Aiming at the observability of the fixed position alignment of a strapdown inertial navigation system (SINS), the observability of each state variable of the system is analyzed by the method of singular value decomposition (SVD), in which the ten-state error equation of SINS is taken as the object of study. The results show that the state variables of the system are not completely observable and the azimuth misalignment angle has a low observability. In order to improve the observability of the alignment system, the state vector is reduced according to the results of observability analysis and the application characteristics of SINS, and the seven-order Kalman filtering model is obtained. Experimental results indicate that the seven-order model is more tolerant to the filter parameter and the navigation accuracy is higher than the original model．