## 1 Introduction  
The growth in Maritime Autonomous Surface Ship (MASS) technologies and their journey towards commercialization have drawn global attention, with both showing robust upward trends [1]. The plans of the International Maritime Organization (IMO) to roll out the non-mandatory MASS CODE in 2025, coupled with accelerated research, development, and onboard trials in major maritime nations, signals a bright future for MASS technologies in maritime applications [2]. Among the many enabling technologies, communication stands out. It underpins remote ship control and autonomous navigation, covers data transfer and ship monitoring, and enables interaction between ships and shore-based systems. At present, MASS communication scenarios are fraught with many challenges. Node mobility, link persistence, and routing adaptability are the most prominent of these issues, which also interact with each other [3, 4]. The dynamic nature of nodes in a mobile communication network determines the network's topology and fluctuations, thereby directly affecting link persistence. Poor link persistence can directly lead to link disruption. When a link within a path fails, the network must repair the path by finding an alternative link or establishing a completely new path. These re-routing operations consume precious radio resources, and re-routing delays may affect service quality and overall network performance. Therefore, evaluating communication link persistence directly impacts the quality of ship-to-ship communication services and is crucial for ensuring the continuity, stability,and efficiency of maritime communication services. In the resource-constrained MASS communication scenario, link persistence is the key indicator for selecting the optimal communication path. An accurate node mobility model is an essential prerequisite for the estimation of link persistence. In the field of mobility modeling, as early as 1926, [PERSON] proposed the concept of Random Walk Mobility (RWM) to simulate Brownian motion [5]. Subsequently, researchers developed a series of simple and easy-to-implement mobility models, including random waypoint models and random direction models, based on this concept [6; 7]. These models have been widely used, and they have become the most commonly used default mobility models in various network simulation platforms due to their simplicity and ease of theoretical analysis. However, such models do not take relative motion between nodes into consideration. In mobile ad hoc networks, the relative speeds and directions of nodes significantly affect link persistence. When two nodes move in opposite directions or at a high relative speed, link persistence tends to be poor. Therefore, to achieve a more accurate estimation of link persistence, it is crucial to design a mobility model that incorporates the relative motion between nodes, thereby better capturing their relative movement trends. Regarding communication link states, researchers have also conducted extensive and in-depth studies. In [8], the characteristics of wireless links at sea and the factors influencing communication are examined through data obtained from sea-testing experiments conducted on multiple fishing vessels. In [9], the authors define transmission reliability to measure the transmission performance of mobile ad hoc networks, considering the impact of interference and utilizing genetic algorithms for optimization. In [10], a Bayesian tracking algorithm is proposed to predict the duration of links by learning the environment and predicting node motion parameters. In [11], the authors present a link availability analysis of two cities in India under fog weather conditions, and propose a novel model to calculate the link availability. The authors of [12] present random graph analysis that allows for advanced link models in which the probability of link failure decreases with increasing distance between nodes, helping to determine the network availability of planned mesh networks as a function of the number of redundant nodes.