Journal of Surveying Engineering

Since the advent of the Global Positioning System (GPS), geodetic azimuths can be accurately computed by simple implementation of well-known 3D concepts. However, when GPS alignment surveys involving azimuths are designed in advance, and later observed and reduced (e.g., during kinematic GPS work), corrections due to the convergence of the meridians should be kept in mind and not ignored. In this study a practical algorithm was used to compare accurately determined “meridian convergence” against the classical formalism available in standard textbooks. The typical approximate formulation available in the open literature was found adequate for GPS engineering surveys such as airport runway profiles, alignment of power lines or conveyor belts, stake positioning in highway construction, etc. A practical GPS survey was used to corroborate the results. Finally, a new 3D alternative to computing meridian convergence, which is equivalent to the rigorous formalism, is presented.

A number of parameterizations of rotations in three-dimensional space are compared with respect to their formulas and qualitative characteristics relevant for practical use. The number and uniqueness of parameters, singularities, visualization, and constraint equations within one parameter set are considered. Formulas are given for the transformation to and from rotation matrices and symmetric Euler parameters as well as for the rotation of a vector, the inverse rotation, the combination of two rotations, and the kinematic differential equations. The list of parameters includes the five-parametric Hopf parameters. Symmetric rotation matrices are treated separately. All properties are given in comprehensive tables with formulas ready for programming.

Radar altimeters were designed to collect height data over ocean surfaces where there are few sudden changes in elevation to send the instrument off-lock. Because land surfaces are not smooth over the fairly large footprint of present day satellite altimeter systems (typically 10 km), severe restrictions are placed on the information that can be obtained in most situations. The work presented here makes use of the free data from the Topex/Poseidon mission using a test site in the Saudi Arabian desert. The study was limited to an assessment of measurement accuracy and a feasibility study of using such data for mapping purposes. Results were compared with retracked elevation data and a digital terrain model over different types of terrain, varying from mountain to desert. It was found that, over desert areas, over 90% of the data contained valid difference height data, and it is concluded that, in principle, satellite altimetry could be used for accurate mapping purposes but that its use in all but a few cases will need to await the launch of instruments with greater spatial resolution, both in terms of footprint size and sample spacings.