Accuracy of differential shift estimation by correlation and split-bandwidth interferometry for wideband and delta-k SAR systems

Estimation of differential shift of image elements between two synthetic aperture radar (SAR) images is the basis for many applications, like digital elevation model generation or ground motion mapping. The shift measurement can be done nonambiguously on the macro scale at an accuracy depending on the range resolution of the system or on the micro scale by employing interferometric methods. The latter suffers from phase cycle ambiguities and requires phase unwrapping. Modern wideband high-resolution SAR systems boast resolutions as small as a few tens of a wavelength. If sufficiently many samples are used for macro-scale shift estimation, the accuracy can be increased to a small fraction of a resolution cell and even in the order of a wavelength. Then, accurate absolute ranging becomes precise enough to support phase unwrapping or even make it obsolete. This letter establishes a few fundamental equations on the accuracy bounds of shift estimation accuracy for several algorithms: coherent speckle correlation, incoherent speckle correlation, split-band interferometry, a multifrequency approach, and correlation of point scatterers in clutter. It is shown that the performance of split-band interferometry is close to the Crame´r-Rao bound for a broad variety of bandwidth ratios. Based on these findings, Delta-k systems are proposed to best take advantage of the available radar bandwidth.