The accurate estimation of battery state of charge (SOC) and state of energy (SOE) are the key technologies in researching battery management systems. Due to the uncertainty of prior noise in practical engineering, traditional cubature Kalman filters (CKF) have lower filtering accuracy. This paper proposes an improved limited memory-Sage Husa-cubature Kalman (LM–SH–CKF) algorithm to estimate the SOC and SOE of lithium-ion batteries. During the filtering process, the Sage-Husa estimator is introduced to estimate the noise, correcting the statistical characteristics of the noise in real-time, thereby improving the estimation accuracy. Meanwhile, establish a filtering divergence criterion to determine whether the filtering is abnormal and ensure the real-time performance of the algorithm. To improve the accuracy of parameter identification, the Hysteresis Effect-Dual Polarization (HE-DP) model is established and the limited memory recursive least square (LMRLS) algorithm is proposed. The results show that the LM–SH–CKF has the smallest mean absolute error (MAE) and root mean square error (RMSE). Under the dynamic stress test (DST) at 15 °C, the estimated MAE and RMSE of SOC and SOE are both less than 1 %. The LM–SH–CKF has high accuracy and robustness, and short calculation time, providing a reference for battery status monitoring.