Differential GNSS-R Surface Deformation Monitoring Method and Simulation Experiment Verification

Objectives: GNSS-R technology utilizes GNSS reflected signals to determine the physical properties of the reflecting surfaces. It boasts advantages such as operational capability around the clock and in all weather conditions, a wide range of available signal sources, low cost, and being unaffected by weather conditions. However, research on the application of GNSS-R technology in the field of deformation monitoring is still in its exploratory stage, and there are certain limitations: long-term monitoring data are scarce, and most studies have used metal plates as ideal reflecting surfaces, which differs from real-world scenarios. Previous studies have focused on modulating GNSS signals from a single satellite, rather than using carrier-phase observation data as the source of information. The relationship between the measured deformation and the carrier phase of the reflected signal follows a complex 3D geometric pattern, and currently, only deformations in the normal direction of the reflecting surface can be detected. Methods: This paper proposes a differential GNSS-R method for monitoring ground deformation based on carrier-phase observation data. This approach simplifies the geometric relationship between deformation and carrier phase. It is demonstrated that GNSS signals can undergo specular reflection on approximately bare ground surfaces, thus satisfying the requirements of this simplified geometric model. Experimental tests conducted in real outdoor environments have confirmed the feasibility of this method for deformation monitoring by integrating carrier-phase data from multiple satellite systems and types. Results: The study indicates that the standard deviation (STD) of the GNSS-R height measurement inversion results is 1.17 cm, and the root mean square (RMS) is 1.23 cm, indicating a high degree of stability. This confirms that the reflection type of GNSS signals after being reflected by the ground is specular reflection, and it also verifies the feasibility of using simplified geometric configurations. The results of surface deformation monitoring show that although the accuracy of the dual-GEO satellite combination is slightly inferior to that of other combinations, it is capable of providing continuous and seamless monitoring throughout the entire observation period. The variations in surface shape across different time periods for all combinations are mainly within the range of ±2 cm, with an STD of less than 1 cm for all cases. The average STD for all combination types is 4 mm, achieving sub-centimeter-level monitoring accuracy. Conclusions: This method requires a small number of satellites—only two are necessary at minimum—and it provides new approaches and methods for surface deformation monitoring.