Deformation Process Fusion Acquired by GNSS and SBAS-InSAR Based on a Spatiotemporal Kalman Filter

This paper proposes a new method [the improved spatiotemporal random effect model (ISTRE)] based on the spatiotemporal Kalman filter model for fusing Global Navigation Satellite System (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) deformation to obtain high spatiotemporal resolution deformation. This method realizes the fusion of GNSS vertical and InSAR LOS deformation based on the spatiotemporal random effect model (STRE) combining robust estimation theory and correlation analysis. During modeling, the model parameters of an improved STRE model (ISTRE) including the spatial basis, state transfer matrix, observation noise, and state noise were determined using the small baseline subset (SBAS)-InSAR deformation. Then the vertical deformation value of small baseline subset interferometric synthetic aperture radar (SBAS-InSAR) was calculated by the forward ISTRE with the reweighted observation noise due to the deformation replacement of SBAS-InSAR by the nearest GNSS site. And the final deformation fusion in the vertical direction was carried out using the corrected SBAS-InSAR and GNSS. The study applies SBAS-InSAR and GNSS deformation data from a tailings pond in Fushun City to validate the vertical correction and fusion quantity of ISTRE, explores the impact of the root mean square error (RMSE) accuracy improvement rate and cross-correlation ratio between GNSS and SBAS-INSAR on the accuracy of vertical correction, and analyzes the superiority of ISTRE by comparing with the improved kriging Kalman filter (IKKF) and spatial-temporal Kalman filter (ISTKF). The results indicate a strong correlation between the vertical correction accuracy of deformation velocity and the cross-correlation coefficient. The deformation velocity accuracy of GNSS point P02 has the best cross-correlation coefficient quality with an average of 0.9053 and can be improved by approximately 70% specifically. The accuracy of cumulative deformation shows a strong correlation with both the cross-correlation ratio and GNSS cross-correlation; the deformation accuracy of GNSS point P05 with an average GNSS cross-correlation of 0.8950 can be enhanced by up to 240%. The RMSEs of the ISTRE fusion results with four of the five sets of GNSS data are smaller than those of IKKF and ISTKF, and the RMSEs of the SBAS-InSAR vertical correction results are similarly generally smaller. ISTRE shows superiority over IKKF and ISTKF in terms of stability, vertical correction, and fusion accuracy by comparative analysis.