# Portable and Easily-Deployable Air-Launched GPR Scanner
## 2 Working Principle of the Portable Setup
### GPR-SAR Processing  
Once the hardware is initialized and the operator verifies the correct configuration of the acquisition system, it is possible to start taking measurements. Raw radar data and positioning information are sent to the base station (laptop) where they are stored. The data processing flowchart is summarized in Figure 4, and it is based on the data processing presented in Section 3 of [14] for the case of the UAV-based GPR system.  
Positioning and geo-referring information are provided by the RTK module and the IMU embedded in the micro-computer. As shown in the scheme of Figure 4, the positioning information is transformed into a local positioning system (_x,y,z_). Then the filtering algorithm described in [14] is applied to discard the data that could degrade the GPR image, mainly due to non-uniform sampling.  
Pre-processing of radar data begins with the retrieval of the impulse response function, which requires performing a cross-correlation of the received raw radar data with the theoretical transmitted sequence. Then, the range of interest is selected (performing a time-window) to remove the coupling between the transmitting and receiving antennas and to discard measurements due to reflections too far from the radar. In the case of air-launched GPR, the reflection on the air-soil interface is strong enough so it can be used to set the zero reference for the _z_-axis. The next step is performing average subtraction in order to reduce radar clutter [14; 21].  
For each selected measurement position (_x,y,z_), radar measurements \(E_{\text{scatt}}(t)\) are transformed into the frequency domain in order to select the frequency band of interest, mainly based on the frequency response of the transmitting and receiving antenna parameters: radiation pattern, return losses, and phase center. As indicated in the flowchart of Figure 4, antenna phase center compensation can be applied at this stage if required.  
Figure 4: Flowchart of the GPR system processing algorithm.  
Given the acquisition (\(x\),\(y\),\(z\)) and imaging domains (\(x^{\prime}\),\(y^{\prime}\),\(z^{\prime}\)) (i.e., the area where the radar image is computed), Synthetic Aperture Radar (SAR) processing [25] can be applied to the radar measurements in the frequency domain, \(E_{\text{scatt}}\)(\(f\),\(x\),\(y\),\(z\)), to recover a 3D image of the reflectivity, \(\rho(x^{\prime}\),\(y^{\prime}\),\(z^{\prime}\)),  
\[\rho(x^{\prime},y^{\prime},z^{\prime})=\sum_{N_{f}}\sum_{N_{obs}}E_{scatt}(f,x, y,z)\exp(+jk_{0}(f)R(x,y,z;x^{\prime},y^{\prime},z^{\prime})), \tag{1}\]  
being \(N_{f}\) the number of discrete frequencies in which the selected bandwidth is discretized, and \(N_{obs}\) the number of observation points. \(k_{0}\)(\(f\)) is the wavenumber in free-space. \(R(x\),\(y\),\(z\); \(x^{\prime}\),\(y^{\prime}\),\(z^{\prime}\)) is defined as the distance between the transmitting antenna and the point of the imaging domain (\(x^{\prime}\),\(y^{\prime}\),\(z^{\prime}\)), plus the distance from that point to the receiving antenna. Although the soil composition can be taken into account when calculating the path length [14; 21], for the sake of clarity, results presented in this contribution are obtained considering free-space propagation (i.e., the relative permittivity, \(\varepsilon_{\text{r}}\), of the entire imaging domain is set to 1).  
The frequency response of the GPR is not uniform due to several factors such as the variation of the gain of the antennas with frequency. Besides, higher frequencies suffer from more attenuation and losses when propagating through the soil. Equalization techniques can be applied so that the contribution of each individual frequency to the SAR image has the same weight [21]. The main advantage is that the vertical resolution (range resolution) is improved. However, the dynamic range in the SAR image of the echoes of buried targets is decreased, resulting in a trade-off between range resolution and detection capabilities.