A maximum likelihood estimator to simultaneously unwrap, geocode and fuse SAR interferograms from different viewing geometries into one digital elevation model

Abstract

This paper presents theory, algorithm and results of a maximum likelihood algorithm that is capable to fuse a number of heterogeneous SAR interferograms into a single digital elevation model (DEM) without the need for the critical phase unwrapping step. The fusion process takes place in the object space, i.e. the map geometry, and considers the periodic likelihood function of each individual interferometric phase sample. The interferograms may vary regarding their radar wavelength, their baseline, their heading angle (ascending or descending) and their incidence angle. Geometric baseline error estimates and a-priori knowledge from other estimates like existing DEMs are incorporated seamlessly into the estimation process. The presented approach significantly differs from the standard DEM generation method where each interferogram is first phase unwrapped individually, then geocoded into a common map geometry and finally averaged with DEMs generated from other interferograms. By avoiding the phase unwrapping step the proposed algorithm does not depend on gradients between samples and is therefore capable to reconstruct the arbitrary height of each single scatterer. Because the height of each DEM sample is determined individually, spatial propagation of phase unwrapping errors is avoided. The algorithm is targeted to fuse an ensemble of interferometric multi-angle or multi-baseline observations in areas of rugged terrain or highly ambiguous data where algorithms based on phase unwrapping may fail. The algorithm is explained and examples with real data from the Shuttle Radar Topography Mission are given. Conditions of future mission are simulated and optimization criteria for the viewing geometry are discussed.