Journal of Surveying Engineering

The estimation of the atmospheric refraction coefficient by conducting simultaneous and mutual zenith observations is a well-known geodetic procedure. The respective mathematical model is based on certain assumptions regarding the actual path followed by the optical ray while propagating in the atmosphere (spherical symmetric model). Starting from this model an approximate solution can be derived, which is generally accepted in the literature on the subject. The present paper examines the mathematical model of this geodetic technique in a rigorous manner, which results in an exact solution for the computation of the atmospheric refraction coefficient or equivalent for the zenith angle correction that is due to the effect of the atmospheric refraction. As the direct computation of the exact solution is rather complicated, an iterative way of computing the same quantity is derived, which can be realized easily on any pocket calculator. In order to assess the derived formulas we investigate the applicability of the exact, the convergence rate of the iterative and the errors introduced by the approximate formulas, by conducting a representative series of synthetic numerical experiments. The overall discussion aims to provide a helpful insight into the geometric and theoretical features of this traditional geodetic method. To practitioners that attempt to apply the standard correction formulas to zenith observations in order to compensate the effect of atmospheric refraction in the frame of typical surveying applications, such as trigonometric leveling, the paper also points out possible numerical errors introduced by the traditional approximate formulas.

This paper presents a novel line accuracy assessment technique by measuring the offsets of a typical measured line from the true reference line. These measurements are assumed to follow a Gaussian distribution. Buffers of gradually increasing widths, drawn around the true line, are used to measure the magnitudes of line offsets from true locations. A nonlinear least-squares estimation is used to determine the mean and the standard deviation of the line offset. The purpose of the proposed parameter estimation technique is to improve, using the two Gaussian parameters of mean and standard deviation, the line error modeling, and to uncover the physical meaning of the magnitude and variability of line offsets, respectively. The feasibility of the parameter estimation technique is demonstrated by a series of tests that confirm the assumption of a nonzero mean Gaussian distribution. The proposed methodology is expected to provide better insight into the spatial data quality of linear features in geographical information systems.

Robust estimation yields more accurate results than least-squares estimation in the presence of undesirable errors. It has been recently applied to the process of GNSS differential positioning in the standard fashion of iteratively reweighted least squares. We propose an improvement of the technique, based on a previous result by which robust estimation is truly robust only if considered as a global optimization problem. Robust estimation by global optimization techniques will prove to be an even more powerful method, capable of solving problematic baselines that are nonsolvable by classic methods.

A simulation process is implemented in order to generate synthetic populations of positional-planimetric errors and later, by a bootstrap process, a family of acceptance curves (nomogram) has been derived. These curves allow us to learn the acceptance level, or pass level, of a geographic database when a positional control test based on bias and on variability is applied to it against a given standard. Acceptance curves allow us to report user’s risk and to determine the adequate size of the sample in order to reduce this risk to a desired level.

Different methods for estimating simple vertical curves that optimally fit observed profile data have been developed. In 1999, the author developed a linear programming (LP) method for estimating simple vertical curves using LINGO optimization software. To obtain the global optimal solution, the LP formulation was manually solved for different combinations of the two unknown nonlinear variables (using $5\mathrm{m}$ increments). In 2004, an improved method that automates the iterations using Visual-Basic in Excel Solver was published. The global optimal solution required $10\mathrm{h}$ for an increment of $0.1\mathrm{m}$ . This technical note presents an extension of the previously developed LP formulation that converges to the global optimal solution in a minute. The formulation involves no iterations of the nonlinear variables. Instead, the start and end points of the parabolic curve were modeled using three binary variables, and the resulting mixed-integer nonlinear model was solved using LINGO global option that has been recently developed. The proposed method, which is applicable to both crest and sag vertical curves, should be of interest to surveying professionals.