The State of Charge of lithium-ion batteries plays a significant role in managing their performance for energy storage systems, especially when repurposed for second-use applications. This research focuses on resolving the challenges involved in accurately predicting the State of Charge of repurposed lithium-ion batteries, assuming that the actual capacity of these batteries is already known, utilizes a Square Root Cubature Kalman Filter algorithm based on a second-order resistor-capacitor equivalent circuit model for State of Charge estimation in lithium batteries. The simulation verification uses the charge-discharge test experimental data of the second-life lithium battery SOUL-ISR18650HP, and evaluates the performance of alternative filtering methods under identical experimental conditions, including other Kalman filter-derived algorithms. The results of the experiments indicate that, when the actual capacity of second-life lithium-ion batteries is known, the selected algorithm yields improved accuracy in estimating State of Charge.