Relativistic Effects in Bistatic Synthetic Aperture Radar

This paper addresses relativistic effects in bistatic and multistatic synthetic aperture radar (SAR) systems and missions. It is shown that the use of different reference frames for bistatic SAR processing and bistatic radar synchronization is prone to notable phase and time errors. These errors are a direct consequence of the relativity of simultaneity and can be explained in good approximation within the framework of Einstein´s special theory of relativity. Using the invariance of the space-time interval, an analytic expression is derived that shows that the time and phase errors increase with increasing along-track distance between the satellites. The predicted errors are in excellent agreement with measurements from TanDEM-X and provide a satisfactory explanation for previously observed digital elevation map (DEM) height offsets that exceeded ±10 m. Consideration of the unexpected relativistic effects is essential for accurate DEM generation in TanDEM-X and has in the meantime been implemented in the operational processing chain.