The accurate estimation of the state of charge (SOC) of lithium-ion batteries plays an important role in the performance and safety of the battery management system (BMS) of clean-energy vehicles. To improve the accuracy of SOC estimation, in this study, the ternary lithium-ion battery is taken as the research object. With a second-order RC equivalent circuit model, a bias compensated recursive least squares (BCRLS) is constructed for online parameter identification and weakens the influence of uncertain noise. Building on this, the multi-innovation unscented Kalman filter (MIUKF) algorithm is proposed to estimate the SOC of the lithium-ion batteries, which improves the accuracy and stability of the prediction results of high-strength nonlinear lithium-ion battery system. To verify the rationality of the constructed SOC estimation model, the SOC is estimated under different working conditions. The experimental results show that when the system is stable, the error of SOC estimation under HPPC and BBDST working conditions is stably controlled by 1.61% and 1.43% respectively. The results show that the BCRLS-MIUKF can estimate lithium-ion SOC with high precision and strong robustness. The proposed algorithm lays a foundation for the efficient operation of BMS.