Strapdown inertial navigation system (SINS) initial alignment error model is presented under moving base. SINS navigation error models and the integrated navigation error models are proposed. The state observability during the initial alignment under moving base was thoroughly studied according to the piece-wise constant system method and singular value decomposition method. Simulation experiments were carried out under different vehicle movements with same integration and different integration with same vehicle movements respectively. Simulation experiments show that the observability degree of states variables can be improved under linear or rotation movement, furthermore, the outer measurements aided SINS can also improve the observability degree of system state variables accordingly. The observability degree increases of state variables improve the accuracy of estimation and the speed of convergence of Kalman filter applied in the integrated inertial navigation system.