Aiming at the coupling relationship between the three key states of battery (state of charge -- SOC, state of health -- SOH, state of power -- SOP), and considering that their estimation accuracy is affected by the time-varying internal parameters of battery and other factors, an online joint estimation algorithm of battery key states based on Autoregressive equivalent circuit model (AR-ECM) is proposed. The method proposes a new battery ECM based on the AR model, and gives the state space equation that characterizes the SOC，SOH and internal voltage drop of the battery simultaneously, as well as the differentiated parameter updating strategy. Based on this, considering the problem that the state equation is prone to non-positive definiteness, the Square Root Unscented Kalman Filter (SR-UKF) algorithm is used to achieve the joint estimation of the battery states. The advantage of this algorithm is that it truly achieves the joint estimation of the key battery states and ECM parameters, which is more in line with the practical engineering application requirements. The simulation verification shows that the joint estimator can obtain high accuracy and stability under noise disturbance.