A simple and effective phase demodulation method is 3  ×  3 coupler demodulation, owing to its simpler structure than phase-generated carrier demodulation. However, it is difficult to obtain ideal demodulation results because of the diversity of noise sources in an optical fiber sensor system, particularly due to polarization fading. We present a noise processing method based on morphological filtering. First, the characteristics of various noises and their effects on the demodulation of a 3  ×  3 coupler are analyzed. Subsequently, the polarization fading phenomenon in a single-mode fiber is analyzed, and the effect of polarization fading on the elliptic fitting demodulation of 3  ×  3 couplers is described. The method uses morphological filtering based on an elliptic template to overcome the distortion in the demodulation signal due to polarization fading and other factors. Simulation and experimental results show that the proposed method can improve the stability and precision of phase demodulation technology based on the 3 × 3 coupler.