**2. Materials and Methods**

Lithium ion cells were set to well defined states, where SoHC, SoC and temperature parameters were varied. For each state, an electrochemical impedance measurement (EIS) was performed; every EIS spectrum is related to a defined state. To simulate dynamic working conditions, the EIS measurements were performed as soon as the SoC was adjusted, without relaxation. Since it was not possible to perform EIS measurements for every possible combination of SoHC, SoC and temperature, different series of measurements were performed; each series mainly focused on one state, e.g., temperature. These series of measurements are described in the following subsections. The EIS datasets were separated into a training dataset and a test dataset. The training dataset was used to train the ANN. In the first step, the ANN was trained by using the EIS spectra as input and the related data of the cell states as target values. After the training process, the ANN was evaluated with the test data set. The ANN needed to estimate the related state by itself, and at last the estimated states were compared with the measured states to evaluate the estimation quality.
