# A Performance-Based Airspace Model for Unmanned Aircraft Systems Traffic Management
## 3 Urban Airspace Model
### CNS Risk Protection Volume Generation  
This sub-section covers the generation of the CNS risk protection volume. The methodology as illustrated in Figure 5 is adopted from the approach introduced in [36], which is used for solving the autonomous Detect-and-Avoid (DAA) problem.  
The navigation component of the volume is generated by developing a sensor measurement model that accounts for both nominal and off-nominal performance of the sensors utilized by the UAS. These typically include a GNSS receiver, inertial sensors, visual sensors and altimeter.  
The distributions characterizing these errors from these sensors can be, in theory, completely arbitrary. However, the long-standing practise for certifying systems in aviation has been to replace the true arbitrary distributions with a simpler distribution. This simpler distribution, called the overbounding distribution, must be such that it overestimates the true error by a small margin (Since this is preferable to underestimation of the true error, which would constitute hazardously misleading information).  
Figure 4: Dual approach of performance-based airspace model.  
Figure 5: CNS risk protection volume determination methodology.  
Navigation systems in aviation have conventionally been modelled as Gaussian distributions. The use of Gaussian distributions has been the basis for the design of all algorithms in safety-of-life GNSS-based systems, including SBAS and GBAS. In GNSS for instance, the characterization of positioning errors as Gaussians are well documented in current standards [37].  
Replacing the expected distribution by the overbounding Gaussian distribution is necessary for at least two reasons. First, an arbitrary distribution would require an amount of data too large to be sent through typically low bandwidth channels between different participants in the encounter whereas a Gaussian is described by only two parameters (a mean value and standard deviation). Second, combining different error sources is accomplished through convolution of distributions. Computing the convolution of many error sources characterized by arbitrary distributions is likely to be prohibitive. However, Gaussian convolutions are simple to perform. The residual error from each error source is combined and the resulting Gaussian distribution is a conservative error budget of the sensor measurements. The conservative sensor errors are then translated from the sensor measurement domain to the aircraft position domain and the Gaussian sphere bounding this position error distribution is the navigation protection volume.A similar process is adopted for the surveillance sensor(s) involved in the scenario. Worst-case sensor measurement error overbounds are translated to the position domain and constitute the surveillance layer of the risk protection volume.  
The communication layer is essentially a buffer which accounts for the transaction time taken to conduct a manoeuvre to maintain separation or avoid a collision. As detailed in Figure 5, this transaction time depends on a combination of human and technical factors. The overall risk protection volume is illustrated in Figure 6.  
In addition to CNS performance, the volume can also be inflated to account for operational and environmental factors such as relative aircraft dynamics and wake turbulence [36].