In order to develop electric vehicles, it is vital to be able to accurately estimate the state charge (SOC) of a lithium battery. To address the problem that the Extended Kalman Filter (EKF) algorithm leads to the Taylor expansion truncation of the higher-order system. In this paper, a system of state-space equations is established based on the second-order equivalent circuit model, and a simplified-sphere sample approach is used to improve the Unscented Kalman Filter (UKF) algorithm. The SOC estimation performance of the three algorithms is tested under constant current discharge, pulse discharge conditions, and UDC conditions, respectively. The simulation results show that Simplified-spherical Unscented Kalman Filtering (SUKF) has smaller errors between SOC estimation and theoretical reference values than EKF and UKF. The SUKF is less computationally intensive than UKF and has better timeliness in the onboard battery management system.