In recent years, Lithium Iron Phosphate (LFP) has become a popular choice for Li-ion battery (LIB) chemistry in Electric Vehicles (EVs) and energy storage systems (ESS) due to its safety, long lifecycle, absence of cobalt and nickel, and reliance on common raw materials, which mitigates supply chain challenges. State-of-charge (SoC) is a crucial parameter for optimal and safe battery operation. With advancements in battery technology, there is an increasing need to develop and refine existing estimation techniques for accurately determining critical battery parameters like SoC. LFP batteries' flat voltage characteristics over a wide SoC range challenge traditional SoC estimation algorithms, leading to less accurate estimations. To address these challenges, this study proposes EKF and PF-based SoC estimation algorithms for LFP batteries. A second-order RC Equivalent Circuit Model (ECM) was used as the dynamic battery model, with model parameters varying as a function of SoC and accounting for temperature variations. The Hybrid Pulse Power Characterization (HPPC) test was performed at 15°C, 25°C, 35°C, and 45°C, and model parameters were obtained using the Nelder-Mead simplex algorithm. Simulations were conducted on MATLAB Simulink and validated using the Worldwide Harmonized Light Vehicle Test Procedure (WLTP) and Modified Indian Drive Cycle (MIDC). The proposed methods were evaluated for Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and computation time. Results showed that PF outperformed EKF by 40% regarding RMSE for WLTP and MIDC profiles. However, EKF computations were 90% faster than PF. The study concludes that EKF and PF can effectively be utilized for SoC estimation of LFP batteries, providing valuable insights for future Battery Management Systems (BMSs).