## 4 Error Budget of Height Estimation Accuracy
### Height Estimation Accuracy  
The analysis of the error sources allows evaluation of single contributions to height accuracy for each method. As expected, these contributions are not constant along the orbit since all the sensitivities depend on the actual acquisition geometry, but also the uncertainties related to image resolutions are affected by the instantaneous orbital configuration. Figures 9 and 10 report the principal parameters contributing to relief reconstruction errors, respectively, for projection method and bistatic rigorous SAR stereo problem: \(\sigma_{h|By}\) and\(\sigma_{h|By}\) are the height uncertainties due to horizontal and vertical baseline components, \(B_{y}\) and \(B_{z}\); \(\sigma_{h|r}\) and\(\sigma_{h|r}\)- depend on monostatic and bistatic slant range uncertainties, whereas \(\sigma_{h|r\,\cdot\,r^{\prime\,-}}\) is the height uncertainty relevant to correlated errors in monostatic and bistatic slant ranges; finally, \(\sigma_{h|R\,\cdot\,}\)is the height uncertainty due to monostatic platform positioning errors. Projection method and bistatic rigorous SAR stereo problem share the main error sources and provide very similar results. The largest height uncertainties are due to the vertical baseline components, bistatic slant range accuracy and correlation terms between monostatic and bistatic slant ranges. The contributions of both horizontal baseline components, and monostatic slant range respect the principle of the stereo effect perfectly. Indeed, the larger is the bistatic angle, the lower is the height estimation error. This effect is more manifest when the off-nadir angle of the bistatic sensor is large, while it fades away decreasing \(\theta\)_\"_. Height uncertainties due to bistatic slant range and to the correlations terms deserve more attention: actually the worsening of bistatic slant range resolution with the bistatic angle exceeds the benefits of a better stereo geometry, thus making acceptable the increased height uncertainty for small off-nadir angles of the bistatic sensor [17]. Finally, it is worth noting that an error in monostatic platform position merely produces an identical error on target altitude, a result shared with SAR interferometry [7]. Figure 11 shows the height error due to parallax uncertainty for the hybrid method, representing the single factor causing a meaningful relief reconstruction error. Since the hybrid method is based on the calculation of the parallax from monostatic and bistatic measurements of ground range and azimuth positions [17], it is more sensitive to variation of the bistatic slant range resolution with the bistatic angle. It is worth noting that previous simulation results show practically constant performances in measurement accuracy within the range of latitudes where stereo radargrammetric coverage can be achieved with satisfactory baselines and bistatic angles, thus demonstrating that the unavoidable non perfectly parallel trajectories and limited along-track separations are not destructive for the quality of height determination. According to international standards assessed to specify DEM accuracy [41], Figure 12 shows the overall relative height uncertainty for each method expressed as point-to-point 90% linear error (LE\({}_{90}\)). The term \"point-to-point\" indicates the difference of height estimation error between two pixel of the imaged area, while LE\({}_{90}\) is the error range which include 90% of the pixels. Figure 10: Contributions to height uncertainty as a function of target latitude in the bistatic rigorous SAR stereo problem for four bistatic antenna off-nadir angles (1/10 of an image pixel assumed as co-registration uncertainty). Figure 9: Contributions to height uncertainty as a function of target latitude in the method of projection of bistatic parameters for four bistatic antenna off-nadir angles (1/10 of an image pixel assumed as co-registration uncertainty). The height uncertainty exhibits the same order of magnitude for all methods.