In power electronic applications, aging of the electric double layer capacitors (EDLCs) is considered as a serious issue since it may lead to failure. Their degradation is usually evaluated by an increase of the internal resistance or a decrease of the equivalent capacitance. These aging indicators have a good correlation with the supercapacitor's state-of-health (SoH). Generally, SoH is measured by electrochemical impedance spectroscopy (EIS). However, this technique must be performed offline and requires interruption of the system's operation. In this paper, a sliding mode observer is designed to estimate online the EDLC's aging indicators. Unlike several online estimators, the supercapacitor's parameters are considered as a nonlinear random distribution with external noises which yields accurate estimation. In addition, the relationship between the capacitance and the bias voltage is considered to be nonlinear. Lyapunov stability analysis is also provided. The proposed approach is validated experimentally using a standardized dynamic current profile. Furthermore, comparison against EIS is carried out for different aging phases and under different environmental temperature conditions.