In this study, the basic concept of height nonlinear velocity field modeling in the CORS station is described. The noise results in a large deviation between the observation and predicted height. An ARCH testing method for heteroscedasticity of CORS height residual square series was proposed and the non-stationary characteristic of CORS height residual square time series was proved. A CORS height nonlinear velocity field reconstruction method based on the GARCH model was proposed. First, a nonlinear LS periodic fitting model was established for CORS height series data. Then, a GARCH model was established for the fitted non-stationary residual series. Finally, the signal term, linear trend term, and GARCH model noise term of nonlinear LS modeling were combined to reconstruct the nonlinear velocity field of the CORS height. The RMSE of nonlinear LS cycle modeling for 25 CORS stations worldwide ranged from 5 to 10 mm. The differences between the velocity, approximate annual and semi-annual amplitudes, and SOPAC results were 0.73 mm/a, 0.94 mm, and 0.51 mm, respectively. Compared with the centimeter amplitude of the CORS station height, the accuracy of the nonlinear model established in this study met the requirements. The results of height nonlinear velocity field reconstruction at 25 CORS stations worldwide showed that the mean square error of prediction of the one-year height movement reached 9 mm, and the average prediction accuracy of the semi-annual was 7 mm. Compared with the calculation accuracy of the current global CORS elevation component of 3–5 mm, the prediction error in this study was about 3 mm. The expected goal was achieved regarding the accuracy of the CORS station height nonlinear velocity field model.

Addressing the persistent trade-off between computational accuracy and execution efficiency in generating high-resolution geospatial grids, this paper proposes a novel high-precision interpolation algorithm specifically designed for rapid, large-scale geospatial grid generation. The algorithm first employs a Gaussian weighted quadratic surface as its interpolation kernel—a method that balances the smoothness of results with adaptability to non-linear terrain variations to ensure high accuracy. Subsequently, to tackle the model's high computational cost, a targeted hybrid optimization framework was designed, leveraging a KD-Tree to accelerate neighbor searches and multithreading to parallelize the independent grid computations, thereby substantially enhancing execution efficiency. Experimental results demonstrate that: 1) The proposed algorithm outperforms three traditional methods (Moving Surface Fitting, Natural Neighbor Interpolation, and Spline Interpolation), achieving reductions in Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) of up to 63.6% and 61.2%, respectively, while attaining a coefficient of determination (R²) as high as 0.998611. 2) The optimization framework delivers a 24-fold speedup in overall runtime without any loss of accuracy. This study offers a high-precision, high-efficiency solution for large-scale geospatial data processing.

The elevation datum is a critical element in surveying and mapping, as variations in elevation systems can lead to discrepancies between Digital Surface Model (DSM) products generated from satellite imagery. To eliminate these differences and ensure high-precision data consistency, this study constructs an elevation datum conversion scheme for multi-source DSM products using the SGG-UGM-2 (2190 degree) global gravity field model to calculate elevation anomalies. While traditional serial algorithms suffer from significantly decreased efficiency as the volume of DSM image files increases, this paper proposes a novel HDC-MPI elevation datum conversion algorithm based on Message Passing Interface (MPI) parallel technology. By leveraging distributed memory parallel computing, the processing task is partitioned into multiple sub-tasks, substantially enhancing overall throughput. Experimental results demonstrate that: (1) the HDC-MPI algorithm improves conversion efficiency by approximately 8 times compared to the serial approach when processing 12 image scenes; (2) the algorithm’s efficiency is primarily governed by image memory usage rather than terrain complexity; and (3) the conversion accuracy of the HDC-MPI algorithm remains fully consistent with serial results, ensuring the reliability of the elevation datum transformation.