Single channel Blind Source Separation (SCBSS) is a challenging problem for several real-world practical applications. The existing SCBSS methodologies depend upon the properties of the sources present in the mixture and hence do not remain truly blind. Also, the solutions are found to be suboptimal and limited in application. In this paper, we present an SCBSS methodology using a state-parameter estimation approach to eliminate the constraints on the source signals such as statistical independence and frequency disjoint spectra. A Dual Square Root Unscented Kalman Filter (D-SRUKF) estimator has been proposed, which demonstrates higher numerical accuracy and improved stability compared to the widely used Dual Extended Kalman Filter (D-EKF). The proposed methodology demonstrates higher Signal-to-Interference Ratio (SIR) and Signal-to-Distortion Ratio (SDR) when the current methodologies even fail to separate the sources. The results also show that the proposed D-SRUKF SCBSS is 15% more accurate than the state-of-the-art D-EKF SCBSS and has higher stability owing to the square root formulation of the D-SRUKF source estimator.