This dissertation is concerned with problems in statistical processing of Radar, Sonar and optical signals including model order selection, parameter estimation, power spectral density estimation, signal detection and classification.
It is proved that the exponentially embedded families (EEF), which is a recently proposed model order selection criterion, is consistent. It is also found in computer simulations that the EEF works well in difficult situations.
A method is proposed to evaluate the CRLB via the characteristic function. With the proposed method, the CRLBs of the scale parameter and the shape parameter of the K-distribution are successfully computed. It is also proved in general, that the Cramer-Rao lower bound of the shape parameter does not depend on the scale parameter.
A prewhitened PSD estimator based on matrix prewhitening is proposed. Compared to the traditional prewhitened PSD estimators, the proposed estimator has smaller overall mean square error for short data records.
For composite hypothesis testing, the generalized likelihood ratio test (GLRT) and the Bayesian approach are two widely used methods. These two methods are investigated for signal detection with distributed sensors. It is proved that the performance of the GLRT can be poor and two types of improved GLRTs are proposed. The improved GLRT of the second type is in fact an approximate Bayesian detector.
The performance analysis of the GLRT for composite detection with distributed sensors led to a conjectured property of the noncentral chi-squared distribution. For the special case of complex data and a weak signal, the conjecture is proved. The implications of the conjectured property are discussed.
From the assumption of a stationary background and based on the autoregressive (AR) spectrum modeling, a two-step approach for chemical identification in Raman spectra is proposed. Some practical problems are also discussed, such as setting the detection threshold, extension to non-stationary backgrounds, and the identifiability of chemicals.
