Overview

Statistical signal processing for signal parameter estimation is an ever-evolving field, with continuous research for efficient methods for the ever-changing needs of various systems that require signal processing tasks to be accomplished. Three types of parameter estimation techniques exist: parametric, nonparametric, spectral, and Bayesian. Over the past fifty years, digital signal processing has seen a virtual surge in ideas, techniques, and applications for military and commercial products/systems. The radar is one such system that is extensively employed for detecting and locating target objects. Radars can perform well for long or short distances and under conditions unreceptive to infrared and optical sensors. These qualities render a complex system that can operate in darkness, rain, snow, fog, and haze. Therefore, radar finds use in various surveillance, defense, space, ship and aircraft navigation, and remote sensing applications. These critical applications accentuate the significance of radars and prompt scientists and researchers to continuously improve the efficiency of signal processing algorithms in terms of accuracy and computational complexity. In this dissertation, we have considered two types of radar signals for our study; the multiple sinusoids, which models a radar interference signal, and a passive bistatic radar (PBR) signal. The issue of multiple sinusoid estimation is a fundamental research problem that has been the topic of research for a long time. Passive bistatic radar has also recently gained traction due to its widespread military and civilian use for surveillance and stealth purposes. Under the parametric estimation approach, the maximum likelihood estimator (MLE) is the most widely used practical method that provides optimally accurate estimates and achieves the Crámer-Rao lower bound (CRLB) for the radar signals mentioned above. However, its computational complexity is enormous if we use the grid search (GS) technique for maximization of the likelihood function of the data. Thus, other iterative methods were devised instead of GS, like Gauss-Newton technique. Still, the MLE is a computationally costly approach, and iterative algorithms require an excellent initial guess and do not guarantee convergence to the maximum. In this thesis, we have proposed a novel hybrid technique that combined two statistical concepts of data-supported optimization (DSO) and contracting-grid search (CGS) to reduce the time-complexity of grid-search based MLE (GS-MLE). The proposed estimator, named data-supported contracting GS-MLE (DSC-GS-MLE), has been found to be computationally efficient compared to GS-MLE for two and three sinusoid cases. It also yielded estimates close to that of GS-MLE and achieved the Crámer-Rao lower bound (CRLB) like GS-MLE, a performance benchmark for estimators, for two sinusoids. We found that the proposed DSC-GS-MLE approach was still computationally burdensome. To circumvent this problem and make the estimators more practical, prior information about the parameters could be incorporated into the estimators. This is accomplished using Bayes' theorem, where we use prior knowledge in the form of a PDF. Two Bayesian techniques are minimum mean squared error (MMSE) and maximuma- posteriori (MAP), which require multidimensional integration or optimization. However, using GS or EM techniques for these purposes still caused computational complexity issues. Fortunately, Markov chain Monte Carlo (MCMC) methods provide an alternative cheaper solution in this regard. Metropolis-Hastings (MH) is the most general and frequently used MCMC.

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