# Small-UAV Radar Imaging System Performance with GPS and CDGPS Based Motion Compensation
## 2 Materials and Methods
### Imaging Approach  
The block diagram of the applied data processing strategy is described in Figure 3. The strategy takes as input the raw radargram, which represents the radar signals collected at each measurement position (during the slow time and along the flight path) versus the fast time. The final output is a focused and easy interpretable image, referred to as tomographic image, which accounts for the reconstruction of the targets into the vertical slice defined by the flight trajectory (along-track direction), which is assumed to be a straight line, and the nadir direction. Initially, raw data are processed by means of the background removal step [34]. Background removal is a filtering procedure herein adopted for mitigating the undesired signal due to the electromagnetic coupling between transmitting and receiving radar antennas. Since this undesired signal is typically spatial and temporal invariant, the background removal step replaces each single radar trace of the radargram with the difference between the trace and the mean value of all the traces collected along the flight trajectory. After, the motion compensation (MoCo) stage is performed. The MoCo is a key element of the proposed signal processing strategy and its main steps are depicted in Figure 3. The MoCo takes as input the UAV positions estimated by GPS or CDGPS (defined as \"estimated\" trajectory), it generates a straight flight trajectory (i.e., the along-track direction) and it modifies the radar signals by means of the range alignment and the along-track interpolation procedures. The range alignment compensates the altitude variations, occurred during the flight, by realigning each radar signal, along the nadir direction, with respect to a constant flight altitude. This latter is obtained from the UAV altitudes, as estimated by GPS or CDGPS, by an averaging operation, and it is assumed as the altitude of the radar system in the following processing steps. The along-track interpolation accounts for the deviations occurring in the north-east plane between the estimated flight trajectory and a straight one. In details, a straight trajectory approximating the GPS or CDGPS estimated UAV flight trajectory in the north-east plane is computed by means of a fitting procedure. The straight trajectory in the north-east plane is taken as along-track direction, and is considered as the measurement line in the following processing steps. After the along-track direction is computed, the range aligned radar signals are interpolated and resampled in order to obtain evenly spaced radar data along the along track direction. Attitude variations are not considered in the MoCo. Indeed, the limited distance between the radar antennas and the UAV center of mass and the wide antenna radiation pattern imply that UAV attitude variation has a negligible effect on the data accuracy in terms of two travel time. Figure 4a shows a schematic representation of the MoCo. As indicated in Figure 4a,b, originally, the flight trajectory \(\Gamma\) has an arbitrary shape and each measurement points can be indicated by the following unevenly spaced vector: \(r_{m}=x_{m}\hat{x}+y_{m}\hat{y}+z_{m}\hat{z}\). By applying the MoCo, the actual flight trajectory (and accordingly the collected data) is first modified by the range alignment operation as in Figure 4c and, then, by performing the along-track interpolation, the measurements points are evenly spaced, as shown in Figure 4d. Note that the imaging plane, i.e., the plane wherein the targets are supposed to be located, is the vertical plane defined by the along-track and the nadir directions, from now on indicated as \((x,z)\) coordinates, respectively. After MoCo, the radar data pre-processing step is performed (see Figure 3). At this step, time-domain radar preprocessing procedures as dewow and time gating are carried out. The dewow step aims at mitigating the bias effect induced by internal electronic radar components by removing the average value of each radar trace [34].