Lithium-ion and Lithium polymer batteries are fast becoming ubiquitous in high-discharge rate applications for military and non-military systems. Applications such as small aerial vehicles and energy transfer systems can often function at C-rates greater than 1. To maximize system endurance and battery health, there is a need for models capable of precisely estimating the battery state-of-charge (SoC) under all temperature and loading conditions. However, the ability to perform state estimation consistently and accurately to within 1% error has remained unsolved. Doing so can offer enhanced endurance, safety, reliability, and planning, and additionally, simplify energy management. Therefore, the work presented in this paper aims to study and develop experimentally validated mathematical models capable of high-accuracy battery SoC estimation. In this work, experiments are performed with Lithium Polymer battery cells to measure performance parameters such as current, battery capacity, temperatures, and voltage. Next, physics-based and machine learning modeling approaches are developed to study their ability to predict SoC. Measurements performed at high C-rates (1C – 4C) are used for model training and calibration, validation, and testing. The results show that the Pseudo-2D electrochemical model can predict SoC within about 2 % root-mean-squared-error (RMSE) at different C-rates. However, the Feed Forward Neural Network modeling approach with Butterworth and Hampel filters achieved lower than and close to 1 % RMSE for battery SoC estimations.