity test that utilizes the nonhomogeneity of DFT outputs for the transient-present data was proposed using an “overdispersed” model. The proposed test statistic is naturally CFAR with respect to the noise power, and exhibits competitive or superior performance to other approaches, such as the CFAR power-law statistic. A sequential implementation, i.e., a Page's test using the statistic, is developed using the asymptotically optimal bias that maximizes the asymptotic efficiency of Page's test. The procedure was further justified by the fact that the input nonlinearity to the Page detector happens to be the generalized log likelihood ratio for testing against the exact overdispersed exponential model, which turns out to be a Gamma distribution. ^