Online evaluation of battery State of Function (SOF) is crucial for battery management systems of autonomous mobile robots. Battery State of Charge (SOC) represents its remaining energy available, whereas internal resistance and capacity reflect its State of Health (SOH). In this paper, an improved equivalent circuit model is proposed to estimate SOC, internal resistance and capacity using an Unscented Kalman Filter (UKF). The proposed method not only estimates SOC, but also evaluates SOH and SOF. Experimental results have shown the effectiveness of the proposed method using resistive loads and a robot prototype for inspecting power transmission line.