Publication Date

Spring 4-15-2020


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


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

Jens Lorenz

Second Committee Member

Mohammad Motamed

Third Committee Member

Jehanzeb Hameed Chaudhry




TDOA, Levenberg, Marquardt, anomaly, dilution, metric

Document Type