•A smoothing method for IC curves based on Kalman filter is proposed.•Battery standard and non-standard charging experiments are designed and conducted.•The influence of battery aging and charging condition on IC curves is revealed.•The adaptive ICA for capacity estimation takes the charging initial SOC into account. Incremental capacity analysis (ICA) has been widely employed to investigate the degradation mechanism and perform the capacity estimation of lithium-ion batteries. However, the traditional capacity estimation based on ICA is limited by the computational efficiency and charging condition. In this paper, a rapid acquisition method of the incremental capacity (IC) curve is established, then an adaptive capacity estimation framework based on ICA considering the charging condition is proposed. Aiming at improving the computational efficiency, the Kalman filter is employed to acquire the smooth IC curves expeditiously, which requires small data length to handle the IC value. A considerable number of battery standard and non-standard charging experiments are designed and conducted. The influence of battery aging status, charging initial state of charge (SOC), and temperature on IC curves is revealed. Three features of the IC curve during standard charging are selected to investigate the relationship between battery capacity and the height of features. Furthermore, an adaptive correction method for capacity estimation considering the charging initial SOC is established, and the validation results show the effectiveness of the proposed correction method, which provides high accuracy and robustness.