## 4 Error Budget of Height Estimation Accuracy
### Error Sources and Sensitivities  
In order to produce an estimate for height reconstruction error, sensitivities (i.e. the partial derivatives) must be computed and the uncertainty of the error sources must be estimated. Sensitivities can be derived by numerical differentiation of (15) for each method and each orbital position. In more details projection method and hybrid one lead to an explicit formulation for the target altitude that can be differentiated, whereas a least square solution of the bistatic SAR rigorous stereo problem is required to numerically evaluate the sensitivities. The uncertainties of the monostatic antenna position and velocity depend on the accuracy of the absolute navigation system. A value of 1 m for each component of position and 1 cm/s for each velocity component is compatible with medium accuracy Global Positioning System (GPS) measurements [38; 39]. As regard the baseline and the relative velocity, differential GPS algorithms allow dynamic relative state with decimetre-to-centimetre accuracy to be computed, therefore a conservative value of 0.5 m can be assumed for the uncertainties of each baseline component along with 1 cm/s for relative velocity. \begin{table}
\begin{tabular}{|c|c|} \hline
**Method** & **Functional Model** \\ \hline Projection of & \\ Bistatic Parameters & \\ Bistatic rigorous SAR stereo & \\ problem & \\ Hybrid & \\ \hline \end{tabular}
\end{table} 
Table 3: Functional models of proposed monostatic-bistatic methods for terrain relief reconstruction. Figure 8: Bistatic antenna azimuth angle (a) and bistatic spacecraft yaw steering angle (b) for four bistatic antenna off-nadir angles within the range of covered latitudes. Monostatic slant range uncertainties are linked to the dimension, \(\Delta r\)', of monostatic slant range resolution element [15]:  
\[\sigma_{r^{\prime}}^{2}=\frac{1}{12}\big{(}\Delta r^{\prime}\big{)}^{2} \tag{18}\]  
COSMO-SkyMed narrow angle stripmap products are characterized by a final ground range resolution of 3-15 m [40], so values of 3 m and 0.75 m can be assumed, respectively, for ground range and azimuth resolution of single-look-complex data. Bistatic slant range uncertainty depends on bistatic slant range resolution, as the monostatic one, and it is also related to the error resulting from the application of co-registration procedures required to form stereopairs. A value of 1/10 of an image pixel is compatible with areas where the correlation is high [17]. Hence, bistatic slant range uncertainty can be calculated as follows:  
\[\sigma_{r^{\prime}}^{2}=\frac{1}{12}\big{(}\Delta r^{\prime}\big{)}^{2}+\left( \frac{\Delta r^{\prime\prime}}{10}\right)^{2}+\left(\frac{\Delta r^{\prime \prime}}{10}\right)^{2} \tag{19}\]  
where \(\Delta r\)\" is the dimension of bistatic slant range resolution element. Due to orbital constrains the simple geometry reported in Section 2 must be generalized to tracks that are not perfectly parallel, also accounting for the presence of a time-varying along-track separation between the monostatic and bistatic antennae [Figure 6(a)]. In such conditions (1) and (2) are no longer valid, and more general approaches must be used to calculate bistatic resolutions.