A novel 3D model for joint estimation of the repositioning and tilting error in GPRI-II terrestrial radar interferometry

Abstract

Long-term deformation monitoring with ground-based interferometric radar (GBIR), such as the GPRI-II, is often conducted with a discontinuous strategy, i.e., discontinuous GBIR, which requires repeated instrument setup. While prior studies have addressed repositioning errors during this process by correcting phase ramps, it is difficult to provide parameters essential for instrument reconfiguration. This paper introduces a novel 3D model to estimate and correct re-setup errors for the GPRI-II based on the polar-coordinate geometry frame. The model employs a dual-component approach, separating errors into repositioning (locational changes) and tilting (tilting angle variations) components. A joint estimation model is designed to estimate both errors simultaneously. More important, for the first time, the instrument reconfiguration becomes enabled based on the estimated results from the proposed model. The effectiveness of the proposed model is verified through real-world experiments and compared against existing methods. The results indicate the repositioning-only model achieved the highest accuracy, showing improvements of 16.93 % and 50.48 % in repositioning error correction and 10.87 % and 10.66 % in tilting error correction compared to polynomial fitting and the traditional model, respectively. The joint estimation achieved 30.10 %, 32.58 %, and 48.09 % improvements over the repositioning-only estimation, polynomial fitting, and traditional model. The instrument reconfiguration achieved accuracies of 2.12 mm (horizontal), 1.07 mm (vertical), 0.25° (horizontal angle), 2.02° (tilt direction angle), and 0.17° (tilt angle). In addition, we determine the upper bounds of error tolerance for the system, establishing maximum correctable errors of 0.64 m (horizontal) and 0.30 m (vertical). All the study results highlight the robustness of the proposed model and its potential to significantly enhance the precision of discontinuous GPRI-based deformation monitoring.