# Small-UAV Radar Imaging System Performance with GPS and CDGPS Based Motion Compensation
## 3 Experimental Results
### First Test Case
In Figure 8a, the three hyperbolas related to the three targets have apexes placed at 6 s, 15 s and 21 s along the slow time axis. In this first test case, GPS and CDGPS provide similar trajectories along the east-north plane, with a slowly varying offset of the order of 1 m (Track 1) or 2 m (Track 2), whereas GPS altitudes are higher than those estimated by CDGPS. Moreover, for Track 1, the GPS and CDGPS UAV altitude profiles differ of a quasi-constant bias; whereas for Track 2 the GPS altitude are affected by a drift (see Figures 7c and 8c, respectively). Given the statistics about the estimated CDGPS uncertainty (based on residuals), reported in Section 4, CDGPS measurements can be assumed as a benchmark for standalone GPS. Thus, the drift of the altitude differences can be interpreted as a vertical error drift for the standalone GPS solution. Figures 9 and 10 depict the aligned and interpolated radargram after the MoCo and standard time-domain radar preprocessing for Tracks 1 and 2, respectively. Figure 9 corroborates that in Test 1-Track 1, by using both GPS and CDGPS information, MoCo allows at compensating the altitude variations and, indeed, the air-soil interface appears as an almost flat profile, as it is actually. Conversely, Figure 10 shows that in Test 1-Track 2, while MoCo driven by CDGPS achieves a result similar to Test 1-Track 1, the result based on GPS is worse because the air-soil interface does not have an almost flat profile. This uncompensated effect is due to the drift affecting the estimated GPS altitude (see Figure 8c). Figure 8: Test 2-Track 1: (**a**) raw data; (**b**) east–north UAV positions estimated by GPS (solid blue line) and CDGPS (solid red line), along-track direction defined by GPS (dashed blue line) and CDGPS (dashed red line); (**c**) UAV Altitude estimated by GPS (solid blue line) and CDGPS (solid red line), average altitude defined by GPS (dashed blue line) and CDGPS (dashed red line). Tables 2 and 3 list the signal processing parameters adopted to process the radargrams for Track 1 and Track 2 (after MoCo), respectively. The frequency step represents the step used to sample the frequency spectrum of the collected data (ranging from fmin and fmax) and is calculated according to the Nyquist criterion for avoiding aliasing problems [42] in the reconstruction process. The horizontal (i.e., x-axis) size of the overall investigated domain is equal to the extent of the along-track measurement line as defined by the MoCo. Conversely, the vertical (i.e., z-axis) size is such to consider about 1 m up and 2 m below the air-soil interface, whose position is set according to the average altitude value as computed from standalone GPS and CDGPS data. In other words, the zero of the z-axis is in correspondence to the average vertical position of the radar antenna system. Moreover, Tables 2 and 3 gives the subdomain apertures used to apply the Shift and Zoom procedure, which correspond to 5 m and 7 m for Track 1 and Track 2, respectively. These parameters have been chosen by measuring the target hyperbola extent in the processed radargram and take into account that the hyperbola extent is dictated by the antenna footprint and thus by the flight altitude. This justified why the subdomain aperture considered for the Track 2 is larger than the one used for Track 1. The tomographic images referred to Test 1-Track 1 and Test 1-Track 2, are depicted in Figures 11 and 12, respectively. These Figures show focused images wherein the metallic corner reflectors are clearly distinguishable, whereas the response of wooden trunk is low due to its lowest reflectivity. Moreover, these figures allow an approximate positioning of the targets. Figure 11a,b provide an accurate estimation of the altitude of the targets with respect to the air-soil interface; while they give an overestimation of the relative distance among the targets, which is of 1 m in the worst case (i.e., distance between target 2 and target 3 by using GPS data).