Model-based estimation of the internal states of the battery is very robust and accurate. However, separate estimation of the states, such as State-of-Charge (SOC), State-of-Health (SOH), and State-of-Power (SOP), leads to erroneous estimation since the states are highly interdependent. This paper proposes a co-estimation methodology using a highly accurate and stable Dual Square Root Unscented Kalman filter. Using experimental battery test data, the co-estimated SOC has an estimation error of 0.44%, which is 77.60% more accurate than separate state estimation using the D-SRUKF estimation and 58.02% more accurate than the EKF-RLS co-estimation method. Comparing SOH estimation to the most recent EKF-RLS co-estimation, the accuracy has also increased by 16.98%.