Lightning strokes can cause an ultrafast rotation of the state of polarization (RSOP) in an optical ground wire cable, which leads to communication interruptions. To address this, a simplified radius-directed linear Kalman filter (S-RD-LKF) for blind polarization demultiplexing was developed. The ultrafast RSOP under thunderstorm weather conditions was simulated based on the Heidler model, and the simulation results indicated that the proposed S-RD-LKF algorithm effectively compensated for the RSOP impairment caused by the first and subsequent lightning strokes. Moreover, the RD-LKF algorithm and the proposed S-RD-LKF algorithm exhibited a similar performance; however, the computation complexity of the proposed algorithm was lower.