AbstractsMathematics

Robust Estimation and Model Order Selection for Signal Processing

by Michael E. Muma




Institution: Technische Universit├Ąt Darmstadt
Department: Fachbereich Elektrotechnik und InformationstechnikSignalverarbeitung
Degree: PhD
Year: 2014
Record ID: 1099132
Full text PDF: http://tuprints.ulb.tu-darmstadt.de/3867/


Abstract

In this thesis, advanced robust estimation methodologies for signal processing are developed and analyzed. The developed methodologies solve problems concerning multi-sensor data, robust model selection as well as robustness for dependent data. The work has been applied to solve practical signal processing problems in different areas of biomedical and array signal processing. In particular, for univariate independent data, a robust criterion is presented to select the model order with an application to corneal-height data modeling. The proposed criterion overcomes some limitations of existing robust criteria. For real-world data, it selects the radial model order of the Zernike polynomial of the corneal topography map in accordance with clinical expectations, even if the measurement conditions for the videokeratoscopy, which is the state-of-the-art method to collect corneal-height data, are poor. For multi-sensor data, robust model order selection selection criteria are proposed and applied to the problem of estimating the number of sources impinging onto a sensor array. The developed criteria are based on a robust and efficient estimator of the covariance of the r-mode unfoldings of a complex valued data tensor. Both in the case of Gaussian noise and for a brief sensor failure, the proposed robust multi-dimensional schemes outperform their matrix computation based counterparts. In the context of robustness for multi-sensor data, we next investigate the problem of estimating the complex-valued amplitude of sinusoidal signals in a completely unknown heavy-tailed symmetric spatially and temporally independent and identically distributed (i.i.d.) sensor noise environment. A selection of non-robust and robust estimators are compared to a proposed semi-parametric robust estimator. A third research focus in the area of multi-sensor data is that of analyzing the robustness of spatial time-frequency distribution (STFD) estimators. We provide a robustness analysis framework that is based on the influence function. The influence function is a robustness measure that describes the bias impact of an infinitesimal contamination at an arbitrary point on the estimator, standardized by the fraction of contamination. In addition to the asymptotic analysis, we also give a definition of the finite sample counterpart of the influence function. Simulation results for the finite sample influence function confirm the analytical results and show the insensitivity to small departures in the distributional assumptions for some recently proposed robust STFD estimators. A large part of this thesis concerns the topic of obtaining and analyzing robust estimators in the dependent data setup. First, some practical issues concerning the detection, and robust estimation in presence of patient motion induced artifacts in biomedical measurements are addressed. In particular, we provide an artifact-cleaning algorithm for data collected with an electrocardiogram (ECG). This is especially important for the monitoring of patients with…