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.