Combination of GPS and Leveling Observations and Geoid Models Using Least-Squares Variance Component Estimation

Abstract

In the last few years, satellite-based positioning techniques, such as the Global Positioning System (GPS), proved their abilities in various geodetic fields. Height determination, as one of such applications, requires a more likely correct geoid model to provide reliable geoid heights for transformation of the ellipsoidal heights to orthometric heights. An important step is then to establish such a model by optimal combination of the available geoid models. This can be achieved via variance component estimation (VCE) methods, which provide appropriate weights to GPS and leveling observations as well as the geoid models. The authors demonstrate the efficacy of the least-squares VCE (LS-VCE) to this problem. The algorithm is applied to real data sets in Shahin-Shahr, Isfahan, Iran, to evaluate the EGM2008 and GGMplus Earth geopotential models and a regional geoid model (named IRGeoid10) in terms of agreement to the GPS/leveling observations and introduce the more likely correct model over the case-study area. The results indicate that the EGM2008 model shows a good agreement (2-mm precision on the fitted surface) with the results of the GPS/leveling observations in this very small area. It is notable, however, that the present contribution is mainly of interest from an algorithmic point of view because concrete conclusions cannot be made when comparing the results due to the small case-study area used. By optimal combination of these data sets, the weights of which are estimated by LS-VCE, a geometric surface is presented to approximate the local vertical datum in the case-study region. This surface can convert the ellipsoidal heights, which can be obtained from GPS, to the orthometric heights with high precision. individual papers. This paper is part of the Journal of Surveying Engineering, © ASCE, ISSN 0733-9453. © ASCE 04016023-1 J. Surv. Eng. J. Surv. Eng., 04016023 Downloaded from ascelibrary.org by Vahab Nafisi on 07/31/16. Copyright ASCE. For personal use only; all rights reserved. © ASCE 04016023-9 J. Surv. Eng. J. Surv. Eng., 04016023 Downloaded from ascelibrary.org by Vahab Nafisi on 07/31/16. Copyright ASCE. For personal use only; all rights reserved. © ASCE 04016023-11 J. Surv. Eng. J. Surv. Eng., 04016023 Downloaded from ascelibrary.org by Vahab Nafisi on 07/31/16.

Establishment of a corrective geoid surface by spline approximation of Iranian GNSS/levelling network

“…Fotopoulos (2005) applied various polynomial functions to adjustment of geoid models and showed that the type of functional model affects the estimated values of standard deviations [6]. Khazraei et al (2017) used the bi-linear and the bi-quadratic polynomials to approximate and analyze the accuracy of the geoid models in a small area (~100 km 2 ). The results prove that the bi-quadratic polynomial was the best model fitted in this study [7].…”

“…Khazraei et al (2017) used the bi-linear and the bi-quadratic polynomials to approximate and analyze the accuracy of the geoid models in a small area (~100 km 2 ). The results prove that the bi-quadratic polynomial was the best model fitted in this study [7]. Das et al (2017) developed the geoid surface using second, third and fourth degree polynomials [8].…”

Combination of regional and global geoid models at continental scale: application to Iranian geoid

“…Saadat et al [2018] determined the regional geoid model of Iran, IRG2016, based on the radial basis functions. Combination of regional and global geoid models, in a small-scale region in Iran, has been studied by Khazraei et al [2017]. They used LS-VCE to evaluate the EGM2008 and GGMplus Earth geopotential models and IRGeoid10 in terms of agreement to the GNSS/leveling observations.…”