Date of Award

3-14-2014

Document Type

Thesis

Degree Name

Master of Science in Electrical Engineering

Department

Department of Electrical and Computer Engineering

First Advisor

Julie A. Jackson, PhD.

Abstract

This research develops a new Bayesian technique for the detection of scattering primitives in synthetic aperture radar (SAR) phase history data received from a sensor platform. The primary goal of this research is the estimation of size, position, and orientation parameters defined by the “canonical” shape primitives of Jackson. Previous Bayesian methods for this problem have focused on the traditional maximum a posteriori (MAP) estimate based on the posterior density. A new concept, the probability mass interval, is developed. In this technique the posterior density is partitioned into intervals, which are then integrated to form a probability mass over that interval using the Gaussian quadrature numerical integration techniques. The posterior density is therefore discretized in such a way that the location of local peaks are preserved. A formal treatment is given to the effect of locally integrating the posterior density in the context of parameter estimation. It is shown that the operation of choosing the interval with the highest probability mass is equivalent to an optimum Bayesian estimator that places zero cost on a “range” of parameters. The range is user-controlled, and is akin to the idea of parameter resolution. Additionally the peak-preserving property allows the user to begin with coarse intervals and “zoom” in as they see fit. Associated with these estimates is a measure of quality called the credible interval (or credible set). The credible interval (set) is a region of parameter space where the “true” parameter is located with a user-defined probability. Narrow credible intervals are associated with high-quality estimates while wide credible intervals are associated with poor estimates. The techniques are implemented in state-of-the-art graphics processor unit (GPU) hardware, which allows the numerical integration to be performed in a reasonable time. A typical estimator requires several hundred million computations and the GPU implementation reduces the computation time from several hours to a few seconds. The mass interval estimation technique may be used on any Bayesian problem, but is demonstrated here using each of the canonical shape models of Jackson. The technique successfully estimates parameters in different scenarios including simple shapes, multiple shapes, incorrect shape (i.e. trying to estimate parameters using the wrong model). The results of this research are a new exploration of the posterior distributions of the canonical shape model, improved numerical integration strategies, and a new statistical technique for the Bayesian estimation of parameters.

AFIT Designator

AFIT-ENG-14-M-62

DTIC Accession Number

ADA601482

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