## 1 Introduction  
Air transport is considered to be the safest mode of mass transportation [1]. ATM systems constitute one of the fundamental pillars that contribute to these high levels of safety. The essential function of ATM systems is to ensure that aircraft flying in the same airspace are kept separate from each other and from the ground. The International Civil Aviation Organization (ICAO) defines ATM as \"the dynamic, integrated management of air traffic and airspace including air traffic services, airspace management, and air traffic flow management--safely, economically, and efficiently--through the provision of facilities and seamless services in collaboration with all parties and involving airborne and ground-based functions\". Each country is responsible for ensuring that its airspace has an adequate ATM system. The main objective of an ATM system is, therefore, to manage and reduce the risk of accidents. As such, the minimum separation distances between aircraft are defined as the minimum separation between two aircraft in the airspace to ensure that they do not collide with one other. The ATM is responsible for ensuring that these separation minima between aircraft are not violated and, in this way, managing the risk of collision between aircraft. The safety of ATM systems has steadily improved over the last decades thanks to a number of measures including better equipment, technologies, and work procedures, as well as the deployment of additional safety barriers. However, the sustained growth of air transport imposes increasing demands and requirements on the safety, capacity, and efficiency of the ATM system. ATM systems are currently facing their greatest challenge to date, namely the evolution towards multi-faceted, hyper-dimensional, highly distributed, and mutually dependent systems, with levels of complexity that were unimaginable just a few decades ago [2]. The Single European Sky ATM Research (SESAR) project proposes a new paradigm for the ATM system of the future, primarily focused on technology and automation [3,4]. This system implies an architecture heavily influenced by digitalization and the geographic relocation of services. It is increasingly challenging to maintain extremely high levels of safety in this complex and ever-changing environment. Ensuring that the level of safety provided by ATM systems is consistent with future needs and expectations, and that it is not negatively affected during the process of transition, is a priority for the aeronautical community. Within the framework of the Single European Sky (SES), the European Union has several mechanisms to promote the cohesion, efficiency, and modernization of ATM systems. One of these mechanisms is the definition of a performance measurement framework that sets objectives in four key performance areas for European ATM systems, namely, safety, capacity, efficiency, and the environment. Safety is the most relevant of these areas, over and above the other three. As part of this monitoring and evaluation model, stakeholders must collect and study safety-related information to predict and anticipate not only current safety risks, but also emerging ones. The main risk that an ATM must safeguard against is the occurrence of violations of the separation minima between aircraft, the so-called separation minima infringements (SMIs) [5]. According to the European Aviation Safety Agency (EASA), the occurrence of SMIs is the second most important risk for European aviation [6]. EUROCONTROL registered 827 and 930 incidents of severities A and B (high severity) during 2017 and 2018, respectively [7]. Of these, 287 incidents in 2017 and 341 incidents in 2018 corresponded to non-compliance with separation minima between aircraft. According to the Airborne Conflict Safety Forum, there are approximately 150 losses of separation for every million flights in European airspace [8]. Considering that, on average, each flight receives 15 instructions from air traffic control en route, this means one loss of separation for every 100,000 instructions.