Fast maximum likelihood estimation of parameters in crowded signal environments
This dissertation is directed towards developing computationally efficient estimation algorithms whose performance are comparable to those of Maximum Likelihood (ML) estimators. Since the motivation for developing such algorithms is to be able to apply them to real-world problems, it is important that they work well even in crowded signal environments. The computational efficiency of these algorithms lies in reducing the multi-dimensional search involved in ML estimation into multiple one-dimensional searches. This is achieved by using our knowledge of the shape of the Compressed Likelihood Function (CLF) in the parameter space. The attributes of this shape may vary because the signal model is different for different problems. However, in many problems the global maximum can be shown to be situated at specific intersections of the ridges of the CLF. In some signal models, it may be difficult to characterize the shape of the CLF for multiple components. For such models, we propose an iterative estimation method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the CLF.^ In this dissertation, estimation algorithms for three specific signal models are developed--undamped sinusoids, exponentially damped sinusoids, and hyperbolic frequency modulated signals. The algorithms developed in this dissertation are applied to the analysis of two real-world data sets: (i) Nuclear Magnetic Resonance (NMR) spectroscopy data of the human blood plasma and (ii) Active sonar reverberation data. ^
Statistics|Engineering, Electronics and Electrical
"Fast maximum likelihood estimation of parameters in crowded signal environments"
Dissertations and Master's Theses (Campus Access).