Exploiting Prior Information in Parametric Estimation Problems for Multi-Channel Signal Processing Applications

Abstract: This thesis addresses a number of problems all related to parameter estimation in sensor array processing. The unifying theme is that some of these parameters are known before the measurements are acquired. We thus study how to improve the estimation of the unknown parameters by incorporating the knowledge of the known parameters; exploiting this knowledge successfully has the potential to dramatically improve the accuracy of the estimates.For covariance matrix estimation, we exploit that the true covariance matrix is Kronecker and Toeplitz structured. We then devise a method to ascertain that the estimates possess this structure. Additionally, we can show that our proposed estimator has better performance than the state-of-art when the number of samples is low, and that it is also efficient in the sense that the estimates have Cram'er-Rao lower Bound (CRB) equivalent variance.In the direction of arrival (DOA) scenario, there are different types of prior information; first, we study the case when the location of some of the emitters in the scene is known. We then turn to cases with additional prior information, i.e.~when it is known that some (or all) of the source signals are uncorrelated. As it turns out, knowledge of some DOA combined with this latter form of prior knowledge is especially beneficial, giving estimators that are dramatically more accurate than the state-of-art. We also derive the corresponding CRBs, and show that under quite mild assumptions, the estimators are efficient.Finally, we also investigate the frequency estimation scenario, where the data is a one-dimensional temporal sequence which we model as a spatial multi-sensor response. The line-frequency estimation problem is studied when some of the frequencies are known; through experimental data we show that our approach can be beneficial. The second frequency estimation paper explores the analysis of pulse spin-locking data sequences, which are encountered in nuclear resonance experiments. By introducing a novel modeling technique for such data, we develop a method for estimating the interesting parameters of the model. The technique is significantly faster than previously available methods, and provides accurate estimation results.