Give

## Nicholas Klausner

M.S. Final
July 30, 2010, 10:00 am
Engr B105
Underwater Target Detection Using Multiple Disparate Sonar Platforms

Abstract: The detection of underwater objects from sonar imagery presents a difficult problem due to various factors such as variations in the operating and environmental conditions, presence of spatially varying clutter, variations in target shapes, compositions, and orientation. Additionally, collecting data from multiple platforms can present more challenging questions such as how should I collaboratively perform detection to achieve optimal performance?'',''how many platforms should be employed?'', when do we reach a point of diminishing return when adding platforms?'', or more importantly when does adding an additional platform not help at all?''. To perform multi-platform detection and answer these questions we use the \textit{coherent} information among all disparate sources of information and perform detection on the premise that the amount of coherent information will be greater in situations where a target is present in a region of interest within an image versus a situation where our observation strictly consists of background clutter. To exploit the coherent information among the different sources, we recast the standard Neyman-Pearson, Gauss-Gauss detector into the Multi-Channel Coherence Analysis (MCA) framework. The MCA framework allows one to optimally decompose the multi-channel data into a new appropriate coordinate system in order to analyze their linear dependence or coherence in a more meaningful fashion. To do this, new expressions for the log-likelihood ratio and J-divergence are formulated in this multi-channel coordinate system. Using the MCA framework, the data of each channel is first whitened individually, hence removing the second-order information from each channel. Then a set of linear mapping matrices are obtained which maximizes the sum of the cross-correlations among the channels in the mapped domain. To perform detection in the coordinate system provided by MCA, we first of all construct a model suited to this multiple sensor platform problem and subsequently represent observations in their MCA coordinates associated with the $H_{1}$ hypothesis. Performing detection in the MCA framework results in a log-likelihood ratio that is written in terms of the MCA correlations and mapping vectors as well as a local signal-to-noise ratio matrix. In this coordinate system, the J-divergence, which is a measure of the difference in means of the likelihood ratio, can effectively be represented in terms of the multi-channel correlations and mapping vectors. Using this J-divergence expression, one can get a more clear picture of the amount of discriminatory information available for detection by analyzing the amount of coherent information present among the channels. New analytical and experimental results are also presented to provide better insight on the effects of adding a new piece of data to the multi-channel Neyman-Pearson, Gauss-Gauss detector represented in the MCA framework. To answer questions like those posed in the first paragraph, one must carefully analyze the amount of discriminatory information that is brought to the detection process when adding observations from an additional channel. Rather than attempting to observe the increase (or lack thereof) from the full detection problem it is advantageous to look at the change incrementally. To accomplish this goal, new updating equations for the likelihood ratio are derived that involve linearly estimating the new data from the old (already existing) and updating the likelihood ratio accordingly. In this case, the change in J-divergence can be written in terms of error covariance matrices under each hypothesis. We then derive a change in coordinate system that can be used to perform dimensionality reduction. This can especially become useful when the data we wish to add exists in high-dimensional space. To demonstrate the usefulness of log-likelihood updating, we conduct two simulation studies. The first simulation corresponds to detecting the presence of dynamical structure in data we have observed and corresponds to a \textit{temporal} updating scheme. The second is concerned with detecting the presence of a single narrow-band source using multiple arrays in which case we consider a \textit{platform} updating scheme. A comprehensive study is carried out on the MCA-based detector on three data sets acquired from the Naval Surface Warfare Center (NSWC) in Panama City, FL. The first data set consists of one high frequency (HF) and three broadband (BB) side-looking sonar imagery coregistered over the same region on the sea floor captured from an Autonomous Underwater Vehicle (AUV) platform. For this data set we consider three different detection schemes using different combinations of these sonar channels. The next data set consists of one HF and only one BB beamformed sonar imagery again coregistered over the same region on the sea floor. This data set consists of not only target objects but also lobster traps giving us experimental intuition as how the multi-channel correlations change for different object compositions. The use of multiple disparate sonar images, e.g. a high frequency, high resolution sonar with good target definition and a multitude of lower resolution broadband sonar with good clutter suppression ability significantly improves the detection and false alarm rates comparing to situations where only single sonar is utilized. Finally, a data set consisting of synthetically generated images of targets with differing degrees of disparity such as signal-to-noise ratio (SNR), aspect angle, resolution, etc., is used to conduct a thorough sensitivity analysis in order to study the effects of different SNR, target types, and disparateness in aspect angle. The performance of the MCA-based detector on these data sets is measured in terms of probability of detection/false alarm and Receiver-Operator-Characteristic (ROC) curve attributes.