The Derivation of Phase Integer Ambiguity from Single Insar Pairs : Implications for Differential Interferometry

SAR Interferometry (InSAR) is a technique that is fast becoming an attractive prospect for routine derivation of land deformation parameters in events of a long-term and cataclysmic nature. The technique involves the analysis of the interferometric phase gradient, in both temporal and spatial dimensions, as it is generally difficult to derive the absolute value of the phase due to an integer ambiguity. Thus, InSAR methods are generally restricted to the measurement of deformation change from an arbitrary baseline rather than in the derivation of absolute position. This paper describes a rigorous InSAR geometry based on a range-Doppler approach similar to that used in radargrammetry. An analysis of this geometry in the spaceborne case highlights the deficiency of the far-field approximation but also shows that a simple derivation of the phase integer ambiguity is possible from a single InSAR phase measurement. The accurate geolocation of wrapped phase values is then possible, limited only by the values of the pseudorange contained in the image headers. Only very coarse ground control, if necessary at all, is needed to locate a full interferogram. The rigorous geometry presented is applicable to all airborne and spaceborne configurations and the generalised position vector may be transformed to height and position related to any reference datum and map projection through standard geodetic transformations. The implications for Differential InSAR are highlighted. Principally, a reduced reliance on accurate third party Digital Terrain Models is possible, allowing greater automation and, for cataclysmic events, a much faster reaction time.