Journal of Surveying Engineering

A new method of weighting that realizes equiredundancy design is introduced, and its convergence is better than the method introduced by Koch. However, if Koch's method is modified, it gives the best results compared to the others. Furthermore, it is shown that balanced weights depend only on the positions of observations and not on the initial weights. If the equiredundancy design is taken into consideration in the generalized form of maximum likelihood estimation (M-estimation), the finite sample breakdown point (FSBP) (or reliability) increases. This problem has been studied using a coordinate transformation simulation. After obtaining the balanced weights, which provide the equiredundancy, they are used as the pseudoweights of observations in M-estimation. This is called the equiredundancy-designed generalized M-estimation (GM-estimation). In addition, another GM-estimation is developed by balancing the partial redundancy numbers at every step of the reweighted and iterated least-squares solution of M-estimation. This is called the GM-estimation with balanced case. Both methods have the same FSBP. Using both methods of GM-estimation in the robustifying conventional outlier detection procedures, such as the method of Baarda or Pope, the new robustifying outlier detection procedures are obtained with a higher FSBP.

In this paper, a method of volume computation that combines the advantages and avoids the drawbacks of current methods is presented. Earlier methods of computing pit excavation volume were based on the trapezoidal or Simpson-type rules. These methods provide direct formulas for volume computation, but their disadvantage is that they approximate the ground surface by piecewise surfaces that have sharp connections. The existing cubic spline method is based on a smooth ground surface, but its disadvantage is that it requires solving a system of linear equations and integrating a function many times. The proposed method provides a direct formula for volume computation and is based on a smooth approximating surface. The method employs a cubic Hermite polynomial for individual intervals in both directions of the grid, the intervals of which may be unequal. A cubic Hermite volume formula is developed by integrating the surface function in both coordinate directions. The proposed method, which provided comparable accuracy to that of the more elaborate cubic spline method, should be of interest to surveyors concerned with both accuracy and ease of volume computations.

Hydrologic modeling increasingly involves the use of a geographic information system (GIS), usually in order to obtain the topographic features relevant to the hydrology of a study area. However, despite the increasing availability of digital spatial data (in vector and raster formats) and the growing sophistication of modeling softwares, it is important that hydrologists and surveyors be aware of the effects of errors on their models and subsequent applications. This paper examines the nature and consequences of spatial errors in GIS, and explores ways of mitigating the risks of error propagation in digital hydrologic models.