S U M M A R YThe applications of eigentheory to many branches of mathematical physics (e.g., rotational dynamics, continuum mechanics) is an unquestionable fact. This work expands the conventional methodology by introducing equations to compute the covariance matrices of eigenvalues and eigenvectors of second-rank 3-D symmetric tensors in terms of their six distinct elements error estimates. New analytical expressions derived herein are general and should be of interest to anyone concerned with the accuracy of the computed orientation of principal axes and their associated principal quantities (e.g., moments of inertia, stress, strain).

The use of Global Positioning System (GPS) technologies has expanded to perform traffic data collection for transportation studies such as work zone studies. To generate reliable results from the data acquired by using GPS devices, it is necessary to investigate such factors as sample size requirements that may affect a specific study and to establish a consistent method for data collection. It has been confirmed that the Institute of Transportation Engineers’ Manual of Transportation Engineering Studies usually underestimates the sample sizes for travel time and delay studies. However, the hybrid method developed by Quiroga and Darcy overestimates the sample sizes. A modified equation is presented to estimate the minimum sample sizes for collecting field data with GPS devices. Travel speed may be more stable and can be easily measured for travel time and delay studies. Stopped delay varies considerably at intersections, and the sample sizes depend to a large extent on the permitted errors. Work zone layout and construction activities will create variations in vehicle flow within the work zone. To estimate the sample size requirements, it is advisable to use the standard deviation to measure the data dispersion, and a minimum of three initial test runs is required. GPS devices with sufficient accuracy usually require 5 to 10 samples for travel time and delay studies and work zone studies. Stopped delay studies may require a large sample of up to 30 test runs.

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An often neglected but important role is played by differential scale changes in transforming geodetic datums. A rigorous account of scale variations in any transformation involving reference ellipsoids and its effects on geodetic heights is essential. This role provides a plausible explanation for the reported z-shift between the Doppler defined terrestrial systems and the satellite laser ranging frames.

Terrestrial network solutions prepared by different institutes and/or at different epochs imply different reference frame definitions, since various reference stations and processing strategies may be involved. A combination procedure, utilizing a time-variant similarity transformation model, enables a geometric integration of multiple solutions into a common reference frame definition. Additional benefits, including an elimination of systematic bias and a cross check on the quality of each individual network solution, could also be achieved. In this study, a combination approach which takes into account complete geometric interrelations between multiple solutions is developed. With the observable dependency analysis procedure, the proposed approach guarantees a self-consistent, more meaningful, combination solution regardless of the choice of a reference solution. Numerical tests have been performed on actual International Global Navigation Satellite System ͑GNNS͒ Service ͑IGS͒ and National Geodetic Survey ͑NGS͒ solutions using the Geodetic Network Analysis Tool software developed along with this study. Results reveal potential problems if the proposed analysis procedure is not implemented in a combination solution.