Kalman filter-based integration of GNSS and InSAR observations for local nonlinear strong deformations

The continuous monitoring of ground deformations can be provided by various methods, such as leveling, photogrammetry, laser scanning, satellite navigation systems, Synthetic Aperture Radar (SAR), and many others. However, ensuring sufficient spatiotemporal resolution of high-accuracy measurements can be challenging using only one of the mentioned methods. The main goal of this research is to develop an integration methodology, sensitive to the capabilities and limitations of Differential Interferometry SAR (DInSAR) and Global Navigation Satellite Systems (GNSS) monitoring techniques. The fusion procedure is optimized for local nonlinear strong deformations using the forward Kalman filter algorithm. Due to the impact of unexpected observations discontinuity, a backward Kalman filter was also introduced to refine estimates of the previous system's states. The current work conducted experiments in the Upper Silesian coal mining region (southern Poland), with strong vertical deformations of up to 1 m over 2 years and relatively small and horizontally moving subsidence bowls (200 m). The overall root-mean-square (RMS) errors reached 13, 17, and 35 mm for Kalman forward and 13, 17, and 34 mm for Kalman backward in North, East, and Up directions, respectively, in combination with an external data source - GNSS campaign measurements. The Kalman filter integration outperformed standard approaches of 3-D GNSS estimation and 2-D InSAR decomposition.