An extended Kalman smoothing approach for InSAR phase unwrapping

The phase of a complex signal is uniquely defined in the principal value interval [-π, π). The phase samples extracted from a time and/or space varying two-dimensional complex signal are ambiguous by integer multiples of 2π, hence the phase is said to be wrapped. Phase unwrapping (PU) entails the estimation of an absolute phase from the observation of its noisy principal (wrapped) values. In this paper we focus on the specific field of interferometric synthetic aperture radar (InSAR) where PU plays an important role in reconstructing the digital elevation model (DEM) of the imaged scene from InSAR data. This wor k addresses the derivation of an InSAR recursive phase unwrapping algorithm based on a two-dimensional extended K alman filter (E K F) that simultaneously performs noise filtering and phase unwrapping. To this end we restate the PU problem in state space form introducing a state model that describes the spatial variation of the phase signal and an observation model that describes the measurement process. The proposed algorithm operates as an optimal smoother in the sense that the phase estimate at each grid point (or pixel) uses all of the measurements in the SAR interferogram. The performance of the proposed algorithm is verified on synthetic InSAR data proving the validity of our method. The algorithm is also compared to other existing phase unwrapping techniques thus resulting as a valid counterpart to other well established PU methods.