Publication Date
Spring 4-15-2020
Abstract
This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements specification applications. The maximum machine epsilon and the maximum number of iterations to reach the least squares solution without loss of source location accuracy are estimated. Improvements in accuracy of least squares solutions over closed form solutions are measured.
Degree Name
Mathematics
Level of Degree
Masters
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Jens Lorenz
Second Committee Member
Mohammad Motamed
Third Committee Member
Jehanzeb Hameed Chaudhry
Language
English
Keywords
TDOA, Levenberg, Marquardt, anomaly, dilution, metric
Document Type
Thesis
Recommended Citation
Bredemann, Michael V.. "Nonlinear Least Squares 3-D Geolocation Solutions using Time Differences of Arrival." (2020). https://digitalrepository.unm.edu/math_etds/148
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