To solve the Bit errors caused by rapid polarization rotation in fiber optic links, this paper analyzes the specific representation of matrix coefficients in Kalman filters for polarization demultiplexing scenarios and proposes an extended simplified Kalman filter design. The proposed approach transforms the update process into a multi-input multi-output structured algorithm. The performance of this algorithm was validated in a coherent 28 GBaud polarization-multiplexed quadrature phase-shift keying system. The results show that the algorithm complexity is reduced by more than 30% compared to the constant modulus algorithm, and it has the ability to balance polarization rotation speeds exceeding 60 Mrad/s at an optical signal-to-noise ratio of 15 dB; Compared to the classical extended Kalman filter, it has an additional optical signal-to-noise ratio margin of about 3 dB.