Lithium-ion batteries(LIBs) are essential in electronics and electric vehicles. The effective management of these batteries in modern applications requires accurate estimation of State of Charge (SoC), State of Energy (SoE), and State of Health (SoH). This work mainly focuses on the co-estimation of SoC and SoE using the H-infinity filter (HIF) algorithm considering uncertainties in their initial states. In the present work, a new approach is developed to establish a relationship between SoE and SoC based on its SoC-OCV characteristics corresponding to different SoC levels. To validate the aging effect, a comparison has been made between the actual SoE obtained from the Watt-hour method and the proposed SoE obtained from SoC. This aging effect of the battery is shown in the form of a bar graph. It also deals with the SoH estimation based on energy. In this work, SoH has been calculated for the energy obtained from the proposed SoE and the energy obtained from the estimated proposed SoE. This approach allows for a comprehensive evaluation of battery performance and longevity, providing valuable insights into its degradation patterns. The simulation results indicate that the proposed SoE is better than the actual SoE.