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 km(2) and in Southern California covering approximately 100,000 km(2). 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.
