On a Theoretical Background for Computing Reliable Approximations of the Barankin Bound

The Barankin bound is locally the greatest possible lower bound for the variance of any unbiased estimator of a deterministic pa- rameter, under certain relatively mild conditions. Much more essential, Barankin's work determines the su cient and necessary conditions un- der which an unbiased estimator with nite variance exists. Nevertheless, the computing of this bound, along with the proof of existence or non- existence of the estimator, has shown to be extremely challenging in most cases. Thereby, many approaches have been made to attain easily com- putable approximations of the bound, given it exists. Focusing on the rather central matter of existence, we provide a simple theoretical frame within which our approximations of the bound give a clear insight on whether an unbiased estimator does exist.Sociedad Argentina de Informática e Investigación Operativa (SADIO

On a Theoretical Background for Computing Reliable Approximations of the Barankin Bound

The Barankin bound is locally the greatest possible lower bound for the variance of any unbiased estimator of a deterministic pa- rameter, under certain relatively mild conditions. Much more essential, Barankin's work determines the su cient and necessary conditions un- der which an unbiased estimator with nite variance exists. Nevertheless, the computing of this bound, along with the proof of existence or non- existence of the estimator, has shown to be extremely challenging in most cases. Thereby, many approaches have been made to attain easily com- putable approximations of the bound, given it exists. Focusing on the rather central matter of existence, we provide a simple theoretical frame within which our approximations of the bound give a clear insight on whether an unbiased estimator does exist.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Underwater Direction-of-Arrival Finding: Maximum Likelihood Estimation and Performance Analysis

In this dissertation, we consider the problems of direction-of-arrival: DOA) finding using acoustic sensor arrays in underwater scenarios, and develop novel signal models, maximum likelihood: ML) estimation methods, and performance analysis results. We first examine the underwater scenarios where the noise on sensor arrays are spatially correlated, for which we consider using sparse sensor arrays consisting of widely separated sub-arrays and develop ML DOA estimators based on the Expectation-Maximization scheme. We examine both zero-mean and non-zero-mean Gaussian incident signals and provide detailed estimation performance analysis. Our results show that non-zero means in signals improve the accuracy of DOA estimation. Then we consider the problem of DOA estimation of marine vessel sources such as ships, submarines, or torpedoes, which emit acoustic signals containing both sinusoidal and random components. We propose a mixed signal model and develop an ML estimator for narrow-band DOA finding of such signals and then generalize the results to the wide-band case. We provide thorough performance analysis for the proposed signal model and estimators. We show that our mixed signal model and ML estimators improve the DOA estimation performance in comparison with the typical stochastic ones assuming zero-mean Gaussian signals. At last, we derive a Barankin-type bound: BTB) on the mean-square error of DOA estimation using acoustic sensor arrays. The typical DOA estimation performance evaluation are usually based on the Cram\u27{e}r-Rao Bound: CRB), which cannot predict the threshold region of signal-to-noise ratio: SNR), below which the accuracy of the ML estimation degrades rapidly. Identification of the threshold region has important applications for DOA estimation in practice. Our derived BTB provides an approximation to the SNR threshold region