Journal of Surveying Engineering

A rapidly convergent algorithm for fitting clothoids to measured points is developed and tested. The second-order, reduced Hessian method, broadly applicable to the class of scalable, C² parametrizations, is orthogonal distance regression with four-parameter similarity transformations. The local parameters, or state variables, are implicitly eliminated, and second-order solutions are rigorously computed in the model parameter space (rank ≤4). The algorithm is further distinguished from earlier works by the inclusion of approximation procedures that yield very good starting values. Additionally, a strong connection between the Helmert transformation and the total least-squares problem is established, and a fixed point method is suggested.

The parameter estimation problem in surveying adjustment is considered when outliers and multicollinearity exist simultaneously. A class of new estimators—generalized shrunken-type robust estimators—are proposed by grafting the biased estimation techniques philosophy into the robust estimator, and their statistical properties are discussed. By appropriate choices of the shrinking parameter matrix, we obtain many useful and important estimators. A numerical example is used to illustrate that these new estimators can not only resist the influence of outliers but also effectively overcome difficulty caused by multicollinearity.

Interference and multipath are the main error sources of Global Positioning System (GPS) measurement in engineering surveying. This paper describes an algorithm that mitigates specular multipath as well as interference in GPS differential carrier phase measurement by using signal-to-noise ratio (SNR). The focus is on multipath because it accounts for most of the total error budget in differential carrier phase measurement. The algorithm is demonstrated on static platforms in severe multipath environments. The accuracy is tested with predefined displacements on an X-Y-Z stage, and the experimental results are compared to sidereal day-to-day repeatability. The data sets used for investigation are six-epoch measurements, and the accuracy of the six-epoch solution is shown.

In this paper, simple approximate methods have been given to calculate the true value of an area on a Mercator chart. The introduction touches on the general characteristics of Mercator projection, and the area deformation on this projection is studied. As is known, in this conformal projection area deformations increase with the latitude and differentiate according to the location of the region. Therefore, the areas calculated or measured directly on these commonly used charts are not the true values. First, these two approximate methods—of which area values very close to the true values can be obtained—are introduced. Then, these methods have been applied to the regions located at low, middle, and high latitudes. In the conclusion, calculated areas have been compared with the true areas, closeness of the results have been examined, and the validity of the methods has been proved.