Abstract: Investigates the observability of SINS. On the basis of piece wise constant discrete system’s observability, a further discussion of parameter perturbation is done to the system, and a sufficient condition is given. The conclusion is applied to the three position alignment of strapdown systems. Simulation results reveal that on the range of 0 002 m·s -2 variation of gravity acceleration, it has little effect on the observability of the system. The minimum eigenvalue, number of conditions, reciprocal of trace are linear to the gravitational acceleration. The maximum eigenvalue of the perturbation system is a quadratic function of the gravitational acceleration. This demonstrates that the SINS observability is robust to the parameter perturbation.