## 7 Ground-Segment Optimization Aspects
### Applicable Optimization Methods for Ground Segment
#### 7.2.2 Long Short-Term Memory (LSTM)
Other similar metrics from Table 2 that look at the error percentage of a particular parameter are the handover and failure percentages, which can be written in terms of Equation (33) by replacing bits with the parameter of interest. However, one should also note that these types of metrics can also be utilized together with models, as seen with BER in [36]. A slightly different but very informative performance metric we still need to address is the Root Mean Square Error (RMSE), which is a widely utilized error metric in data-driven optimization approaches. RMSE is a comparative metric that provides a performance relative to something else; ML methods typically use a test dataset for this purpose, and in the case of using RMSE as a tracking error, it is simply the actual trajectory of the tracked target. We provide the RMSE calculation in Equation (34), and we also provide a similar comparative error metric called Mean Absolute Error (MAE) in Equation (35). In both equations, \(n\) refers to the total number of data points, \(y_{i}\) refers to the prediction in point \(i=1,\ldots,n\) (i.e., the output of a NN or the estimated point in trajectory), and \(x_{i}\) refers to the true value in point \(i\) (e.g., the labels of the data in a NN or the point in the real trajectory for tracking). More examples of comparative error metrics can be found in the literature, for example, in [158]. \[\texttt{RMSE}=\sqrt{\frac{1}{n}\sum_{i}(y_{i}-x_{i})^{2}} \tag{34}\]

\[\texttt{MAE}=\frac{1}{n}\sum_{i}|y_{i}-x_{i}| \tag{35}\]

As for the other metrics that include models, the user segment also utilizes coverage as a metric, which we have discussed in the space and ground segments. Another such metric is the network energy calculation for the UAV data acquisition problem. We will provide an example by following the network energy consumption model from [36], where a wireless sensor network is optimized and energy consumption is one of the three major metrics utilized. In [36], the authors model the total energy consumption of the network as in Equation (36), where \(E_{ij}\) refers to the energy consumed for communication between node \(j\) and the channel head node \(i\), \(E_{iu}\) refers to the energy consumed for communication between the UAV node \(u\) and the channel head node \(i\), and \(N\) refers to the total number of channel head nodes. \[E_{tot}=\sum_{i}^{N}\sum_{j}^{N_{i}}E_{ji}+\sum_{i}^{N}E_{iu} \tag{36}\]

\(E_{ji}\) is modeled as in Equation (37), where \(P_{ij}\) is the transmit power and \(R_{ji}\) is the bit rate of the communication channel between node \(j\) and channel head node \(i\). \(E_{iu}\) is modeled similarly as in Equation (38) but between channel head node \(i\) and the UAV node \(u\). \[E_{ji}=\frac{P_{t_{ji}}}{R_{ji}} \tag{37}\]\[E_{iu}=\frac{P_{li_{u}}}{R_{iu}} \tag{38}\]

Lastly, a more arbitrary metric could be the overall complexity of a design. Given a satellite selection problem from the point of view of the user receiver, a first approach could be trying to reduce the complexity by reducing the number of satellites being tracked. In this sense, we can make use of DOP metrics such as GDOP and TDOP, received power strength such as \(C/N_{0}\), or even simple parameter metrics, such as the satellite elevation from the user location, to optimize the number of satellites to be tracked. In the literature, we can find some studies that utilize a similar idea but are typically applied to GNSS scenarios. For example, in [159], the authors proposed a DOP optimization based on TDOP, in which the subset of satellites with the best TDOP were used for obtaining the PNT solution. In [160], the authors proposed a method called the 'Quasi-Optimal Technique', in which more than four satellite DOP measurements are considered to optimize the satellite subset selection. The authors in [161] proposed a less computational intensive method compared to [160] but using a similar approach. In [162], the authors propose a weighted least-squares-based DOP algorithm.