# A Performance-Based Airspace Model for Unmanned Aircraft Systems Traffic Management
## 3 Urban Airspace Model  
The proposed performance-based airspace model is conceptually illustrated in Figure 2. The model is underpinned by a two-stage approach. During the offline planning stage, the reference grid is generated as a set of _elementary cells_ according to the baseline CNS performance. In our approach, the elementary cells are parameterized as cuboids with a square base, but the methodology could easily be extended to other 3D shapes. The length (r\({}_{\text{x}}\)), width (r\({}_{\text{y}}\)) and height (r\({}_{\text{z}}\)) of the cuboidal cells are formulated as a function of the expected baseline CNS performance for the region:  
\[\text{r}_{\text{x}},\,\text{r}_{\text{y}},\,\text{r}_{\text{z}}=\text{f} \big{(}C_{\text{perf}},\text{N}_{\text{perf}},\text{S}_{\text{perf}}\big{)} \tag{1}\]  
where C\({}_{\text{perf}}\), N\({}_{\text{perf}}\), S\({}_{\text{perf}}\)\(\in\) R\({}^{\text{n}}\) are the set of performance metrics for communication, navigation, and surveillance respectively. A summary of applicable metrics which quantify the CNS performance is provided in Table 2. The model is applied in two timeframes: offline planning and online airspace management. Figure 2: High-level overview of the performance-based airspace model. For communication systems in aviation applications, one measure of performance is the latency in staging an intervention due to human operator and equipment limitations. These are typically not measured in real-time but are determined apriori either analytically, or more frequently, using experimental data. For navigation systems, under the PBN framework, performance is quantified using four metrics [35]:  
* Accuracy
* Integrity
* Continuity
* Availability  
System accuracy requirements are specified as an upper bound on position error, which is the difference between the estimated position and the actual position. Navigation state estimators typically output the standard deviation of the computed position solution as a measure of confidence. A 2\(\sigma\) value which bounds approximately 95% of the navigation errors is taken as an online indicator of accuracy. Integrity is a measure of trust that can be placed in the correctness of the positioning solution supplied by the navigation system. Integrity includes the ability of a system to provide timely and valid warnings to the user (alerts) when the system must not be used for the intended phase of flight. To ensure integrity in practice, the standard deviation of the computed position solution is inflated by a requisite factor to bound all but a small fraction of errors (corresponding to an 'integrity' risk or maximum allowable probability that the solution is out of bounds). The inflation also accounts for the maximum allowable false alarm rate of the system, which dictates the continuity of the system. Continuity is a measure of reliability that ensures that the system will perform nominally without interruption for a given mission segment. Availability is the proportion of the overall mission time for which the navigation system meets accuracy, integrity and continuity requirements. For GNSS, the well-known Dilution of Precision (DOP) factors are also used as an easily obtained online measure of performance.