Date of Award
9-1996
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Department of Electrical and Computer Engineering
First Advisor
Michael Clark, PhD
Second Advisor
Joseph J. Sacchini, PhD
Abstract
This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood (ML) estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar (SAR) data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations (exponentials frequencies) are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as (1) stationary noise, (2) autoregressive (AR) noise and (3) autoregressive moving-average (ARMA) noise and in two dimensions as (1) stationary noise, and (2) white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood (IQML) methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation (MODE) techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise.
AFIT Designator
AFIT-DS-ENG-96-09
DTIC Accession Number
ADA321650
Recommended Citation
Pepin, Matthew P., "Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target Identification in Synthetic Aperture Radar Images" (1996). Theses and Dissertations. 6059.
https://scholar.afit.edu/etd/6059