Realistic lower bound on elevation estimation for tomographic SAR

The noise in a tomographic synthetic aperture radar (Tomo-SAR) model is normally assumed to be independent and identically distributed (i.i.d.) Gaussian. In this paper, the correlated Tomo-SAR model is introduced by studying the effect of random residual phase and correlated additive Gaussian noise, and a realistic and general hybrid Cramér-Rao bound (HCRB) on elevation estimation is derived for such a model. Then, a simplified calculation of the HCRB is proposed when the bound of elevation is the main focus. Computer simulations are performed to analyze the proposed HCRB for elevation estimation. The results obtained from estimators based on compressive sensing and distributed compressive sensing show that the proposed HCRB can provide a more realistic bound than the CRB derived with the white additive noise and perfect phase compensation assumption. This is also validated through processing results on real data acquired by TerraSAR-X/Tandem-X sensors.