Abstract: To investigate the observability of a strapdown inertial navigation system, on the basis of piece-wise constant system's observability and singular value decomposition, the variation of singular value in the observability matrix with time is discussed. Simulation results reveal that the system observability is determined mainly by the orientation angle,the maximum of minimal singular value is attained when the direction reaches 180 degree, it changes fastest in the range from 0 to 90 degrees and changes less with the pitch and roll angles. The degree of observability is determined by the pitch angle and ranges from 10 to 20 degrees, The article provides a theoretical foundation for the study of the fast and accurate alignment of SINS.