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This paper presents the concept of operations, architecture and trajectory optimisation algorithms of a Next Generation Flight Management System (NG-FMS). The NG-FMS is developed for Four Dimensional (4D) Intent Based Operations (IBO) in the next generation Communications, Navigation, Surveillance and Air Traffic Management system (CNS+A) context. The NG-FMS, primarily responsible for the aircraft navigation and guidance task, acts as a key enabler for achieving higher level of operational efficiency and mitigating environmental impacts both in manned and unmanned aircraft applications. The NG-FMS is interoperable with the future ground based 4DT Planning, Negotiation and Validation (4-PNV) systems, enabling automated Trajectory/Intent Based Operations (TBO/IBO). After the NG-FMS architecture is presented, the key mathematical models describing the trajectory generation and optimisation …