# Inter-Satellite Link Prediction with Supervised Learning: An Application in Polar Orbits
## 2 Encounter Anticipation Problem  
Motivated by the need to coordinate resource-constrained satellites autonomously, this work proposes a cost-efficient solution to solve the encounter anticipation problem without relying on centralized and ground-dependent orbit propagation. Based on our previous works [15; 16], we apply SL to infer future encounters between satellite pairs given their initial states. This process involves (1) generation of input and output data, (2) model training, and (3) model evaluation. In line with previous studies, encounters are defined as the time sequences that define satellite communication opportunities based on a close approach. Specifically, it is assumed that communication can occur if the Euclidean distance between two satellites is below a given threshold and that the directional antenna is equipped with pointing mechanisms. Note that the pointing process is beyond the scope of this study. Additionally, the SGP4 orbital model is utilized to calculate the dynamic distances between satellite pairs, from which the ground-truth encounters are derived. SGP4 is an orbital model for near-Earth objects including the effects of Earth's shape and atmospheric drag. However, some important changes and improvements are introduced as follows. On the one hand, the input data encompass all the necessary information to define the encounters between two satellites. This includes not just the initial position of the satellites (specified by six values known as orbital elements) but also their initial drag terms. In total, seven values define the initial state of a satellite. Based on this reasoning, 2000 synthetic polar satellites are generated and divided into two groups--one used for training and the other for validation. In each group, the satellites are combined into pairs to create a 14-feature input vector, ensuring that 85% of the total synthetic samples are allocated for training and 15% for validation. Two additional datasets are created for testing, namely a synthetic test set with information on 200 synthetic satellites and a Celestrak test set with 200 real LEO polar satellites. Note that synthetic satellites are randomly distributed throughout the entire LEO polar space, whereas real satellites from Celestrak tend to cluster in specific regions due to their organization into different constellations. Details about the generation of synthetic input data are presented in Section 3. On the other hand, the definition of encounter is improved from a simple near/not near decision coming from a single distance threshold to a more complex definition based on two distinct thresholds. Defining a single distance threshold (\(T\)) beyond which the ISL becomes unreachable would lead to the unrealistic and hard-defined encounters used in [15; 16]. In such scenarios, communication opportunities drastically appear or disappear with a minor change in the satellite-to-satellite distance. Therefore, if different \(T\) values need to be considered due to varying antenna characteristics, this approach would require a new training process with different training data, reducing its robustness. Instead, this work proposes an alternative \(T\)-independent encounter definition to anticipate the communication opportunities associated with any threshold within a specific range. This improved definition allows for encounter anticipation for different antenna characteristics based on the same trained model. Figure 1 illustrates the refined encounter definition, depicting the normalized separation distance over a 48-h period between T\({}_{min}\) and T\({}_{max}\). For a more intuitive interpretation, the time instances where the satellite-to-satellite distance exceeds T\({}_{max}\) are set to 0, indicating no potential encounters, while values of 1 indicate times when the distance falls below T\({}_{min}\) and the communication is possible. Based on [20], T\({}_{min}\) and T\({}_{max}\) are set to 1000 km and 3000 km, respectively.