Estimation Problems in Array Signal Processing, System Identification, and Radar Imagery

Abstract: This thesis is concerned with parameter estimation, signal processing, and applications.In the first part, imaging using radar is considered. More specifically, two methods are presented for estimation and removal of ground-surface reflections in ground penetrating radar which otherwise hinder reliable detection of shallowly buried landmines. Further, a study of two autofocus methods for synthetic aperture radar is presented. In particular, we study their behavior in scenarios where the phase errors leading to cross-range defocusing are of a spatially variant kind.In the subsequent part, array signal processing and optimal beamforming is regarded. In particular, the phenomenon of signal cancellation in adaptive beamformers due to array perturbations, signal correlated interferences and limited data for covariance matrix estimation is considered. For the general signal cancellation problem, a class of improved adaptive beamformers is suggested based on ridge-regression. Another set of methods is suggested to mitigate signal cancellation due to correlated signal and interferences based on a novel way of finding a characterization of the interference subspace from observed array data. Further, a new minimum variance beamformer is presented for high resolution non-parametric spatial spectrum estimation in cases where the impinging signals are correlated. Lastly, a multitude of enhanced covariance matrix estimators from the statistical literature are studied as an alternative to other robust adaptive beamforming methods. The methods are also applied to space-time adaptive processing where limited data for covariance matrix estimation is a common problem.In the third and final part the estimation of the parameters of a general bilinear problem is considered. The bilinear model is motivated by the application of identifying submarines from their electromagnetic signature and by the identification of a Hamerstein-Wiener model of a non-linear dynamic system. An efficient approximate maximum-likelihood method with closed form solution is suggested for estimating the bilinear model parameters.