# Cross Sensor Simulation of Tomographic SAR Stacks
## 5 Application to BIOMASS: Impact of Orbital Control  
The concepts illustrated in the previous sections have been used to simulate the spaceborne tomography that is expected from the ESA BIOMASS mission [13]. The effect of non regularly spaced orbital paths was explored; in particular, their impact on the estimated tomographic power and its correlation to the Above Ground Biomass (AGB). The real airborne stack providing the input have been gathered by ONERA in 2009 over the Paracou area in French Guiana in the context of the TropiSAR campaign [26]; the phases of this image stack were further calibrated according to the procedure described in Reference [27]. The parameters of interest of both systems are listed in Table 2; the scene has been cropped to include only the ROIs with the ground truth measurements of the AGB. The azimuth resolution of the spaceborne system was set to 12.5 m by means of a simple low-pass filtering. A description of the site providing the ground truth measurements can be found in Reference [28] and references therein whereas the estimation of the above ground biomass is detailed in Reference [29]. The baseline distribution of the BIOMASS system is designed to span the 90% of the critical baseline with 7 subsequent passes regularly spaced, resulting in a vertical resolution of about 20 m. Any orbital drift changes the spatial sampling of the total baseline aperture which, in turn, modifies the vertical Impulse Response Function (IRF) of the tomographic system. The vertical IRF determines the effectiveness of the system in focusing on a specific elevation and rejecting the surrounding echoes. Then, it is expected that any deviations from the nominal orbits perturb the correlation between tomographic power and AGB [15]. In order to evaluate this perturbation the spaceborne system has been simulated several times, each time with slightly different orbital paths. Then, the spaceborne tomography has been generated and the resulting power was put in relation with AGB. The displacement of each sensor from its nominal position was simulated by means of a Guassian random variable. The displacements involve only the longitude of the orbits, being kept constant the \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Airborne** & **Spaceborne (Simulated)** \\ \hline Number of images & 6 & 7 \\ Wavelength & 75 cm & 69 cm \\ Bandwidth & 125 MHz & 6 MHz \\ \(\theta_{near}\) & 28\({}^{\circ}\) & 27.93\({}^{\circ}\) \\ \(\theta_{far}\) & 46\({}^{\circ}\) & 28.08\({}^{\circ}\) \\ \(k_{max,near}\) & 0.36 rad/m & 0.264 rad/m \\ \(k_{max,far}\) & 0.25 rad/m & 0.262 rad/m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the P-band airborne radar used in the ONERA TropiSAR survey over Paracou and simulated spaceborne system. elevation above the Earth's surface. Also, the total baseline aperture was kept constant and equal to the nominal one, only the five innermost tracks were perturbed. Their fluctuations were modeled by a zero average Gaussian random variable whose standard deviation was increased from 0% to 10% of the critical baseline; for each value of this standard deviation 10 outcomes were generated. Figure 10 shows the nominal positions of the sensors together with the outcomes; each panel refers to a different perturbation strength. The corresponding vertical IRF is shown in Figure 11; the horizontal axis refers to the elevation whereas the vertical represents the attenuation in dB, the vertical bars refer to \(\pm 1\sigma\). It may be observed that driving away from the regular sampling leads to smaller rejection of the echoes coming from surrounding elevations and a larger uncertainty in the exact dB value. For each outcome of the sensors positions, the tomographic power coming from 40 m above the ground level was estimated and then put in relation with AGB. The choice of 40 m rather than 30 m [15] was driven by the need to take the ground level in correspondence of a zero of the vertical impulse response function (see Figure 11) as suggested in Reference [30].