A least squares collocation approach to integrate InSAR and GNSS observations: CoInSAR

Deformation measurements from space-borne Interferometric Synthetic Aperture Radar (InSAR) resolve geodynamic signals at multiple spatial scales and are commonly integrated with ground-based measurements from the Global Navigation Satellite System (GNSS). The integration process requires accounting for reference frame discrepancies and measurement uncertainties. In this study, we propose a new approach, CoInSAR, which uses least squares collocation to transform InSAR displacement time series into the GNSS reference frame while correcting residual tropospheric errors from turbulent atmospheric effects that typically persist in InSAR data. In our approach, we construct the observation vector at each epoch from the displacement differences between GNSS and InSAR, which comprises the reference frame difference, measurement noise, and residual tropospheric errors. We represent the measurement noise via data variances and derive the stochastic model for residual tropospheric errors using an empirical covariance function estimated from InSAR displacements. By accounting for these stochastic components, we use least squares collocation to estimate the transformation parameter between the two reference frames, interpolate corrections for the residual tropospheric errors, and generate the integrated displacements. To assess the performance of our method, we applied CoInSAR to measure land subsidence in the San Joaquin Valley, California, and seismic deformation in Chile. Our results show high agreement between GNSS and CoInSAR time series and variance reduction in regions outside the GNSS network. Moreover, CoInSAR-based deformation estimates are not only consistent with physics-based models but also capture small-scale deformation features, highlighting CoInSAR’s potential to improve the modeling of geodynamic signals in regions with sparse GNSS coverage.