3-D Synthetic Aperture Radar Interferometry Phase Unwrapping Using Extended Kalman Filters
Osmanoglu, Batuhan1; Wdowinski, Shimon2; Dixon, Timothy H.3
1University of Alaska-Fairbanks, UNITED STATES; 2University of Miami - RSMAS, UNITED STATES; 3University of South Florida, UNITED STATES

Time series analysis of synthetic aperture radar interferometry (InSAR) data is a three-dimensional operation, where the spatial coverage of the SAR imagery provide two dimensions and the repeat imagery defines a third dimension. Three dimensional unwrapping is important as it can provide further constraints to the solution resulting in a more robust and accurate analysis. Even though there are efficient algorithms for finding discrete irrotational fields among neighboring pixels in two dimensions, an efficient algorithm for the three dimensional case is proved to be very difficult. In this paper we propose a different approach to the three dimensional unwrapping of InSAR data.

Here we describe a 3-D unwrapping approach using an Extended Kalman Filter (EKF). The current implementation of our EKF algorithm utilizes a piecewise linear approximation in space and a simple model in the third dimension (e.g. time). The algorithm starts from unwrapped, unfiltered interferograms and filters and unwraps the results simultaneously solving for a common deformation rate. The algorithm starting from the highest quality point in the coherent area and proceeds to unwrap highest quality neighbors. The highest quality neighbors are determined according to the Fisher's Distance, which is a phase quality measure similar to the more commonly used phase derivative variance, but also includes the interferometric coherence. A smoothing operation is utilized for previous solutions that originally relied on a small number of constraints in the form of reanalysis by EKF as soon as additional constraints become available. Furthermore, to reduce the effects of possible error propagation, an integrable surface is reconstructed using the phase derivatives estimated by the EKF. Our analysis indicate that the EKF provides more accurate results compared to 2-D unwrapping of individual interferograms and using SBAS or NSBAS algorithms to reconstruct the time series, because the unwrapping errors propagate to the time series. In this paper we present our findings using repeat-pass satellite data for the case of Mexico City subsidence.