Maximum likelihood estimation of exponentials in unknown colored noise for target identification in synthetic aperture radar images

The accurate and computationally efficient estimation of signals in noise has long been a field of intense study. The signal present in natural processes is many times well modeled as the sum of real or complex exponential functions. The noise for computational simplicity is often assumed to be white or uncorrelated. There exist, however, many cases where noise is, in fact, correlated. Accurate and efficient estimates of the signal in these cases require that the noise correlation be taken into account. This is case for the specific application of interest in this dissertation, Synthetic Aperture Radar (SAR), whose images of objects may be modeled as the sum of two-dimensional complex exponentials (the electromagnetic scattering centers on the target).; The maximum likelihood estimate of the signal is often considered the best possible estimate of the signal. While many white and colored noise maximum likelihood estimates have been developed, efficient solutions to the estimation of one- and two-dimensional exponentials in unknown colored noise do not exist.; 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.; Application to SAR data first requires that damped exponentials have not been distorted by SAR processing. Then, 1-D colored noise techniques provide better estimates at low model orders (number of exponentials) than white noise techniques. The 2-D techniques based on the colored noise model also more accurately model SAR data than existing 2-D white noise techniques. With an appropriate focusing technique and matching technique for the exponentials in each dimension, scatterers are located with high resolution in SAR images and colored noise techniques improve these location estimates.