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.

地面变形的连续监测可以通过多种方法提供，例如水准测量、摄影测量、激光扫描、卫星导航系统、合成孔径雷达（SAR）等。然而，仅使用上述方法之一来确保高精度测量的足够时空分辨率可能具有挑战性。这项研究的主要目标是开发一种集成方法，对差分干涉SAR（DInSAR）和全球导航卫星系统（GNSS）监测技术的能力和局限性敏感。使用前向卡尔曼滤波器算法针对局部非线性强变形优化融合过程。由于意外观测不连续性的影响，还引入了向后卡尔曼滤波器来细化对先前系统状态的估计。目前的工作在上西里西亚煤矿区（波兰南部）进行了实验，该地区在两年内发生了高达 1 m 的强烈垂直变形，以及相对较小且水平移动的沉降碗（200 m）。结合外部数据，卡尔曼前向的整体均方根 (RMS) 误差达到 13、17 和 35 毫米，卡尔曼后向的整体均方根 (RMS) 误差分别达到北、东和上方向的 13、17 和 34 毫米。来源 - GNSS 活动测量。卡尔曼滤波器积分优于 3-D GNSS 估计和 2-D InSAR 分解的标准方法。