# A Performance-Based Airspace Model for Unmanned Aircraft Systems Traffic Management
## 3 Urban Airspace Model
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**CNS**} & **Uncertainty** & **Metric** & **Description** \\ \hline \multirow{4}{*}{Communication} & \multirow{2}{*}{Transaction time} & \multirow{2}{*}{Human latency} & Human latency includes all human operator response time such as UTM operator decision-making and response time. \\ \cline{3-4}  & & & Technical latency & Technical latency refers to datalink latency and control link latency. \\ \hline \multirow{4}{*}{Navigation} & \multirow{4}{*}{Position error sources} & Position uncertainty (\(\sigma\)) & The standard deviation of the position solution. This is inflated by multiplicative factors to meet accuracy, integrity, and continuity requirements. \\ \cline{3-4}  & & & Dilution of precision (only for GNSS) & DOP is a ratio factor in positioning which is calculated from the satellites-receiver geometry. \\ \cline{3-4}  & & Drift rate (dead reckoning system) & Drift stems from errors in acceleration and angular velocity measurement \\ \hline \multirow{4}{*}{Surveillance} & \multirow{2}{*}{Transaction time} & \multirow{2}{*}{Latency} & The total latency of position information is the delay between the time of applicability of the position measurement and the time of arrival of the ADS-B message for that position. \\ \cline{3-4}  & & & Navigational Integrity Category specifies the integrity of containment radius aligned with horizontal position which then maps to RNP. \\ \cline{3-4}  & & Tracking error (\(\sigma\)) & The standard deviation of the tracking error. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: CNS Performance metrics. For surveillance systems, as in the case of navigation, state estimators used in radar such as the Extended Kalman Filter or other recursive algorithms output the standard deviation of tracking error. As in the case of navigation, this metric can be inflated to bind a required fraction of the error. In the online stage, the specific CNS performance of each UAS is estimated and used to generate a virtual protection volume bounding the vehicle. This volume is the _CNS protection volume_, which comprises the combined uncertainty of the CNS infrastructure supporting the UAS. This represents a protected volumetric bound which should not be breached by any obstacle to ensure a sufficient margin for Separation Assurance and Collision Avoidance (SA/CA). The methodology to generate the individual components of this volume is presented in Section 3.2. An occupancy grid can successively be derived from the set of elementary cells and from the active CNS protection volumes. Cells that are contained within and on the boundary of the protection volume correspond to occupied space and the remaining cells correspond to unoccupied space. This is also illustrated in Figure 2.  
The occupancy grid supports the demand-capacity balancing by not just considering the number of aircraft simultaneously active in a region, which was the traditional approach for human-centric ATM, but also their specific CNS performance, which supports more automated and autonomous SA/CA concepts. _Airspace sectors_ are then generated as clusters of elementary cells to support efficient management of traffic across the urban region. These sectors need to consist of an optimal number of elementary cells to balance the traffic complexity and the communication overhead due to sector handovers. All the elements of this performance-based airspace model i.e., elementary cells, CNS protection volume, occupancy grid and airspace sectors are visualised in Figure 3. The following sections introduce the underpinning theoretical framework and mathematical models for all these entities. However, the CNS protection volumes will be addressed up front as they form the theoretical basis upon which the overall framework and the elementary cells were defined. This airspace model provides the flexibility for implementation in the planning stage of three different operational timeframes: offline, pre-tactical online and tactical online.