Journal of Surveying Engineering

The three-point resection problem, i.e., the problem of obtaining the position of an unknown point from relative angular measurements to three known stations is a basic operation in surveying engineering. Several approaches to solve this problem, graphically or analytically, have been developed in the last centuries. In this paper, a new analytical approach to solve this problem is presented. The method determines the coordinates of the unknown point by intersecting straight lines through the three stations. The required azimuths of these lines are obtained from the geometric relationship between two similar triangles. Numerical simulations that show the good performance and accuracy of this approach are also reported.

Transformations between local datums/frames have provided an indispensable method for expressing coordinates in the same datum. The advent of space-based geodetic techniques propelled the homogenization of national networks through the definition of conventional earth-centered, earth-fixed datums globally accessible through satellite observations. On the other hand, datum transformations enhanced mapping applications by using different realizations of the conventional reference frames. Realization of conventional datums/frames also led to investigations determining the transformation parameters between conventional terrestrial frames, and local datums rather than between local datums themselves. In this context, both inverse and sequential transformations are needed to express the coordinates of one local datum into another. Obtaining the transformation parameters through a “compound transformation” rather than transforming coordinates in a sequential scheme has several advantages. In this study, avenues to rigorously compute compound datum transformation parameters given two independent sets of transformation parameters are examined and compact analytical equations free of any matrix inversion are derived. New linear equations are presented both in compact matrix notation and in its expanded form to facilitate the propagation of errors from individual sets of transformation parameters to those of the compound datum transformation.

A method for postmission relative positioning by global positioning system based on precise point positioning is presented as an alternative to the traditional double-differencing single-baseline approach. In this method, precise orbits and clock corrections are used at the reference station to estimate corrections to the ionospheric and wet tropospheric errors. For short reference-to-user ranges, these corrections are applied at the rover receiver in addition to the same precise orbits and clock corrections used at the reference to estimate the rover position. For relatively longer distances, a linear combination of dual-frequency measurements is used to eliminate the ionosphere and a residual wet tropospheric parameter is solved for as an additional unknown. The differential initial phase biases can be estimated as a residual ambiguity term, or calibrated from data of reference station network. The proposed approach has significant operational advantages over the traditional single-baseline positioning. The methodology of the proposed method is presented and discussed. To evaluate its performance, land and marine tests were conducted where the rover data were referenced, first using a reference station at a short distance, and second using another station at relatively longer distance. Results show that an accuracy of a few centimeters to subdecimeter level was obtained.

In global positioning system (GPS) positioning, the tropospheric delay is a systematic error. Mismodeling of the tropospheric delay results in a degradation of the estimated height component, and thus constitutes a limitation to high-accuracy GPS applications. As such, it is obvious that the tropospheric delay should be modeled as accurately as possible. Modeling the tropospheric delay for some applications, such as precise airborne kinematic differential positioning, is further complicated due to the large altitude difference between the ground-based receiver and the airborne roving receiver. This study tests and analyzes three methods for modeling the tropospheric delay, in an attempt to improve the accuracy of the height component for airborne GPS kinematic positioning. As there are several other error sources in GPS, the test and evaluation have to be carefully designed, as any improvements in accuracy due to the use of any tropospheric modeling approaches could be masked by other effects, such as residual orbit errors and ionospheric delays. The analysis is performed for real airborne GPS data and data from a multiple-base station network, and model performance evaluation is based on an independently well-determined aircraft trajectory. Test results show that the estimation of residual tropospheric zenith delay simultaneously with the position parameters after applying the tropospheric delay corrections derived from a network of GPS receivers is seen as the best option with an additional 62% improvement for the height component in terms of standard deviation when compared with results from using a UNB3 tropospheric model only.

Over the past decade, the National Oceanic and Atmospheric Administration’s National Geodetic Survey, in collaboration with multiple organizations, has conducted research into airport obstruction surveying using airborne light detection and ranging (LIDAR). What was initially envisioned as a relatively straightforward demonstration of the utility of this emerging remote sensing technology for airport surveys was quickly shown to be a challenging undertaking fraught with both technical and practical issues. We provide a brief history of previous work in LIDAR airport obstruction surveying, including a discussion of both past achievements and previously unsolved problems. We then present a new processing workflow, specifically designed to overcome the remaining problems. A key facet of our approach is the use of a new LIDAR waveform deconvolution and georeferencing strategy that produces very dense, detailed point clouds in which the vertical structures of objects are well characterized. Additional processing steps have been carefully selected and ordered based on the objectives of meeting Federal Aviation Administration requirements and maximizing efficiency. Tests conducted using LIDAR waveform data for two project sites demonstrate the efficacy of the approach.