High precision geoid determination is a challenging task at the national scale. Many efforts have been conducted to determine precise geoid, locally or globally. Geoid models have different precision depending on the type of information and the strategy employed when calculating the models. This contribution addresses the challenging problem of combining different regional and global geoid models, possibly combined with the geometric geoid derived from GNSS/leveling observations. The ultimate goal of this combination is to improve the precision of the combined model. We employ fitting an appropriate geometric surface to the geoid heights and estimating its (co)variance components. The proposed functional model uses the least squares 2D bi-cubic spline approximation (LS-BICSA) theory, which approximates the geoid model using a 2D spline surface fitted to an arbitrary set of data points in the region. The spline surface consists of third-order polynomial pieces that are smoothly connected together, imposing some continuity conditions at their boundaries. In addition, the least-squares variance component estimation (LS-VCE) is used to estimate precise weights and correlation among different models. We apply this strategy to the combined adjustment of the high-degree global gravitational model EIGEN-6C4, the regional geoid model IRG2016, and the Iranian geometric geoid derived from GNSS/leveling data. The accuracy of the constructed surface is investigated with five randomly selected subsamples of check points. The optimal combination of the two geoid models along with the GNSS/leveling data shows a reduction of 21 mm (~20%) in the RMSE values of discrepancies at the check points.@en

The performance of the gravimetric geoid models is usually evaluated by comparison of geoid heights with the GNSS/levelling derived geoid. But the GNSS/levelling network can be infected by significant systematic biases and random errors, especially in large and uneven areas. This contribution addresses the challenging problem of the corrector surface development along with the elimination of biases. To this end, fitting an appropriate geometric surface to the GNSS/levelling geoid heights is required, which is accomplished by applying the least squares B-spline approximation theory to the GNSS/levelling data. In addition, the 3D affine transformation is used to detect systematic effects of the GNSS/levelling network compared to a global geoid model. This strategy is applied to the adjustment of the Iranian GNSS/levelling network. A significant tilt is observed across the country ranging from −0.35 m to 0.04 m. The entire study area is divided into four zones and the corrector surfaces are obtained in each zone. The accuracy of three global geoid models, EGM2008, EIGEN-6C4 and SGG-UGM-1, along with that of the Iranian regional geoid model IRG2016, are then investigated based on the raw GNSS/levelling heights and the corrector surfaces. The evaluations show the reliable results regarding the corrector surfaces against the raw data set. All geoid models show their maximum RMSE values of discrepancies in the mountainous zones and their minimum RMSEs in the zones having lower variety in topography. This indicates that the irregular topographies are not well detected by the global models over the study area.@en

Proper analysis and subsequent interpretation of GPS position time series is an important issue in many geodetic and geophysical applications. The GPS position time series can possibly be contaminated by some abrupt changes, called offsets, which can be well compensated for in the functional model. An appropriate offset detection method requires proper specification of both functional and stochastic models of the series. Ignoring colored noise will degrade the performance of the offset detection algorithm. We first introduce the univariate analysis to identify possible offsets in a single time series. To enhance the detection ability, we then introduce the multivariate analysis, which considers the three coordinate components, north, east and up, simultaneously. To test the performance of the proposed algorithm, we use synthetic daily time series of three coordinate components emulating real GPS time series. They consist of a linear trend, seasonal periodic signals, offsets and white plus colored noise. The average detection power on individual components, either north, east or up, are 32.3 and 47.2% for the cases of white noise only and white plus flicker noise, respectively. The detection power of the multivariate analysis increases to 70.8 and 87.1% for the above two cases. This indicates that ignoring flicker noise, existing in the structure of the time series, leads to lower offset detection performance. It also indicates that the multivariate analysis is more efficient than the univariate analysis for offset detection in the sense that the three coordinate component time series are simultaneously used in the offset detection procedure.@en

Proper analysis and subsequent interpretation of GPS position time series is an important issue in many geodetic and geophysical applications. The GPS position time series can possibly be contaminated by some abrupt changes, called offsets, which can be well compensated for in the functional model. An appropriate offset detection method requires proper specification of both functional and stochastic models of the series. Ignoring colored noise will degrade the performance of the offset detection algorithm. We first introduce the univariate analysis to identify possible offsets in a single time series. To enhance the detection ability, we then introduce the multivariate analysis, which considers the three coordinate components, north, east and up, simultaneously. To test the performance of the proposed algorithm, we use synthetic daily time series of three coordinate components emulating real GPS time series. They consist of a linear trend, seasonal periodic signals, offsets and white plus colored noise. The average detection power on individual components, either north, east or up, are 32.3 and 47.2% for the cases of white noise only and white plus flicker noise, respectively. The detection power of the multivariate analysis increases to 70.8 and 87.1% for the above two cases. This indicates that ignoring flicker noise, existing in the structure of the time series, leads to lower offset detection performance. It also indicates that the multivariate analysis is more efficient than the univariate analysis for offset detection in the sense that the three coordinate component time series are simultaneously used in the offset detection procedure.@en