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https://hdl.handle.net/2142/69248
Description
Title
Topics in Robust Statistical Signal Processing
Author(s)
Vastola, Kenneth Steven
Issue Date
1982
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Abstract
This dissertation addresses several problems in robust signal processing. The term "robust" in this context implies insensitivity to small deviations from the assumed statistical description of the signal and/or noise.
The first part of this thesis considers the problem of linear minimum-mean-square-error estimation of a stationary signal observed in additive stationary noise when knowledge of the signal spectrum and noise spectrum is inexact. First, the performance of robust continuous-time (Wiener) noncausal filters (designed using a method developed elsewhere) is examined. It is shown in a variety of situations that when spectral uncertainty exists the performance of the traditional Wiener filter degrades badly while the robust filter's insensitivity to such deviations makes it an effective alternative. Next, this design approach is developed for the general problem of robust discrete-time (Wiener-Kolmogorov) causal signal estimation, and a simple characterization of solutions to this problem is given. The method of design is then illustrated by a thorough development of the special case of one-step noiseless prediction and numerical examples which illustrate the effectiveness of the general design are given for the problem of robust causal filtering of an uncertain signal in white noise.
In the second part of this dissertation, a previously developed cohesive theory of robust hypothesis testing in which uncertainty is modeled via 2-alternating Choquet capacity classes is considered in light of recent applications of this theory to problems in robust signal processing and communication theory. In particular, a generalization of capacities is given which allows several of the most common uncertainty classes to be considered under a less restrictive compactness assumption. Results are given which generalize this robust hypothesis testing theory and which are of direct consequence for the applications. For example, it is shown how these results allow the problem of robust linear smoothing of an uncertain continuous-time signal in white noise to be fit within a general framework developed previously for robust (minimax) linear smoothing. Finally, some properties of the band model and p-point model (uncertainty classes which are especially appropriate for many applications) are developed within the context of 2-alternating capacities.
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