A new sparse representation method for tropospheric grid models

Abstract With the rapid advancement of high-precision Global Navigation Satellite System (GNSS) positioning, the demand for high-precision tropospheric delay models has grown substantially, intensifying the trade-off between modeling precision and resource consumption. In network-free environments, such as oceans and deserts, satellite-based broadcasting of atmospheric correction products is essential for achieving global coverage, which further exacerbates challenges associated with large data volumes and high storage and transmission costs. Existing learned-dictionary methods for compressing tropospheric delay parameters often incur substantial training costs and exhibit limited generalization capability. To address these limitations, this study integrates compressed sensing theory to propose a block-wise sparse representation method for tropospheric grid models using a simple analytical dictionary, combined with a binary mask encoding strategy. The proposed approach enables efficient compression of all involved parameters without requiring prior training. Experimental results demonstrate significant resource savings while maintaining model accuracy. Compared with the original models, memory usage is reduced by 63.49% for the static empirical Institute of Geodesy and Geophysics Troposphere Semi-annual (IGGtropS) model and by 81.19% for the dynamically updated Vienna Mapping Functions 1 (VMF1) model—outperforming existing mini-batch K-singular value decomposition learned-dictionary algorithms under the tested experimental conditions. The root mean square errors of the resulting reconstructed zenith tropospheric delay are only 1.7 mm and 2.1 mm, respectively. Satellite-based broadcasting simulations further indicate that replacing the original models with the proposed sparse models reduces communication resources requirements by 50%. At a broadcast bandwidth of approximately 15 kbit/s, global VMF1 grid products can be transmitted approximately 30 s, while introducing only a sub-centimeter quantization-error at the user level. The proposed method features low algorithmic complexity, high compression efficiency, and robust reconstruction accuracy, providing a highly generalizable and lightweight technical solution for storing and broadcasting GNSS atmospheric grid products.