In this paper, a comparative study on the state of charge (SOC) estimation of the lithium-rich manganese-based battery (LRMB) has been conducted by systematically considering the equivalent circuit model (ECM), aging state and algorithms. The results show that the first-order RC model combined with the Extended Kalman filter (EKF) is more suitable for the SOC estimation of the LRMB when the battery decays less severely. The maximum value of root mean square error of SOC estimation error no exceeds 1.6 % under various dynamic operating conditions, which can well meet the practical application. Besides, the first-order model based EKF algorithm occupies least computing resource and simultaneously possesses the best convergence velocity against the initial SOC value deviation. When the LRMB suffers a severe aging, the SOC estimation performance decreases significantly with the max error exceeding 6 %, to overcome this, a new algorithm combined deep learning and Extend Kalman filter (EKF) is proposed, which exhibit high SOC estimation accuracy with the RMSE less than 0.16 %. In summary, a systematic study about the SOC estimation of LRMB has been carried out, which can provide great guidance for the future engineering application of LRMB.