Doctor of Philosophy, The Ohio State University, 2007, Electrical Engineering

Distributed sensor networks are growing in popularity for a large number of sensing applications ranging from environmental monitoring to military target classification and tracking. However, knowledge of the individual sensor positions is a prerequisite to obtaining meaningful information from measurements made by the sensors. With the scale of sensor networks rapidly increasing due to advances in communications and MEMS technology, an automatic localization service based on inter-sensor measurements is becoming an essential element in modern networks. This dissertation studies fundamental aspects of localization performance while deriving general results for singular estimation problems. Because inter-sensor measurements, such as distances or angles-of-arrival (AOA), are invariant to absolute positioning of the sensor scene, localizing sensors with an absolute reference, e.g., latitude and longitude, is inherently a singular estimation problem suffering from non-identifiability of the absolute location parameters. This results in a corresponding singular Fisher information matrix. We consider means of regularizing the absolute localization problem and devise novel performance characterizations by showing that the location parameters have a natural decomposition into relative configuration and centroid transformation components based on the singularity of the problem. A linear representation of the transformation manifold, which includes representations of rotation, translation, and scaling, is used for decomposition of general localization error covariance matrices. The unified statistical framework presented – which naturally generalizes to non-localization problems – allows us to quantify and bound performance in the relative and transformation domains. These tools facilitate analysis of relative-only algorithms while enabling new algorithm development to finely tune performance in each subdomain. The analysis is applied to a novel closed-form AOA-based localiza (open full item for complete abstract)

Committee: Randolph Moses (Advisor) Subjects:

Master of Arts, The Ohio State University, 2020, Sociology

Summary birth history (SBH) is a low-cost instrument widely used in developing countries lacking complete vital registration system for estimating demographic statistics. Indirect methods are utilized to estimate mortaliy rates the total number of children born and total number of children surviving data from SBH. However existing methods don't allow estimation for full detailed mortality age schedule with uncertainty. This paper introduces an innovative Singular Value Decomposition(SVD)-based method within the Bayesian framework, the SVD-Bayes model, to jointly estimate full age schedules of mortality for children and fertility for women from SBH data by single-month intervals along with uncertainty estimates. SVD model enables construction of full mortality and fertility age schedules with a few SVD-weight components. Posterior distributions for SVD-weight components are obtained using modified Approximate Bayesian Computation (ABC). Based on the results from simulation study, the SVD-Bayes model estimates full mortality age schedules by single-month age group from summary birth history data for children aged 0-20 years. The model also produces probability of giving birth by single-month age group for women of reproductive age. With SVD-Bayes model, SBH data from censuses and surveys could be used to produce mortality and fertility estimates for evidence-based policy-making and program monitoring and evaluation. The attempt of using ABC algorithm with SVD-Bayes model also shows the promising future of applying this advanced statistical technique in demographic research.

Committee: Samuel Clark (Advisor); Jon Wakefield (Committee Member); David Melamed (Committee Member) Subjects: Demography; Public Health; Sociology

Doctor of Philosophy, The Ohio State University, 2012, Geodetic Science and Surveying

This dissertation is about total least-squares (TLS) adjustments within the errors-in-variables (EIV) model. In particular, it deals with symmetric positive-(semi)definite cofactor matrices that are otherwise quite arbitrary, including the case of cross-correlation between cofactor matrices for the observation vector and the coefficient matrix and also the case of singular cofactor matrices. The former case has been addressed already in a recent dissertation by Fang [2011], whereas the latter case has not been treated until very recently in a presentation by Schaffrin et al. [2012b], which was developed in conjunction with this dissertation. The second primary contribution of this work is the introduction of prior information on the parameters to the EIV model, thereby resulting in an errors-in-variables with random effects model (EIV-REM) [Snow and Schaffrin, 2012]. The (total) least-squares predictor within this model is herein called weighted total least-squares collocation (WTLSC), which was introduced just a few years ago by Schaffrin [2009] as TLSC for the case of independent and identically distributed (iid) data. Here the restriction of iid data is removed. The EIV models treated in this work are presented in detail, and thorough derivations are given for various TLS estimators and predictors within these models. Algorithms for their use are also presented. In order to demonstrate the usefulness of the presented algorithms, basic geodetic problems in 2-D line-fitting and 2-D similarity transformations are solved numerically. The new extensions to the EIV model presented here will allow the model to be used by both researchers and practitioners to solve a wider range of problems than was hitherto feasible. In addition, the Gauss-Helmert model (GHM) is reviewed, including details showing how to update the model properly during iteration in order to avoid certain pitfalls pointed out by Pope [1972]. After this, some connections between the GHM and the EIV model (open full item for complete abstract)

Committee: Burkhard Schaffrin PhD (Advisor); Michael Bevis PhD (Committee Member); Michael Durand PhD (Committee Member) Subjects: Engineering; Mathematics; Statistics

Master of Science, The Ohio State University, 2013, Electrical and Computer Engineering

In spin echo electron paramagnetic resonance (SE-EPR) spectroscopy, traditional methods to estimate T2 relaxation time include fitting an exponential to the peaks or the integrated areas of multiple noisy echoes. These methods are suboptimal and result in lower estimation accuracy for a given acquisition time. Here, two data processing methods to estimate T2 for SE-EPR are proposed. The first method finds the maximum likelihood estimate (MLE) of T2 via parametric modeling of the spin echo and joint least-squares fitting of the collected data. The second method exploits the underlying rank-one structure in SE-EPR data via singular-value decomposition (SVD). The right singular vector corresponding to the largest singular value is then fitted with an exponential to find T2. This method bears strong similarity to a non-parametric MLE-based approach that does not assume a structure of an echo. The methods are validated using simulation and experimental data. The proposed methods provide 41-fold and 3-fold acquisition time savings over the traditional methods of fitting echo peaks and areas, respectively. Interestingly, the results also indicate that the SVD-based approach generates mean squared error nearly identical to that produced by the MLE based on parametric modeling for a wide range of SNR.

Committee: Lee Potter (Advisor); Bradley Clymer (Committee Member); Rizwan Ahmad (Committee Member) Subjects: Electrical Engineering; Medical Imaging