<p>Lithium-ion power batteries are the core components of new energy vehicles, but many core parameters of batteries such as internal temperature and state of charge (SOC) are difficult to observe due to a variety of constraints. Accurate estimation of the internal temperature and SOC of the battery is of great significance for monitoring the state of the battery, ensuring the smooth operation of the battery, and helping to extend the battery life. In this paper, electrochemical impedance spectroscopy (EIS) is used to study the external characteristics of the battery, and the internal temperature and SOC of the battery are estimated. The EIS data of the battery at different temperature and SOC were measured by EIS experiment. The relationship between temperature and EIS is established by fusing the model based on imaginary part impedance and the model based on impedance mechanism. The improved particle swarm optimization (IPSO) algorithm identifies the parameters of the fractional order model with double ZARC elements. An adaptive algorithm is used to correct the noise matrix of UKF in real time, and FOM is merged to form Adaptive Fractional Order Unscented Kalman Filter (AFOUKF) algorithm to achieve high precision SOC estimation. The estimation error of the proposed algorithm is less than 0.4% and has certain robustness. A bench test platform based on Typhoon HIL602 + hardware-in-the-loop equipment was built. Experiments show that AFOUKF algorithm can accurately estimate SOC within 0.7% under the condition of measurement noise.</p> Graphical Abstract <p></p>