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In a typical interferometric synthetic aperture radar (IFSAR) system employed for terrain elevation mapping, terrain height is estimated from phase difference data obtained from two phase centers separated spatially in the cross-track direction. In this paper we show how the judicious design of a three phase center IFSAR renders phase unwrapping, i.e., the process of estimating true continuous phases from principal values of phase, a much simpler process that inherent in traditional algorithms. With three phase centers, one IFSAR baseline fan be chosen to be relatively small so that all of the scene's terrain relief causes less than one cycle of phase difference. This allows computation of a coarse height map without use of any form of phase unwrapping. The cycle number ambiguities in the phase data derived from the other baseline, chosen to be relatively large, can then be resolved by reference to the heights computed from the small baseline data. This basic concept of combining phase data from one small and one large baseline to accomplish phase unwrapping has been previously employed in other interferometric problems. The new algorithm is shown to possess a certain form of immunity to corrupted interferometric phase data that is not inherent in traditional 2D path-following phase unwrappers. This is because path-following algorithms must estimate, either implicitly or explicitly, those portions of the IFSAR fringe data where discontinuities in phase occur. Such discontinuities typically arise form noisy phase measurements derived from low radar return areas of the SAR imagery. When wrong estimates are made as to where these phase discontinuities occur, errors in the unwrapped phase values can appear due to the resulting erroneous unwrapping paths. This implies that entire regions of the scene can be reconstructed with incorrect terrain heights. By contrast, since the new method estimates the continuous phase at each point in the image by a straightforward combination of only the measured phases from the small and large baseline, phase estimation errors are confined to that point. We derive quantitative expressions for the new algorithm that relate the probability of selecting the wrong phase cycle to parameters of the interferometer. We then demonstrate that use of median filtering can very effectively mitigate those cycle errors that do occur. By use of computer simulations, we show how the new algorithm is used to robustly construct terrain elevation maps.
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