Real-time and accurate estimation of battery states has gained immense importance in recent years due to emerging applications of Battery Energy Storage Systems (BESS) in smart grid and Electric Vehicles. The behaviour of BESS modelled as a 2-RC Circuit and State-of-Charge (SOC) and RC parameter estimation using Unscented Kalman Filter (UKF) has emerged as an optimal model for online Battery Management Systems(BMS). However, the stability of UKF degrades due to error covariance matrix becoming ill-conditioned. This paper presents a dual Square Root Unscented Kalman Filter (SRUKF) based SOC and parameter estimation algorithms for BMS. The proposed SRUKF methodology improves the stability of the system as the square root form of the error covariance matrix always remains positive semi-definite. The methodology has been designed and implemented in MATLAB/Simulink and compared with dual EKF and state-of-the-art dual UKF algorithms. The results show that dual SRUKF is 74% more accurate than the state-of-the-art and remains stable once it converges to true SOC value.