This paper proposes a novel integrated robust system identification and state of charge estimation of Li-ion battery. A finite time extended state observer is used for state of charge (SOC) estimation of Li-ion battery. A relay feedback test has been adopted to yield accurate battery parameters in noisy environment. New identification method using state space based relay feedback approach is employed with a disturbance nullifier to extract the parameters of battery model. Thereafter, the objective of SOC estimation is carried out by designing a novel finite time extended state observer based on higher order sliding modes. The unknown battery model parameters are determined first, followed by the estimation of SOC next, under both charging and discharging conditions. This investigation finds a high amount of accuracy in the proposed battery model identification method, besides an accurate and time bound estimation of SOC using the proposed observer scheme.