In this dissertation, two nonlinear regressive models, the forward model and the inverse model, have been developed to determine the pose (position and orientation) of the scanning laser Doppler vibrometer (SLDV) with respect to a structural coordinate system. The parameters in the forward model include the pose and the ranges. The parameters in the inverse model include the pose only. The parameters of those models are obtained by using the least squares technique. A geometrical method is developed to get an estimation of the pose and the ranges. This estimation is used as an initial solution in the iterative procedure for determining the parameters in the nonlinear regressive models. The statistical inferences are made about the inverse model by the linear approximation. The nonlinearity of the inverse modal is measured in order to verify the validity of the linear approximation. Included along with the development of the models, are the implementation of the algorithm (geometrical method and inverse model), the assessment of the inverse model, the calibration of the scanner, and the accuracy evaluation of the algorithm. / Ph. D.