# Inter-Satellite Link Prediction with Supervised Learning: An Application in Polar Orbits
## 5 Results
### Computational Cost  
Prior findings have demonstrated that ML can be used as an alternative to SGP4 to anticipate communication opportunities between satellites. While SGP4 offers precise solutions, our hypothesis suggests that ML can be utilized to trade a degree of accuracy for computational efficiency and battery savings, which are particularly advantageous in resource-constrained systems. In that sense, the proposed SL model solution should anticipate the encounters faster than the state-of-the-art methods based on orbit determination.  
Before analyzing the computational cost, TensorFlow Lite (TF Lite) is used to optimize the trained SL model. While TensorFlow (TF) is a framework used mainly to build and train ML models, TF Lite optimizes a trained model mainly through pruning and quantization. These techniques yield a more compact model and enable resource-constrained devices to make predictions much faster and with less memory usage.  
Table 3 depicts the performance degradation observed upon implementing a 16-bit floating point quantization of the model's trained parameters, which reduces the precision of the trained parameters, originally expressed with a 32-bit floating point. As observed, the error produced by this optimization is minimal, except for \(P\), which experiences a loss of nearly 5% in performance for the synthetic dataset with \(T\) = 1500 km. However, unexpectedly, a few isolated cases exhibit slightly improved performance after the model optimization process.  
To determine the significance of sacrificing this 1% or 2% of performance, Table 4 provides insights into the computational time reduction associated with TF Lite. The computational time is measured as the average duration required for the model to make an inference--specifically, to anticipate the encounters between two satellites given their initial states. The results show a strong decrease in the computational time by three orders of magnitude compared to the default TF model, dropping from around 60 ms to 70 \(\upmu\)s.  
To conclude the evaluation of the proposed ML approach, Table 4 also presents the computational time required for the baseline SGP4 to anticipate the encounters. Notice that encounter computation based on SGP4 involves the following three steps: (1) calculation of the satellite positions every 5 min over 2 days, (2) computation of the satellite-to-satellite distances, and (3) evaluation of the encounter times given a distance threshold. The average time required to complete these tasks is around 400 \(\upmu\)s, with the first task accounting for over 90% of the total time. While TF is two orders of magnitude more time-consuming than SGP4, the optimized model with TF Lite exhibits a speed advantage of approximately six times over SGP4, which could reduce the satellite's battery consumption considerably.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**T = 1500 km**} & \multicolumn{2}{c}{**T = 2000 km**} & \multicolumn{2}{c}{**T = 2500 km**} \\ \cline{2-7}  & **TestS** & **TestC** & **TestS** & **TestC** & **TestS** & **TestC** \\ \hline \(BA\) [\%] & 81.8 & 86.3 & 89.6 & 91.2 & 91.8 & 93.1 \\ \(F1\) [\%] & 63.6 & 71.8 & 78.7 & 81.8 & 83.0 & 86.7 \\ \(P\) [\%] & 82.3 & 83.8 & 83.5 & 86.7 & 84.9 & 89.7 \\ \(R\) [\%] & 63.8 & 73.2 & 79.6 & 83.1 & 84.2 & 87.0 \\ \(AP\) [\%] & 83.0 & 89.0 & 89.4 & 93.5 & 91.8 & 95.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mean performance for each scenario and dataset.  
Previous findings demonstrate that ML could be a promising alternative to SGP4 in resource-constrained environments, such as LEO satellite networks. In these settings, where computational resources are limited, ML offers a potential alternative, trading off some accuracy for reduced computational costs.