Robust adaptive methods and their applications in quadrupole resonance

Signal amplitude estimation and detection problems have been encountered in many practical applications including the emerging quadrupole resonance (QR) technology for the detection of substance of interest (e.g., explosives). In the QR application, the signal waveform is known a priori. The main challenge of applying QR to the detection of substance of interest is that the returned QR signal is often unavoidably corrupted by strong radio frequency interferences (RFIs).; Motivated by the QR application, this dissertation investigates robust adaptive methods for the amplitude estimation of a signal with known arbitrary waveform in the presence of strong RFIs and noise. The main objective is to fundamentally address the signal processing perspectives for explosive detection by QR. The focus is to establish realistic data models, devise innovative signal processing algorithms, and evaluate their performances.; For the single antenna based application, we consider the amplitude estimation of a signal with arbitrary known waveform in the presence of strong interferences and noise. Three adaptive finite-impulse response filter based methods are presented to suppress the strong interferences. We first extend the generalized Capon (GC) estimator to the problem of signal amplitude estimation. Then we devise two robust methods to mitigate the small snapshot number problems by allowing an uncertainty set for the signal covariance matrix.; For the antenna array based application, we propose several adaptive beamforming approaches to improve the QR signal detection performance via exploiting both the spatial and temporal correlations of RFIs. We operate in the framework of signal amplitude estimation with known signal waveform and make use of three adaptive beamforming approaches, viz., the standard Capon beamformer (SCB), the robust Capon beamformer (RCB), and the amplitude and phase estimation (APES) algorithm, to develop several new approaches for mitigating the spatially and temporally correlated RFIs.; For the detection of compound explosives, we derive a joint generalized likelihood ratio test (GLRT) detector based on the outputs of RFI mitigation filters designed for individual QR explosive probings. We also conduct a detailed statistical analysis on the joint GLRT detector and show that it has a constant false alarm rate property.