Only the correct stochastic model can be applied to derive the optimal parameter estimation and then realize the precision global navigation satellite system (GNSS) positioning. The key for refining the GNSS stochastic model is to establish the easy-to-use stochastic model that should capture the error characteristics adequately based on the estimated precisions from the real observations. In this paper, the authors study the GNSS elevation-dependent precision modeling and analyze its impact on the statistic testing involved in the adjustment reliability. With the zero-baseline dual-frequency Global Positioning System (GPS) data, the authors first estimate the elevation-dependent precisions and establish the stochastic models by fitting them with three predefined functions, including the unique precision function and the sine and exponential types of elevation-dependent functions. Three established models are then evaluated by their performance in the overall and w-statistic testing. The results ...

Affine transformation that allows the axis-specific rotations and scalars to capture the more transformation details has been extensively applied in a variety of geospatial fields. In tradition, the computation of affine parameters and the transformation of non-common points are individually implemented, in which the coordinate errors only of the target system are taken into account although the coordinates in both target and source systems are inevitably contaminated by random errors. In this article, we propose the seamless affine error-in-variables (EIV) transformation model that computes the affine parameters and transforms the non-common points simultaneously, importantly taking into account the errors of all coordinates in both datum systems. Since the errors in coefficient matrix are involved, the seamless affine EIV model is nonlinear. We then derive its least squares iterative solution based on the Euler–Lagrange minimization method. As a case study, we apply the proposed seamless affine EIV model to the map rectification. The transformation accuracy is improved by up to 40%, compared with the traditional affine method. Naturally, the presented seamless affine EIV model can be applied to any application where the transformation estimation of points fields in the different systems is involved, for instance, the geodetic datum transformation, the remote sensing image matching, and the LiDAR point registration.

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...

The determination of the land geoid and the marine geoid involves different data sets and calculation strategies. It is a hot issue at present to construct the unified land–ocean quasi-geoid by fusing multi-source data in coastal areas, which is of great significance to the construction of land–ocean integration. Classical geoid integral algorithms such as the Stokes theory find it difficult to deal with heterogeneous gravity signals, so scholars have gradually begun using radial basis functions (RBFs) to fuse multi-source data. This article designs a multi-layer RBF network to construct the unified land–ocean quasi-geoid fusing measured terrestrial, shipborne, satellite altimetry and airborne gravity data based on the Remove–Compute–Restore (RCR) technique. EIGEN-6C4 of degree 2190 is used as a reference gravity field. Several core problems in the process of RBF modeling are studied in depth: (1) the behavior of RBFs in the spatial domain; (2) the locations of RBFs; (3) ill-conditioned problems of the design matrix; (4) the effect of terrain masses. The local quasi-geoid with a 1′ resolution is calculated, respectively, on the flat east coast and the rugged west coast of the United States. The results show that the accuracy of the quasi-geoid computed by fusing four types of gravity data in the east coast experimental area is 1.9 cm inland and 1.3 cm on coast after internal verification (the standard deviation of the quasi-geoid w.r.t GPS/leveling data). The accuracy of the quasi-geoid calculated in the west coast experimental area is 2.2 cm inland and 2.1 cm on coast. The results indicate that using RBFs to calculate the unified land–ocean quasi-geoid from heterogeneous data sets has important application value.

The Gravity Recovery and Climate Experiment (GRACE) and its subsequent GRACE Follow-On (GRACE-FO) missions have been instrumental in monitoring Earth’s mass changes through time-variable gravity field models. However, these models suffer from high-frequency noise and significant north-south striping (NSS) noise. The most widely used spectral filter for addressing these issues is the decorrelation and denoising kernel (DDK) filter, utilized by official processing agencies. The key operation of DDK filtering is to regularize the normal equation built by the Level-1b data. However, the regularization parameter used in original DDK filters is empirically determined by the signal-to-noise ratios and remains unchanged across all months. This is improper due to the heterogeneity of the monthly covariance matrix. Additionally, a single regularization parameter may not effectively address the ill-posedness of the inversion equation. For this reason, we propose a multiple-parameter regularization approach for filtering GRACE gravity field models, with regularization parameters determined by minimizing the mean squared error (MSE) for each month. The proposed method is used to process the ITSG-Grace2018 and ITSG-Grace_operational Level-2 spherical harmonic coefficients with degree/order 96 from April 2002 to December 2022. The results show that our method produces the filtered mass anomalies, global trend, and annual signal amplitudes that align better with three mascon solutions (CSR, JPL, and GSFC) compared to DDK filters and ordinary Tikhonov regularization with a single regularization parameter. In some typical areas with significant signals, our approach retains more detailed characteristics in filtered signals compared to DDK filters and ordinary Tikhonov regularization. Repeated simulations demonstrate that the filtered signals by our approach are closer to the simulated true signals than those by other methods.