Polarization navigation has been an active research direction in navigation fields due to its autonomy and robustness, especially in global navigation satellite system-denied environment. Most existing bionic polarization sensing schemes employed the linear polarizer as the analyzer. However, the quadrature error between the two sets of mutually orthogonal polarizers is usually inevitable, which may cause the sensor output distortion and directly affect the performance of polarization navigation sensors. In this paper, inspired by the special polarization-sensitive structure of insect compound eyes, a polarizing beam splitter (PBS) based polarization navigation sensor is designed. Concerned with the optical path coupling and extinction ratio inconsistency problem between the transmitted beam and the reflected one of the PBS, the novel sensor model is established, where we introduce a coupling coefficient to solve the problems mentioned above. An algorithm of computing the polarization degree and the polarization azimuth angle is presented based on the model. The unscented Kalman filter calibration method is adopted and the calibration experiments are carried out. Finally, the outdoor static accuracy of the sensor is tested, where the results showed that the sensor designed in this paper achieved high accuracy and good stability for a long time.