Journal of Surveying Engineering

The so-called $3\sigma$-rule is a simple and widely used heuristic for outlier detection. This term is a generic term of some statistical hypothesis tests whose test statistics are known as normalized or studentized residuals. The conditions, under which this rule is statistically substantiated, were analyzed, and the extent it applies to geodetic least-squares adjustment was investigated. Then, the efficiency or nonefficiency of this method was analyzed and demonstrated on the example of repeated observations.

In geospatial applications, the datum transformation has been necessarily employed to transform the geospatial outcomes from the data-collection system to the user-interested system. Its key is to compute the transformation parameters that describe the geometric relation between two datum systems. The ordinary least-squares based transformation parameter estimation needs the iterative computations unless the initial values of parameters are approximate enough, which is usually time-consuming. Particularly with the development of (near) real-time data collection techniques, such iterative datum transformation method cannot meet the real-time applications. In this paper, we study the noniterative method in terms of the multivariate least-squares theory with two-dimensional empirical affine transformation as a case study. We address the noniterative transformation for the partially and fully error-affected affine models, respectively. The study indicates that the noniterative solution exists when the variance matrix of coordinate errors is structured as ${\mathbf{Q}}_0\otimes \mathbf{Q}$ with $\mathbf{Q}$ the variance matrix of single point and ${\mathbf{Q}}_0$ the correlation matrix between points. The numerical examples show that the noniterative method can obtain the practically equivalent result with the ordinary method but improve the computation efficiency significantly. Therefore, the noniterative method is promising for the real-time datum transformation applications.

To achieve the best linear unbiased estimation of unknown parameters in geodetic data processing a realistic stochastic model for observables is required. This work is a follow-up to work carried out recently in which the geometry-free observation model (GFOM) was used. Here, least-squares variance component estimation is applied to global positioning system (GPS) observables using the geometry-based observation model (GBOM). The benefit of using GBOM, rather than GFOM, is highlighted in the present contribution. An appropriate stochastic model for GPS observables should include different variances for each observation type, the correlation between different observables, the satellite elevation dependence of the observables’ precision, and the temporal correlation of the GPS observables. Unlike the GFOM, in the GBOM two separate variances along with their corresponding covariances are simultaneously estimated for the phase observations of the L1 and L2 frequencies. The numerical results for two receivers—namely, Trimble 4000 SSi (Trimble Navigation, Sunnyvale, California) and Leica SR530 (Leica Geosystems, Aarau, Switzerland)—indicate a significant correlation between the observation types. The results show positive correlations of 0.55 and 0.51 between the CA and P2 code observations for Trimble 4000 SSi and Leica SR530, respectively. In addition, the satellites’ elevation dependence of the GPS observables’ precision is remarkable. Also, a temporal correlation of about 10 s exists in the L2 GPS observables for the Trimble 4000 SSi receiver.

This paper presents a method for the surveying and reliable processing of Global Navigation Satellite System (GNSS) observations in rapid and ultrarapid static surveying for determination of control-point coordinates. The presented technique allows for reliable determination of coordinates, even in the case of highly difficult observation conditions (e.g., for control points situated along forest edges or entirely in the forest, near buildings, or in the vicinity of power-transmission lines). The paper also analyzes different projects of the global positioning system (GPS/GLONASS) networks from the perspective of their credibility and reliability. The control-point coordinates are determined by three GNSS receivers positioned in line on a special base, providing a credible control of GNSS baselines during rapid and ultrarapid static surveys. The GNSS receivers are separated by the distance of 0.5 m. Given the gross errors in baseline coordinates determined that happen in practice, simultaneous use of three receivers for position determination of a control point allows reliable determination of the coordinates even under significantly obstructed access to satellites. The practical surveys were conducted using Topcon and Trimble receivers using real and virtual reference stations. The presented survey and GNSS data-processing methodology allow obtaining centimeter-level accuracy in a few minutes of GPS/GLONASS observations for control points located in obstructed conditions.

This case study aims to demonstrate a multi-antenna Global Navigation Satellite System (GNSS) technique and quality evaluation approach that can be used to determine the attitude parameters for a moving platform. First, considering the highly dynamic behavior of a moving platform, a noniterative parameter determination approach was introduced. A rigorous error analysis approach was then established to give explicit indications on the obtained attitude parameters. Based on the numerical results from both simulated and real datasets, it has been illustrated that the proposed approach is capable of giving efficient and reliable attitude parameter estimates independently without the need for auxiliary information. Consequently, the multi-antenna GNSS system can serve as an immediate resolution for the attitude determination of moving platforms in modern day applications.