To ensure a safe and economically valuable operation of a battery system over the whole lifetime, a battery management system is used for measuring and monitoring battery parameters and controlling the battery system. Since the battery performance decreases over its lifetime, a precise on-board aging estimation is needed to identify significant capacity degradation endangering the functionality and safety of a battery system. Especially for aviation and space applications, this can result in catastrophic scenarios. Therefore, in this work, a generic battery management system approach is presented considering aerospace application requirements. The modular hardware and software architecture and its components are described. Moreover, it is shown that the developed battery management system supports the execution of data-driven state of health estimation algorithms. For this purpose, aging estimation models are developed that only receive eight high-level parameters of partial charging profiles as input without executing further feature extraction steps and can thus be easily provided by a battery management system. Three different neural network architectures are implemented and evaluated: a fully connected neural network, a 1D convolutional neural network and a long short-term memory network. It is shown that all three aging models provide a precise state of health estimation by only using the obtained high-level parameters. The achieved fully connected neural network provides the best tradeoff between required memory resources and accuracy with an overall mean absolute percentage error of 0.41%.