The aging estimation of lithium-ion batteries is a central mission for a safe and efficient handling of lithium-ion batteries over the whole battery lifetime. However, especially the absence of precise diagnostic measurements within real-world applications yields the aging estimation a complex challenge. Moreover, the non-linear aging of lithium-ion batteries is strongly dependent on various operating and environmental conditions and the specific battery cell chemistry. This paper presents a generalized state of health estimation approach based on a neural network that can be used for different lithium-ion battery chemistries. The presented algorithm is able to estimate the aging of lithium-ion batteries by using information obtained from raw sensor data without executing further preprocessing or feature engineering steps. It is firstly shown that the developed temporal convolutional network accurately estimates the state of health for three different lithium-ion battery chemistries by only using high-level parameters from partial charging profiles. In addition, the obtained high-level parameters can provide relevant information needed for a battery passport. The final neural network is trained using transfer learning approaches to model the state of health development of a Lithium-Nickel-Cobalt-Aluminum-Oxide (NCA), a Lithium-Nickel-Cobalt-Manganese-Oxide (NCM) and, an NCM-NCA battery cell. The overall mean absolute percentage error of the generalized state of health estimation is 1.43%.