Journal of Surveying Engineering

Robust estimation of unknown parameters in linear models with only a single error component has been widely investigated. However only a small percentage of literature treats robust estimate of variance components in heteroscedastically mixed models. The correction-based pseudoobservation method, the $\rho \left(x\right)$ -function-based robust maximum likelihood estimate (MLE) and restricted maximum likelihood estimate methods, as well as the robust Helmert method are the three kinds of typical robust methods for estimating variance components of linear mixed models. However, they are generally affected by different types of scoring functions and various tuning factors based on $M$ estimate defined by Huber from the maximum likelihood type of estimation. In addition, the pseudoobservation method will encounter risks of incorrect corrections due to the misidentification of gross errors. In this paper, gross errors and random or normal errors are assumed to be occasionally additive, independent, normally distributed with different scales, and all are regarded as missing and/or unobservable data. Together with the observations, they form a complete data problem where the unknown parameters and variance components need to be estimated. The expectation-maximization (EM) algorithm for finding the MLEs is robustified by estimating the variances of gross errors by defining weights and proposing to jointly solve the robust estimation of the unknown parameters and variance components. A numerical example of a global positioning system baseline network shows that the robustified EM algorithm can find a reliable estimate of unknown parameters and variance components, and efficiently separate the gross errors and subrandom effects or errors by computing their respective Bayesian estimate.

This paper presents one of the most comprehensive tests conducted about the real-time kinematics (RTK) and continuously operating reference stations (CORS) network using instruments from three global positioning system (GPS) manufacturers (Leica, Topcon, and Trimble). The test was carried out between August and October 2006 in the Marmara Region of Turkey as part of the research project for establishing RTK CORS network covering all of Turkey. Three GPS networks (NET-120, NET-90, and NET-60) were designed, each consisting of six CORS points: with interstation distances of 120, 90, and $60\mathrm{km}$ , respectively. Leica, Trimble, and Topcon directly participated in the tests, each company contributing a $2\text{week}$ effort. RTK surveys were compiled at check points (previously known points) and new points were generally selected in built-up areas. Flachen Korrectur parameter—Spatial correction parameters, virtual reference stations, pseudoreference stations, and master auxiliary concept techniques were used for RTK positioning. Postprocessing by network solution software was also used at check points. The results of network-based RTK and postprocessing were found to be successful at each net, the main exception being the difficulties encountered by one of the firms participating at NET-120. Results are discussed in the paper.

Helmert’s variance component estimation method based on a least-squares adjustment of condition equations is presented, in which the registered area and the coordinates of a cadastral parcel are assumed to be different and independent types of observations with errors in the cadastral parcel area adjustment. The Helmert method is employed for the estimation of variance components of these two types of observations, thus providing a determination of accurate weights between them. At the same time, inconsistencies between the registered and digitized areas of the parcels are adjusted through a least-squares adjustment. The mathematical models for adjusting the boundaries of the parcel areas are derived, incorporating both the area conditions and geometric conditions. An empirical test is conducted and the results are compared to those obtained from the conventional method, assuming that the digitized coordinates are treated as observations while the registered parcel areas are not. The analysis of the results demonstrates that the least-squares adjustment, when based on Helmert’s variance component estimates, refinds the weights of the observations more accurately, improves the accuracy of the adjusted coordinates in parcel digitization, and resolves the inconsistencies between the registered areas and digitized areas of the parcels more rigorously.

Evaluation on the agreement between colocated ties and ties estimated from space geodesy techniques before the intertechnique combination is essential to an accurate combination solution realization. Previous studies evaluate their agreement based on the magnitude of postfit residuals with normalized residuals during the intertechnique combination and magnitude of their differences through intratechnique combination from space geodetic measurement. This study formulates an alternative criterion based on the critical value of the chi-square test statistic through compatibility testing for the evaluation of both ties agreement. Individual terrestrial reference frame solution and corresponding colocated ties data within 14 colocated sites used in ITRF2000 realization were selected for the study. It was found that the devised criterion flagged and retained the same set of colocated ties in common with previous contribution results, which makes itself another alternative for further validation. Given the demand of the fusion of several groups of data for better derived information in geosciences and remote sensing, this criterion could also be applied to outlier detection for each group of data during the fusion process.

Highly redundant or statically undetermined structures, such as a cable-stayed bridge, have been of particular concern to the engineering community nowadays because of the complex parameters that must be taken into account for healthy monitoring. The purpose of this study was to verify the reliability and practicability of using GPS to characterize dynamic oscillations of small span bridges. The test was carried out on a cable-stayed wood footbridge at Escola de Engenharia de São Carlos-Universidade de São Paulo, Brazil. Initially a static load trial was carried out to get an idea of the deck amplitude and oscillation frequency. After that, a calibration trial was carried out by applying a well known oscillation on the rover antenna to check the environment detectable limits for the method used. Finally, a dynamic load trial was carried out by using GPS and a displacement transducer to measure the deck oscillation. The displacement transducer was used just to confirm the results obtained by the GPS. The results have shown that the frequencies and amplitude displacements obtained by the GPS are in good agreement with the displacement transducer responses. GPS can be used as a reliable tool to characterize the dynamic behavior of large structures such as cable-stayed footbridges undergoing dynamic loads.