The spatio-temporal random effects (STRE) model is a classic dynamic filtering model, which can be used to fuse GNSS and InSAR deformation data. The STRE model uses a certain time span of high spatial resolution Interferometric Synthetic Aperture Radar (InSAR) time series data to establish a spatial model and then obtain a deformation result with high spatio-temporal resolution through the state transition equation recursively in time domain. Combined with the Kalman filter, the STRE model is continuously updated and modified in time domain to obtain higher accuracy result. However, it relies heavily on the prior information and personal experience to establish an accurate spatial model. To the authors' knowledge, there are no publications which use the STRE model with multiple sets of different deformation monitoring data to verify its applicability and reliability. Here, we propose an improved STRE model to automatically establish accurate spatial model to improve the STRE model, then apply it to the fusion of GNSS and InSAR deformation data in the San Francisco Bay Area covering approximately 6000 km² and in Southern California covering approximately 100,000 km². Our experimental results show that the improved STRE model can achieve good fusion effects in both study areas. For internal inspection, the average error RMS values in the two regions are 0.13 mm and 0.06 mm for InSAR and 2.4 and 2.8 mm for GNSS, respectively; for Jackknife cross-validation, the average error RMS values are 6.0 and 1.3 mm for InSAR and 4.3 and 4.8 mm for GNSS in the two regions, respectively. We find that the deformation rate calculated from the fusion results is highly consistent with the existing studies, the significant difference in the deformation rate on both sides of the major faults in the two regions can be clearly seen, and the area with abnormal deformation rate corresponds well to the actual situation. These results indicate that the improved STRE model can reduce the reliance on prior information and personal experience, realize the effective fusion of GNSS and InSAR deformation data in different regions, and also has the advantages of high accuracy and strong applicability.

时空随机效应（STRE）模型是经典的动态滤波模型，可用于融合 GNSS 和 InSAR 变形数据。STRE模型利用一定时间跨度的高空间分辨率干涉合成孔径雷达（InSAR）时间序列数据建立空间模型，然后在时域中通过状态转移方程递归地得到具有高时空分辨率的变形结果。结合卡尔曼滤波器，STRE模型在时域不断更新和修改，以获得更高的精度结果。但是，它在很大程度上依赖于先验信息和个人经验来建立准确的空间模型。据作者所知，没有出版物使用具有多组不同变形监测数据的 STRE 模型来验证其适用性和可靠性。在这里，我们提出了一种改进的 STRE 模型来自动建立精确的空间模型来改进 STRE 模型，然后将其应用于旧金山湾区约 6000 km 的 GNSS 和 InSAR 变形数据的融合。²在南加州覆盖约 100,000 公里². 我们的实验结果表明，改进后的 STRE 模型在两个研究领域都能取得良好的融合效果。对于内部检查，两个区域的平均误差 RMS 值对于 InSAR 分别为 0.13 mm 和 0.06 mm，对于 GNSS 分别为 2.4 和 2.8 mm；对于 Jackknife 交叉验证，两个区域的 InSAR 平均误差 RMS 值分别为 6.0 和 1.3 mm，GNSS 分别为 4.3 和 4.8 mm。我们发现，融合结果计算的变形率与已有研究高度吻合，两区主要断层两侧变形率差异明显，变形率异常区域对应好到实际情况。