A flexible polarization demultiplexing method based on an adaptive Kalman filter (AKF) is proposed in which the process noise covariance has been estimated adaptively. The proposed method may significantly improve the adaptive capability of an extended Kalman filter (EKF) by adaptively estimating the unknown process noise covariance. Compared to the conventional EKF, the proposed method can avoid the tedious and time consuming parameter-by-parameter tuning operations. The effectiveness of this method is confirmed experimentally in 128 Gb/s 16QAM polarization-division-multiplexing (PDM) coherent optical transmission systems. The results illustrate that our proposed AKF has a better tracking accuracy and a faster convergence (about 4 times quicker) compared to a conventional algorithm with optimal process noise covariance.