Abstract: A fast alignment and calibration method of inertial navigation system (INS) were approached from a control theory point of view. Using the Lyapunov transformation was proposed for transforming the conventional strapdown inertial navigation system(SlNS)error model. And the equivalence of SINS and gimbaled inertial navigation system (GINS) error model was discussed. Using a semblable transformation which based on physical insight and the so-called pseudostates vector instead of the true states were proposed. Consequently, the observable error states are uncorrelated with the unobservable ones, and the best observable sub-space of INS was found. Based on the simplified model, the fast estimation methods for the azimuth error and calibrating the drift of gyroscopes were creatively proposed. It reveals that the azimuth error and the drift of gyroscopes can be entirely estimated from the estimation of leveling error rate, and without using gyro output signals.