Theses and Dissertations
In location estimation problems, sensor nodes at known locations, called anchors, transmit signals to sensor nodes at unknown locations, called nodes, and use these transmissions to estimate the location of the nodes. Specifically, the location estimation in the presence of fading channels using time of arrival (TOA) measurements with narrowband communication signals is considered. Meanwhile, the Cramer-Rao lower bound (CRLB) for localization error under different assumptions is derived. Also, maximum likelihood estimators (MLEs) under these assumptions are derived.
In large WSNs, distributed location estimation algorithms are more efficient than centralized algorithms. A sequential localization scheme, which is one of distributed location estimation algorithms, is considered. Also, different localization methods, such as TOA, received signal strength (RSS), time difference of arrival (TDOA), direction of arrival (DOA), and large aperture array (LAA) are compared under different signal-to-noise ratio (SNR) conditions. Simulation results show that DOA is the preferred scheme at the low SNR regime and the LAA localization algorithm provides better performance for network discovery at high SNRs. Meanwhile, the CRLB for the localization error using the TOA method is also derived.
A distributed location detection scheme, which allows each anchor to make a decision as to whether a node is active or not is proposed. Once an anchor makes a decision, a bit is transmitted to a fusion center (FC). The fusion center combines all the decisions and uses a design parameter $K$ to make the final decision. Three scenarios are considered in this dissertation. Firstly, location detection at a known location is considered. Secondly, detecting a node in a known region is considered. Thirdly, location detection in the presence of fading is considered. The optimal thresholds are derived and the total probability of false alarm and detection under different scenarios are derived.
Results from this work aim to increase the accuracy and performance of the inverse solution process.
The inverse problem can be approached by constructing forward solutions where, for a know source, the scalp potentials are determined. This work demonstrates that the use of two variables, the dissipated power and the accumulated charge at interfaces, leads to a new solution method for the forward problem. The accumulated charge satisfies a boundary integral equation. Consideration of dissipated power determines bounds on the range of eigenvalues of the integral operators that appear in this formulation. The new method uses the eigenvalue structure to regularize singular integral operators thus allowing unambiguous solutions to the forward problem.
A major problem in the estimation of properties of neural sources is the presence of artifacts that corrupt EEG recordings. A method is proposed for the determination of inverse solutions that integrates sequential Bayesian estimation with probabilistic data association in order to suppress artifacts before estimating neural activity. This method improves the tracking of neural activity in a dynamic setting in the presence of artifacts.
Solution of the inverse problem requires the use of models of the human head. The electrical properties of biological tissues are best described by frequency dependent complex conductivities. Head models in EEG analysis, however, usually consider head regions as having only constant real conductivities. This work presents a model for tissues as composed of confined electrolytes that predicts complex conductivities for macroscopic measurements. These results indicate ways in which EEG models can be improved.
Classification in machine learning is quite crucial to solve many problems that the world is presented with today. Therefore, it is key to understand one’s problem and develop an efficient model to achieve a solution. One technique to achieve greater model selection and thus further ease in problem solving is estimation of the Bayes Error Rate. This paper provides the development and analysis of two methods used to estimate the Bayes Error Rate on a given set of data to evaluate performance. The first method takes a “global” approach, looking at the data as a whole, and the second is more “local”—partitioning the data at the outset and then building up to a Bayes Error Estimation of the whole. It is found that one of the methods provides an accurate estimation of the true Bayes Error Rate when the dataset is at high dimension, while the other method provides accurate estimation at large sample size. This second conclusion, in particular, can have significant ramifications on “big data” problems, as one would be able to clarify the distribution with an accurate estimation of the Bayes Error Rate by using this method.