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.

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.

Covariance determination as the heart of Least Squares Collocation gravity field modeling is based on fitting an analytical covariance to the empirical covariance, which is stemmed from gravimetric data. The main objective of this study is to process different local covariance strategies over four regions with different topography and spatial data distribution in Iran. For this purpose, Least Squares Collocation based on Remove-Compute-Restore technique is implemented. In the Remove step, gravity reduction in regions with a denser distribution and a rougher topography is more effective. In the Compute step, the assessment of the Collocation estimates on the gravity anomaly control points illustrates that data density is more relevant than topography roughness to have a good covariance determination. Moreover, among the different attempts of localizing the covariance estimation, a recursive approach correcting the covariance parameters based on the agreement between Least Squares Collocation estimates and control points shows better performance. Furthermore, we could see that covariance localization in a region with sparse or bad distributed observations is a challenging task and may not necessarily improve the Collocation gravity modeling. Indeed, the geometrical fitness of the empirical and analytical covariances-which is usually a qualitative test to verify the precision of the covariance determination-is not always an adequate criterion.

This paper proposes a novel self-learned integrated framework of active learning (AL) and semi-supervised learning (SSL). SSL methods try to estimate a certain semilabel for unlabeled samples. While AL methods select the most informative unlabeled samples for the current classifying model and provide their labels by human expertise. An excessive human-machine interaction is required for labeling the selected instances. Whereas, providing reliable labels is a sensitive, time-consuming and expensive step. In our framework, we try to decrease the required human supervision by incorporating SSL method. In addition, the participation rate of each AL and SSL methods in the framework is adaptive and determined based on the certainty of the classifier at each iteration. The experiments were carried out on Pavia University image data which is an urban scene. The results showed the efficiency and the excellent performance of the proposed method in both terms of accuracy and computational cost.