A dual-base station constraint method to improve deformation monitoring precision consistency in strip regions

The precision of deformation monitoring with Global Navigation Satellite System (GNSS) relative positioning is significantly influenced by the distance between the monitoring and base stations. In long strip regions, the considerable differences in station spacing lead to inconsistent monitoring precision among multiple stations. This presents a challenge to accurately model and predict the deformation pattern. To tackle this issue, this paper introduces a novel dual-base station constraint method. This method integrates the baseline length constraint between two base stations into the conventional relative positioning model. The formulae of the proposed method are first derived in detail. Then the data collected at eight monitoring stations in two strip regions of 6 km and 8 km over a 28-day period are used to validate the effectiveness of the proposed method. The quantitative analysis of monitoring precision consistency indicators and hypothesis testing on the correlation between monitoring precision and station spacing are conducted. The results show that: (1) median values of the East, North, and Up consistency indicators are reduced from 2.14, 1.41, and 1.83 to 0.91, 0.67, and 0.55 and from 1.85, 1.85, and 2.32 to 0.69, 1.00, and 0.87, respectively, indicating monitoring precision consistency improvement for two case studies; (2) the absolute values of the correlation coefficients between monitoring precision and station spacing decrease from 0.99, 0.94, and 0.98 to 0.09, 0.36, and 0.32. Using the t-test with a significant level of 0.01, it is demonstrated that there is no significant correlation between monitoring precision and station spacing when employing the proposed method.