Cycling and acoustic information for the entire dataset are plotted in Fig. versus the cell charge level (Q). Different colours are used for the different C-rates, and lighter shades represent earlier cycles than deeper shades. Voltage is plotted in the first row and is representative of the electrochemical characteristics of the cells. The remaining rows demonstrate acoustic features which characterise the acoustic response. Namely, the amplitude and the ToF of the second and the last acoustic peaks are shown, as well as the difference between those values from one peak to the other. The second rather than the first peak was chosen for visualisation because the first peak saturated in certain cases (it overshot the maximum value that could be recorded). It is worth noting the hysteresis that is present in most acoustic features, which creates 'boxy' shapes similar to the voltage plots. Voltage hysteresis is a common phenomenon in lithium-ion batteries, and is more pronounced at high currents . The acoustic hysteresis observed here shows a similar dependence on the current as voltage hysteresis, especially when the acoustic amplitude is concerned. The ToF of the last acoustic peak (the 'back wall echo' peak) exhibits less hysteresis during cycling and is relatively linear, providing a compelling parameter for state estimation by linear regression or similar methods . Nevertheless, it is not a consistent feature between different cells, and would therefore require cell-specific model parameterisation. In fact, none of the other acoustic features shown are adequately consistent between all cells. This motivates the use of richer feature configurations for the task of state estimation, together with more advanced models that are capable of capturing non-linear patterns. The next section will proceed in this direction. Cycle (0.2C) Cycle (0.5C) A challenge revealed by Fig. is the presence of some acoustic instability at the beginning of each test. Early cycles (light shades) appear in many cases to produce an acoustic response that rapidly evolves before stabilising. Whether this acoustic instability implies that a cell's electrochemical characteristics are unstable should be the subject of further work, although the investigations of Knehr et al. are instructive and were conducted on the same cell. Some electrochemical instability can in fact be seen in the individual cycling profiles of the seven cells (SI Section 1), where capacity measurements obtained by Coulomb counting indicate that some lithium-consuming processes similar to formation are still taking place in the early stages of cycling. Consequently, the charge level (Q) shown as the x-axis in Fig. is not perfectly accurate because Coulomb counting accounts for all charge passed, including irreversible charge lost to parasitic reactions. Additionally, Coulomb counting is prone to accumulation of rounding errors over time, and each experiment had a duration of approximately 1 week which can make rounding errors problematic. For these reasons, the state estimators trained in the next sections will use voltage as their target variable -the sole dependent variable in the regression tasks.