Lithium-ion batteries are the ubiquitous energy storage device of choice in portable electronics and more recently, in electric vehicles. However, there are numerous lithium-ion battery chemistries and in particular, several cathode materials that have been commercialized over the last two decades. In recent time several automakers have followed trend by announcing their own plans to move their EV production to LFP, due to its high intrinsic safety, fast charging, and long cycle life and cobalt free batteries as well as avoiding other supply chain constrained metals like nickel. Accurate estimation of the state-of-charge (SOC) is crucial for efficient and safe battery applications. However, existing SOC estimation methods (coulomb count, SOC-OCV methods) fail to provide accurate SOC estimation for LFP batteries that have a flat voltage-SOC relationship, and these present model-based methods can be ascribed to their inability to simultaneously accommodate the differences in voltage characteristics between different open-circuit-voltage (OCV) ranges. To address this limitation, offline three RC equivalent circuit model is used to identify OCV and other battery model parameters. Then, the parameters of the extended Kalman filter are adaptively estimated according to the innovation residual error and updated in different OCV ranges, which are distinguished based on the identified OCV. While conventional methods fail to converge, the proposed method ensures both high accuracy and stability, with a maximum absolute error of < 3%. The viability of the proposed method is further verified using data collected from real battery systems.