Journal of Surveying Engineering

Monitoring Earth-surface deformations with surveying instruments plays a key role in the knowledge of dynamics and the evolution of geophysical phenomena. During this stage, it is important to adopt an appropriate check of the statistical significance of point displacements. We verified the advantages of using a statistical Bayesian approach with a simple a priori geophysical model instead of the frequentist methods usually adopted. In particular, we analyzed global positioning system (GPS) coordinate time series in two applications. First, by using a dedicated device, we applied movements of known amplitude to a GPS antenna. Such known imposed values were used as a term of comparison both for the frequentist and for the Bayesian approach. Furthermore, we analyzed data from GPS campaigns carried out on a landslide located in the central part of Italy. The results of both investigations (imposed and unknown movements) show more valuable outcomes by using the Bayesian approach.

This paper presents an improved weighted total least squares (IWTLS) method for the errors-in-variables (EIV) model with applications in linear fitting and coordinate transformation. In addition, an improved constrained weighted TLS (ICWTLS) method is further obtained based on the IWTLS algorithm. Following the weighted TLS solution (WTLSS) method in which the precisions of any two columns of the design matrix differ only by a scalar factor in linear orthogonal regression problems, the IWTLS method is derived for a more generic case in which there is no proportionality assumption for the cofactor matrix of the design matrix in the EIV model. Compared with existing research on the constrained TLS method under the assumption that both the constraining matrix and the right-hand-side (RHS) vector are error-free, or that only the RHS vector contains errors, the ICWTLS method is proposed for resolving the EIV model with constraints by integrating the observation equations and constraint equations under the assumption that the observation vector and design matrix in the observation equations, and the RHS vector and the constraining matrix in the constraint equations, contain errors. The applicability of the proposed methods is illustrated through empirical examples. The performances of our proposed methods are compared with those of existing methods in the applications of linear fitting and coordinate transformation. The analysis of the experimental results demonstrate that (1) the proposed IWTLS algorithm has not only the advantage of the WTLSS algorithm, which takes into account the errors in the design matrix in linear orthogonal regression applications, but also the capability of dealing with a more generic case in which the design matrix contains errors with different distributions; and (2) the proposed ICWTLS algorithm has the advantages of handling both the cases of equal and unequal weights in solving the EIV model with constraints and handling the case in which the constraints contain errors.

For heterogeneous and correlated observations, the variance components and the covariance components sometimes must be estimated. The forms of best invariant quadratic unbiased estimate (BIQUE) and Helmert-type estimation of variance and covariance components have already been derived by Koch and Grafarend, respectively. After obtaining the minimum norm quadratic unbiased estimate (MINQUE) of variance components, Rao derived only the MINQUE of the variance and covariance components for a special case in which the error vector is composed of a linear combination of independent random effect vectors of zero mean and the same variance-covariance matrix whose variance and covariance components were to be determined. However, an explicit expression of the MINQUE suitable to more general situations has not been derived. This paper defines the natural estimation of covariance components from errors and derives the MINQUE of variance and covariance components. The BIQUE and MINQUE of variance components without covariance components have the same iteration solution; the Helmert solution is only a special case of the MINQUE. However, the three estimates of variance and covariance components are different. The two MINQUE methods obtained in this paper have the advantage independence of the error distribution and offer a reasonable alternative in estimating variance and covariance components, and they can be used in the most general case. Numeric results show that the two MINQUE methods obtained in this paper are feasible.

The geographic location of points using global positioning system (GPS) receivers is less accurate in forested environments than in open spaces because of signal loss and the multipath effect of tree trunks, branches, and leaves. This has been confirmed in studies that have concluded that a relationship exists between measurement accuracy and certain variables that characterize forest canopy, such as tree density, basal area, and biomass volume. However, the practical usefulness of many of these studies is limited because they are often limited to describing associations between the variables and mean errors in the measurement interval, when measurements should be made in real time and in intervals of seconds. In this work, machine learning techniques were applied to build mathematical models that would associate observation error and GPS signal and forest canopy variables. The results reveal that the excessive complexity of the signal prevents accurate measurement of observation error, especially in the $Z$-coordinate and in time intervals of a few seconds, but also reveal that forest cover variables have a significantly greater influence than GPS factors, such as position dilution of precision (PDOP), the number of satellites, or error for the base station.

The identification of outliers in global positioning system (GPS) observations—to compare equipment, positioning methods, or working conditions—has traditionally been performed using univariate or multivariate statistics. However, these methods have certain drawbacks when processing data collected by GPS receivers. Such data can be more suitably handled as observations at discrete points of a smooth stochastic process and, consequently, other statistical approaches to the analysis of functional data may prove more suitable. We analyzed the applicability of the concept of functional depth to the identification of outliers in GPS observations. The proposed method was applied to 12 series of GPS receiver data collected in an open space and in similar signal reception conditions. The results obtained adapted better to the expected results, given the signal-reception conditions, than those obtained by the classical statistical approaches used by other writers to compare GPS observations.

Network-based real-time kinematic (NRTK) positioning in local or regional reference networks has been proven to be an efficient technology for high precision global positioning systems (GPS) positioning over the last few years. With a view to GPS modernization and the development of the European Galileo system, considerable improvements are expected, enabling high reliability of real-time kinematic (RTK) rover positioning on distances larger than the typical ones of current RTK networks. This paper evaluates the expected performance of a GPS/Galileo NRTK by assessing the spatial variability of specific quality indicators; namely, the success rates of correct integer ambiguity resolution and the network internal reliability. This approach provides a useful tool for design analysis of RTK networks. The Greek GPS-RTK network is used to simulate different geometric configurations to demonstrate in a practical sense whether or not a particular configuration can meet the user specified requirements. As a result of this study, a priori indication on the network reliability associated with different geometries is obtained, and the limitations of the network as a function of the station geometry can be ascertained.

The problem of determining the required precision in observations in order to obtain a desired precision in final parameters, classically known as the second order design problem, is revisited in this paper and proposed to be solved by the simulated annealing method. An example and a flexible implementation in MATLAB are given.