The bionic polarization sensor (PS)/MEMS inertial measurement unit (MIMU) integrated system can provide reliable attitude and heading information for unmanned vehicles in the case of GNSS rejection. However, the existing measurement methods have poor adaptability to inclining, sheltering, and other harsh environments, and do not make full use of the complementary characteristics of the gyroscopes, accelerometers, and PS, which seriously affects the system performance. Therefore, this paper proposes an attitude and heading measurement method based on an adaptive complementary Kalman filter (ACKF), which corrects the gyroscopes according to the gravity measured by the accelerometers to improve the attitude accuracy and fuses the IMU heading and tilt-compensated polarization heading by Kalman optimal estimation. On this basis, the maximum correlation entropy of the measured gravity and the theoretical gravity is used to construct an adaptive factor to realize the adaptive complementary of the gyroscopes and the accelerometers. Finally, the effectiveness of the method is verified by the outdoor rotation test without occlusion and the vehicle test with occlusion. Compared with the traditional Kalman filter, the pitch, roll, and heading RMSE of the vehicle test are reduced by 89.3%, 93.2% and, 9.6% respectively, which verifies the great advantages.