Matched-field Acoustic Source Localization Under Information Theory Criteria

In this thesis, the concept of machine learning is adopted to formulate the problem of extract-ing the source location information from hydrophone measured data. Directed by optimization algorithm, machine learning minimizes the error between modeled replica and actual measured data under specific criteria to learn the data structure. Traditional matched-field processing (MFP) methods (e.g. the Bartlett correlator, the maximum likelihood estimator and minimum variance distortionless response, etc.) search the parameters in the source location parameter grids and se-lect the parameter values at the corresponding peak of the ambiguity output as the estimates. Here, the inverse power of the ambiguity output can be interpreted as a generalized error, the grid search is a plain searching strategy, and the estimated parameters present the structure of the received data. Thus, the machine learning framework includes the traditional MFP methods. In this thesis, MFP is studied as a machine learning problem under information theory criteria, which measures the distance between the modeled replica and the actual measured data in the information sense.There are many information-theoretic methods to measure the information distance. Diver-gence is the most popular one. This paper focuses on the study of f-divergence, which has been widely applied in information theory and signal detection. The f-divergence includes the well-known relative entropy in information theory, whose symmetric form is known as information divergence. The f-divergence also contains the Hellinger integral, which composes the error prob-ability bound-Chernoff Bound in signal detection theory. The Bhattacharyya coefficient is equal to the Hellinger integral with a constant control parameter of 1/2, which can predict the upper and/or lower error probability bound for the detection problem without the loss of generality. The natural logarithm of the reciprocal of the Bhattacharyya coefficient is called the Bhattacharyya distance, which measures the information distance. Within the information-theoretic framework, this paper selects the Bhattacharyya distance as the cost criterion and obtains the minimum Bhattacharyya distance estimator following the derivation procedure from minimum relative entropy to maximum likelihood estimator.Although the Gaussian distribution may not characterize the true distribution of the data ex-actly, it is generally the most reasonable choice. The Gaussian distribution has become so promi-nent because of the central limit theorem (CLT) and features such as analytical tractability and easy generation of other distributions. Especially, when the first and second moment of a random process are already known, the Gaussian distribution maximizes the Cramer-Rao bound (CRB). Thus, any optimization based on the CRB under the Gaussian assumption can be considered to be min-max optimal in the sense of minimizing the largest CRB. As CRB is the lower bound any unbi-ased estimator could attain, this characteristics is of clear significance for guiding the performance evaluation of any unbiased estimator.In this thesis, both the signal and noise processes are assumed to follow a zero-mean Gaussian distribution, thus the data statistics can be completely characterized by the covariance matrix. In MFP practice, the amount of measured data is limited by the duration of signal stationarity, phase distortionless bandwidth and other factors. Under these conditions, the maximum likelihood es-timated sample covariance matrix will contain errors, relative to the true data covariance matrix, due to the limited data. This will result in statistical mismatch and distortion of the data informa-tion. Therefore, developing MFP methods that are robust to statistical mismatch is an important contribution.The signal, noise and propagation processes for matched-field source location are respectively modeled. Both the signal and noise models are zero-mean complex circular Gaussian processes. Under such an assumption, the minimum Bhattacharyya distance estimator is used as a basis to derive the matched-covariance estimator (MCE), which has a concise and symmetric mathematical form. MCE matches the modeled replica covariance matrix with the measured data covariance matrix, which gives MCE a multi-rank signal processing ability. For the noise, it is modeled as spatial white local noise or spatial correlated propagation noise, which is tailored for MFP. The propagation noise can be divided into discrete noise (e.g. interference noise) and distributed noise (e.g. surface generated noise). The propagation noise and source have spatial similarity as the propagation noise propagates through the similar underwater acoustic information channel as the source, which presents additional challenges for the MFP method. For the signal propagation, three representative models are chosen to model three types of source localization problems:1) for the deep sea free field source localization problem, the single modal planar wave model is used; 2) for the stationary shallow water waveguide source localization problem, the multi modal full- wavefield model is used; and 3) for the fluctuation shallow water waveguide source localization problem, the recently developed multi-coherent modal group model is used.This thesis compares the machine learning system performance under different cost criteria in different types of sound source localization problems to evaluate the machine learning framework matched field source localization performance from different perspectives. The simulation results of the deep sea free field, the shallow water full-wave field and the shallow water fluctuation field source localization problems show that the information-theoretic principle based MCE can out-perform the classical matched field processing method because:1) MCE exploits both signal and noise data structure at the same time; 2) MCE does not depress or cancel noise, and thus avoids the self nulling problem when the source and interference noise are spatially similar; 3) MCE does not demand rank-1 signal space restriction, and has the ability to implement the multi-rank signal esti-mation; and 4) MCE does not require signal-free and long duration data to estimate the covariance matrix, and can effectively mitigate the statistical mismatch problem.