## 4 Simulation Method  
From the point of view of simulation, the required result is the bistatic RCS of the aircraft for the particular incidence and scattering angles required along the flight trajectory. If only monostatic RCS were required, it would likely be practicable to produce a lookup table and then to simply interpolate this to obtain the required RCS for the direction of interest. However, in the bistatic case, significantly more simulation time would be required, since for each incidence direction it would be necessary to determine the RCS for the full sphere around the target. Instead, we performed the simulations on an as-needed basis, explicitly performing a discrete simulation for each incidence and scattering angle pair required for the particular flight. All of the simulations were performed in Ansys HFSS 2019 R3 (also known as version 19.5) on the 3D model of the Pilatus PC-12 aircraft shown in Figure 9a. The model was predominantly treated as perfectly electrically conducting, with only the upper fairing (shown in green) treated as glass-fiber. The fuselage was also largely treated as being a solid body, with only the gap between the rudder and main fuselage currently modeled. All of the simulations were performed in the aircraft's frame of reference. The incidence and scattering directions and incident polarization in that frame of reference for each point to be simulated were precalculated in Matlab based on the positions and orientations of the aircraft, transmitter and receiver. A Python script was then created to configure each individual simulation in HFSS. The aircraft's position and attitude were determined from the GPS-aided IMU mounted onboard the aircraft. In the final version of the simulations, we assumed an ellipsoidal earth and used a four-thirds earth radius model [34] to account for atmospheric bending when determining the incidence and scattering angles, but we also consider alternatives to these approximations in Section 5.2. The need for on-demand simulations at each point along the flight path makes the computational time required for each point significant. There is a need for a trade-off between simulation accuracy and speed. For this work, we used a full version of HFSS's method of moments (MoM) solver (also known as the integral equation (IE) solver) at only a select set of points along the flight path that are used for error analysis. These simulations took around 9 hours per data point (at 5 frequencies). For the bulk of the flight we performed more basic MoM simulations, which differ from the full MoM simulations in that we did not allow the mesh to be iterated. These more basic simulations took around 1 h, 50 min per data point (again at 5 frequencies). We also performed even higher temporal resolution simulations using HFSS's enhanced shooting and bouncing ray (SRR+) solver in two different modes: with physical theory of diffraction (PTD), uniform theory of diffraction (UTD) and creeping wave physics enabled (referred to later as full SBR+), and with these all disabled (referred to later as basic SBR+). The SBR+ simulations took approximately 90 seconds per data point (again at 5 frequencies), with around a 5-second saving when using the basic solver. We used the highest-quality simulations to validate the faster, lower quality simulations. All of the simulation times quoted are for a 2020 workstation with 16 cores and 384 GB of RAM. Figure 9: Images of the modeled aircraft showing: (**a**) the CAD model used; (**b**) the mesh at 482 MHz for the SBR+ solver; (**c**) the mesh at 482 MHz for the basic MoM solver; and (**d**) the surface currents for a sample incident plane wave arriving from the left side of the aircraft. A typical SBR+ mesh for simulations at 482 MHz and consisting of 233,241 elements is shown in Figure 8(b). The equivalent single-pass MoM mesh is shown in Figure 8(c), and consists of 272,277 elements. The higher number of elements is due to the need to have at least a minimum number of mesh elements per wavelength in the MoM model.