Kalman filter for sequential temporal coherence estimation for multi-temporal InSAR
Authors: Haghshenas Haghighi Mahmud , Piter Andreas 
Published: March 2024

Since the launch of the Sentinel-1 mission and with the upcoming NISAR mission, SAR data is continuously and freely available, which can be used for geodetic monitoring and assessing hazards related to infrastructure. Continous deformation monitoring requires a regular update of the displacement time series based on newly acquired images to assess the current structural health status of the observed infrastructure. Existing InSAR time series methods, in particular PSI methods, however, are designed for a fixed SAR stack size of a particular study period and unwrap the phase time series for pixels which exhibit a coherent signal over the whole study period. Therefore, before phase unwrapping, it is essential to assess if the pixels preserve phase coherence in the interferograms related to the new image.Previous studies proposed an amplitude change detection which divides the study period into two subsets and tests whether the amplitude distributions of the subsets stem from different Rayleigh distributions and, hence, from different scatterers. All possible splits of the stack into two subsets are tested and the split with the highest test score is selected as the change point. This approach has the drawback that the changes can hardly be identified if one of the subsets contains only very few images, which would be the case for a sequential update for continuous monitoring purposes. Moreover, other studies demonstrated that the time of change in the amplitude might not coincide with the time of change in the coherence of the phase. Therefore, they suggested an unwrapping-based change point refinement to the amplitude-based method to identify the change point in the temporal coherence of the phase.Here, we propose a new method for assessing the decorrelation in a sequential updating framework using a Kalman filter.Our approach estimates the temporal coherence for the newly acquired image. We extend the Temporal Phase Coherence (TPC) approach from Zhao and Mallorqui (2019) which approximates the phase noise of a scatterer by subtracting the spatial low-pass filtered phase of the immediate neighbourhood of the scatterer in each interferogram. To assess the coherence of the new image, we connect the new image to all previous images within a fixed time of e.g. one year. We use the Kalman filter to predict and update the TPC for each new image and apply a threshold on the TPC to distinguish coherent from incoherent pixels. This approach comes with the advantage that neither amplitude analysis nor unwrapping of the phases is required to assess the coherence of a scatterer in the new image.We perform a case study in Nordrhein-Westfalen, Germany, along the Sauerland-Autobahn to demonstrate the effectiveness of the proposed Kalman filter for sequential coherence estimation. Along the Sauerland-Autobahn, several highway bridges need to be rebuilt due to structural health problems arising from their ageing process. We coregister a stack of Sentinel-1 images using the InSAR Scientific Computing Environment (ISCE).The dataset covers eight years of data from ascending and descending orbits. We compare our proposed phase-based coherence estimation with the results from amplitude-based change detection.