Credible Set Estimation, Analysis, and Applications in Synthetic Aperture Radar Canonical Feature Extraction
AIR FORCE INSTITUTE OF TECHNOLOGY WRIGHT-PATTERSON AFB OH GRADUATE SCHOOL OF ENGINEERING AND MANAGEMENT
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Traditional estimation schemes such as Maximum A Posterior MAP or Maximum Likelihood Estimation MLE determine the most likely parameter set associated with received signal data. However, traditional schemes do not retain entire posterior distribution, provide no confidence information associated with the final solution, and often rely on simple sampling methods which induce significant errors. Also, traditional schemes perform inadequately when applied to complex signals which often result in multi-modal parameter sets. Credible Set Estimation CSE provides a powerful and flexible alternative to traditional estimation schemes. CSE provides an estimation solution that accurately computes posterior distributions, retains confidence information, and provides a complete set of credible solutions. Determination of a credible region becomes especially important in Synthetic Aperture Radar SAR Automated Target Recognition ATR problems where signal complexity leads to multiple potential parameter sets. The presented research provides validation of methods for CSE, extension to high dimensionlarge observation sets, incorporation of Bayesian methods with previous work on SAR canonical feature extraction, and evaluation of the CSE algorithm. The results in this thesis show that the CSE implementation of Gaussian-Quadrature techniques reduces computational error of the posterior distribution by up to twelve orders of magnitude, the presented formula for computation of the posterior distribution enables numerical evaluation for large observation sets greater than 7,300 observations, and the algorithm is capable of producing M-th dimensional parameter estimates when applied to SAR canonical features. As such, CSE provides an ideal estimation scheme for radar, communications and other statistical problems where retaining the entire posterior distribution and associated confidence intervals is desirable.
- Numerical Mathematics
- Statistics and Probability
- Active and Passive Radar Detection and Equipment