Closed-Form Evaluation of the Second-Order Statistical Distribution of the Interferometric Phases in Dual-Baseline SAR Systems

Multichannel inteferometric synthetic aperture radar (InSAR) systems allow to improve the accuracy of the estimation of the height profiles of the observed scenes. Multichannel images can be acquired by using different sensors operating at different frequencies (multifrequency InSAR) or acquiring multiple images with slightly different view angles (multibaseline InSAR). The enhanced accuracy height estimation is obtained exploiting the multichannel interferometric phases and an a priori inaccurate ground profile and requires the knowledge of the joint probability distribution of the multichannel interferometric phases, whose evaluation in a closed form is very complicated and is not found in literature. In this paper, we evaluate the analytical form of the second-order probability density function (pdf) of dual-baseline InSAR phase in- terferograms, obtained from three mutually correlated interfero- metric images. The evaluation exploits the Gaussian model for the complex SAR images, takes into account the mutual correlation of all the images, and does not use any approximation. The closed form of the second-order joint pdf can be usefully adopted in statistical digital elevation model (DEM) estimation methods using dual-baseline SAR systems, which commonly use an approximate expression of the joint pdf of measured interferometric phases, given by the product of the marginal pdfs of each phase interfero- gram, obtained in the assumption of independent interferograms. The effect of this approximation is evaluated by computing the Cramer–Rao lower bounds and the mean square estimation errors obtained using the exact and the approximate model. Presented re- sults represent the basis for the generalization to the case of more than two interferograms.