Battery state-of-charge (SoC) and state-of-power capability (SoP) are two of the most significant decision factors for energy management system in electrified vehicles. This paper tries to make two contributions to the existing literature. (1) Based on the adaptive extended Kalman filter algorithm, a data-driven joint estimator for battery SoC and SoP against varying degradations has been developed. (2) To achieve accurate estimations of SoC and SoP in the whole calendar-life of battery, the need for model parameter updates with lowest computation burden has been discussed and studied. The robustness of the joint estimator against dynamic loading profiles and varying health conditions is evaluated. We subsequently used data from cells that have different aging levels to assess the robustness of the SoC and SoP estimation algorithm. The results show that battery SoP has close relationship with its aging levels. And the prediction precision would be significantly improved if recalibrating the parameter of battery capacity and resistance timely. What's more, the method reaches accuracies for new and aged battery cells in electrified vehicle applications of better than 97.5%.