24 August 2000 Optimal antenna spacings in interferometric SAR
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In practice, a synthetic aperture radar (SAR) reconstructs the complex reflectivity function of a scene, modulated by phase terms that capture 3-D imaging geometry. INSAR (interferometric SAR) attempts to obtain the geometric information by interfering two images (from two antennas) to cancel the same scene reflectivity and recover the scene topography transduced by the image-phase data. This approach, however, leads to a phase-unwrapping problem, which causes ambiguities in estimates of elevation. The phase-unwrapping problem can be solved in a pointwise fashion by using more than two antennas. This approach can effectively prevent error propagation which occurs in traditional phase-unwrapping algorithms. In this work, we study the optimal antenna spacings for pointwise terrain height estimation. In particular, we start from the maximum likelihood estimates of the phase using neighborhood pixels collected by any pair of antennas. The phase estimation noise is approximated as Gaussian with variance prescribed by the Cramer-Rao lower bound on the phase estimate. The ambiguous terrain height derived from any pair of antennas is modeled by a periodic waveform with each period having an approximately Gaussian shape. For multiple pairs of antennas, the corresponding functions describing the ambiguous elevation have different periods, which acts to help resolve the ambiguity. We derive and analyze the ML estimate of elevation at each scene point using multiple pairs of antennas. For the three-antenna case, by analyzing the tradeoff between cycle errors and measurement errors, a closed-form formula approximating the mean squared error (MSE) of the estimated terrain height is derived as a function of antenna spacing. By minimizing the MSE, we determine the optimal antenna spacing. The algorithm is tested with simulated data.
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Shu Xiao, Shu Xiao, David C. Munson, David C. Munson, } "Optimal antenna spacings in interferometric SAR", Proc. SPIE 4053, Algorithms for Synthetic Aperture Radar Imagery VII, (24 August 2000); doi: 10.1117/12.396321; https://doi.org/10.1117/12.396321

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