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Methods Of Uncertainty Quantification For Physical Parameters, Kellin Rumsey
Methods Of Uncertainty Quantification For Physical Parameters, Kellin Rumsey
Mathematics & Statistics ETDs
Uncertainty Quantification (UQ) is an umbrella term referring to a broad class of methods which typically involve the combination of computational modeling, experimental data and expert knowledge to study a physical system. A parameter, in the usual statistical sense, is said to be physical if it has a meaningful interpretation with respect to the physical system. Physical parameters can be viewed as inherent properties of a physical process and have a corresponding true value. Statistical inference for physical parameters is a challenging problem in UQ due to the inadequacy of the computer model. In this thesis, we provide a comprehensive …
Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann
Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann
Mathematics & Statistics ETDs
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 …