## 5 Simulation Method Uncertainties
### Angular Error
#### 5.2.5 Effect on RCS  
To determine which, if any, of these effects are significant, it is important to determine the impact of azimuth and elevation errors on the simulated RCS along our flight path. With the four-thirds earth radius approximation, we have simulated the RCS at each of the 13 error points (Figure 10), whilst adding offsets to the incidence and scattering angles of \(-0.15^{\circ}\) to 0.15\({}^{\circ}\) in 0.02\({}^{\circ}\) increments. The incidence and scattering azimuth and elevation angles were varied separately, in all cases with the other three values fixed at their central values, leading to a total of 832 different angles being simulated, each at 5 frequencies. The simulations were performed using the full SBR+ solver.  
From these bistatic RCS values, the mean, median and 90 th percentile of the fractional RCS error (relative to the central RCS value) were calculated and are shown in Figure 17. From these it is quite clear that for our geometries the error introduced by changing the angle to the transmitter is more significant than that introduced by changing the angle to the receiver.  
These results, combined with the fact that the error in elevation angle from the transmitter due to the four-thirds earth radius model is so small (median 0.00023\({}^{\circ}\), max 0.0013\({}^{\circ}\)), allow us to conclude that the error introduced by the atmospheric assumption is negligible.  
The same is not, however, true for the attitude and position errors. From Figure 10, we can estimate that the median fractional errors introduced in the calculated RCS values are approximately 0.14 for the transmitter azimuth, 0.13 for the receiver azimuth, 0.085 for the transmitter elevation and 0.02 for the receiver elevation. A quadrature combination of these yields an overall error estimate of 0.21. Note that this is really only a measure of the typical error. If we take instead the 90 th percentile, the resultant overall error estimate is actually 1.48.  
This still leaves the error due to neglecting the aircraft's movement during the measurement integration time. This error will largely be in azimuth, and we further know that the dominant effect is the error to the transmitter for our flight path. From the same RCS dataset used for the earlier error analysis, we calculated the fractional error in the RCS as a function of the range of the integration angle (relative to the center-point RCS of each simulation), which is shown in Figure 18. Finally, since the measurements are integrated over 573 ms and the aircraft moves in that time, the measurement is really the integrated RCS across these angles and orientations. Since the IMU update rate is far higher than the integration time, we know the location and aircraft at 11-12 points for each measurement time. We can therefore calculate the variation of the incidence and scattering angles over these times for our flight. The median variation in the azimuth angle of the transmitter is 0.12\({}^{\circ}\) and to the receiver of 0.023\({}^{\circ}\). The equivalent median elevation variations are 0.00031\({}^{\circ}\) and 0.016\({}^{\circ}\), respectively. Treating the 0.12\({}^{\circ}\) as by far the dominant effect, we can then estimate that this leads to a 90 th percentile fractional uncertainty in the RCS of around \(\pm\)0.31.  
Figure 17: RCS errors as functions of increasing angular errors for each of the incidence angles, calculated separately.