## 1 Introduction  
The concept of autonomous navigation is expected to find large applications in the near feature, revolutionizing the conventional approach of maritime navigation. Maritime Autonomous Surface Ships (MASSs) refer to cutting-edge vessel ships that are equipped with advanced technologies exploiting the potential of artificial intelligence together with sensors and communication systems, enabling them to navigate and carry out various tasks at sea autonomously [1]. The driving force behind the adoption of autonomous commercial ships arises from the aspiration to improve safety, cut expenses, and minimize environmental issues associated with shipping operations [2]. Another study presented in [3] has assessed and quantified the positive impact on energy savings and environmental pollution prevention of adopting autonomous navigation systems by analyzing hundreds of conventional ships and their energy consumption and environmental impact. In recent years, the developers of Digital Twin (DT) technology within the maritime industry have shown a growing interest in the autonomous navigation field due to its potential, among others, to enhance real-time monitoring of vessel performances and aid in decision-making processes to maximize operational efficiency [4; 5]. The implementation of cutting-edge models such as DTs and their integration with system automation or other technologies aimed at achieving autonomous navigation all necessitate a substantial exchange of data between the vessel and the land-based systems. One potential solution for data transmission could involve conducting ship-to-land data exchange via low-orbit satellites (LOSs). Among the systems that can be considered for optical satellite-ship communication, the main ones are Free-Space Optical Communication (FSO) [6], laser communication [7] and Hybrid Systems that combine different technologies, such as via the integration of optical communication systems with radio frequencies. In the case of FSO-type communication, the systems are susceptible to atmospheric conditions and alignment issues due to motion, vibration or pointing errors [8]. Autonomous shipping requires a high level of security and the exchange of huge volumes of data between ships and satellites. Quantum laser communication presents a possible approach for the realization of autonomous navigation technology due to its lower sensitivity to adverse weather conditions, but it requires high pointing accuracy [9]. In the context of laser communication between the ground and satellites, it is crucial to create a direct line of sight between the ground-based station and the satellite in orbit. This is necessary to guarantee the reliability of the system. Given that the optical beam is highly focused, precise acquisition, tracking and pointing (ATP) systems are crucial, particularly for long-distance communication. \"Pointing\" is the term used to describe the action of aligning the transmitter with the receiver's Field of View (FOV), while \"tracking\" refers to the track of the satellite once has been pointed [10]. Optical satellite communication is closely influenced by the presence of errors that affect pointing and, thus, establishing a secure connection. The study reported in [11] identifies, among others, geometric errors (manufacturing errors), installation errors and attitude errors as the major sources of error that influence the satellite pointing of an optical communication terminal and introduces a mathematical model for their reduction. Other studies such as [12; 13] have used filters and algorithms with the aim of improving the accuracy of the LOS's pointing, reducing the size of the field of uncertainty, and providing reference and guidance for the design of space optical communication systems.