Journal of Surveying Engineering

In the case of traditional Global Positioning System (GPS) data processing algorithms, systematic errors in GPS measurements cannot be eliminated completely, nor accounted for satisfactorily. These systematic errors can have a significant effect on both the ambiguity resolution process and the GPS positioning results. Hence this is a potentially critical problem for high precision GPS positioning applications. It is therefore necessary to develop an appropriate data processing algorithm which can effectively deal with systematic errors in a nondeterministic manner. Recently several approaches have been suggested to mitigate the impact of systematic errors on GPS positioning results: the semiparametric model, the use of wavelets, and new stochastic modeling techniques. These approaches use different bases and have different implications for data processing. This paper aims to compare the above three methods, in both the theoretical and numerical sense.

The zero error of electromagnetic distance measuring instruments is a near-constant systematic error, which has the same effect on the measured distances. This paper presents a least-squares formula for this correction based on the division of a baseline into m subbaselines, and measuring all possible distances between the marked points. The validity of the formulation is verified by two examples.

The purpose of this paper is to look into several common idempotent matrices of interest in the context of any mixed model least-squares adjustment. The cofactor (scaled covariance) matrices, based on the law of error propagation, are incorporated into the least-squares estimation solutions. The rank of an idempotent matrix is given by taking the matrix trace, which leads to an unbiased estimate of the unit weight variance. The orthogonality between two projected vector subspaces is proven by using the generalized inner products, or equivalently, according to the cosine law. The Lagrange multiplier vector and its associated cofactor matrix are then employed to verify the already determined idempotent as well as orthogonal properties, reflecting the correctness of the formulated matrix equations.

This paper describes geometric modeling systems that are being applied with computer systems in construction surveying of highway tunnels. These modeling systems include sweeping, skinning, mesh generation, combined constructive solid geometry and boundary representation modeling systems, and computational geometry for irregular surfaces and tunnel intersections.

All spatial data in a geographic information system (GIS) intrinsically contain uncertainty. Simulations could be used for many GIS applications in order to estimate confidence ranges of certain analyses and project worst-case scenarios. For those applications, generation of Gaussian random fields is essential to simulate the uncertainty effects, because errors in spatial data are assumed dependent upon the Gaussian distribution. Gaussian fields with no spatial dependency could be assumed because of their simple concept and easy computation, but the reality is that spatial errors have a spatially correlated nature. For this reason, the intensive matrix computation for generating spatially autocorrelated Gaussian random fields requires the solution of a large, sparse linear system: $\mathbf{X}=\rho \mathbf{WX}+\mathbf{\epsilon }\text{.}$ There has been substantial development of direct and iterative methods for solving a large, sparse linear system. In this research, those methods are presented and compared in terms of computation complexity for the particular system. The writer presents the steepest descent method as the best possible method with linear complexity.

This article presents some theoretical and practical aspects of using geographic information system (GIS) data to support feature extraction from high-resolution aerial and satellite images. GIS data have been used to calculate parameters for objects belonging to major classes of man-made objects represented on large-scale topographic maps. A moment-based mathematical approach was used for the formal description of objects and calculation of their shape parameters. A decision tree method was employed to formulate classification rules applied to classify objects extracted from high-resolution aerial or satellite images.

In this contribution, optimal ionosphere-free combinations for a modernized triple-frequency global positioning system (GPS) are derived. It is shown that these ionosphere-free combinations are directly related to the model based on carrier phase observations only, in which the ionospheric delays are estimated. For this model and thus for the ionosphere-free combinations, integer ambiguity estimation is possible, in contrast to what is often read in GPS positioning literature. In this article the estimable integer ambiguities are presented and the expected success rates when trying to resolve these ambiguities are given. In addition, the baseline precision is analyzed for both the ambiguity-float and ambiguity-fixed ionosphere-free cases.