# Error Sources of Interferometric Synthetic Aperture Radar Satellites
## 2 Intrinsic Height Errors and Location-Induced Errors
### Intrinsic Height Errors  
Intrinsic height inaccuracies are caused by issues in determining topographic height [30]. In other words, intrinsic height errors cause inaccuracies that result in erroneous measurements and are separate from errors related to incorrect positioning. These height errors are the main focus of this paper.  
For a repeat-pass interferometry SAR system, two single-look complex (SLC) SAR images are acquired from similar positions in space over the same terrain. The interferogram is formed by cross-multiplying two SAR images and deriving the phase difference between the two SLC SAR images. A SAR interferogram is a superposition of the different phase components, including the topographic phase (\(\Delta\varphi_{\text{topo}}\)), flat-Earth phase (\(\Delta\varphi_{\text{flat}}\)), orbital phase (\(\Delta\varphi_{\text{orb}}\)), tropospheric delay (\(\Delta\varphi_{\text{tropo}}\)), ionospheric advance (\(\Delta\varphi_{\text{iono}}\)), liquid water delay (\(\Delta\varphi_{\text{lijq}}\)), scatterer's phase shift (\(\Delta\varphi_{\text{scatt}}\)), deformation phase (\(\Delta\varphi_{\text{defo}}\)), and the noise phase (\(\Delta\varphi_{\text{noise}}\)) (Equation (1)) [27; 41; 42; 43].  
\[\Delta\varphi=\Delta\varphi_{topo}+\Delta\varphi_{flat}+\Delta\varphi_{orb}+ \Delta\varphi_{topo}+\Delta\varphi_{iono}+\Delta\varphi_{liq}+\Delta\varphi_{ scatt}+\Delta\varphi_{defo}+\Delta\varphi_{noise} \tag{1}\]  
If the goal of the InSAR measurement is topographic mapping, then the topographic phase is the phase of interest, and all others will produce measurement error. Similarly, if the goal is deformation mapping, only the deformation phase is of importance, then all other components will contribute to inaccuracies. As a consequence, one of the most crucial components of InSAR processing is to remove as much undesired phase noise as possible in order to acquire accurate measurements. If each undesirable phase term is not appropriately eliminated from the overall phase variation, the unwanted phase will be mistaken as topographic/deformation phase, thereby resulting in inaccurate measurements.  
Interferometric SAR only works under coherent conditions [44; 45] in which the received backscatter is correlated between the two SAR images [28]. The signal in each interferogram pixel is composed of two parts: the coherent portion that generates fringe patterns; and the incoherent portion that appears as phase noise [35; 46]. The intrinsic height errors can therefore be further categorized into two types: (1) systematic errors and (2) random errors. Systematic errors exist in the coherent portion of Equation (1) (i.e., \(\Delta\varphi_{\text{topo}}\), \(\Delta\varphi_{\text{flat}}\), \(\Delta\varphi_{\text{orb}}\), \(\Delta\varphi_{\text{topo}}\), \(\Delta\varphi_{\text{iono}}\), \(\Delta\varphi_{\text{ligq}}\), \(\Delta\varphi_{\text{scatt}}\), and \(\Delta\varphi_{\text{defo}}\)). Random errors are the sources that contribute to phase noise (represented as \(\Delta\varphi_{\text{noise}}\) in Equation (1)). When the phase variation caused by a scatterer's movement and/or surface deformation are incoherent, \(\Delta\varphi_{\text{scatt}}\) and \(\Delta\varphi_{\text{defo}}\) can also contribute to random errors. The systematic errors influence the accuracy while the random errors determine the precision of the interferometric system [30].