On the spatial-temporal resolution of synthetic aperture radar: Uncertainty principle?

Synthetic aperture radar (SAR) systems have been successful in applications of monitoring stationary terrain as well as detecting long-term changes. Recently, new technologies in SAR such as GEO SAR, Circular SAR and SS-BiSAR allow observing an area continuously and provide potential to detect sudden changes. The generalized ambiguity function is extended to analyze the spatial-temporal resolution for change detection. The lower bound of temporal resolution is derived and utilized to establish an uncertainty principle analogous to the uncertainty principle in signal analysis. The influence of the type and extent of changes in two typical cases is studied. The results show that the product of spatial and temporal resolution is bounded no matter how the synthetic aperture time is configured. The theoretic results are verified by simulation.