Traditional orthogonal strapdown inertial navigation system(SINS) cannot achieve satisfactory selfalignment accuracy in the stationary base: taking more than 5 minutes and all the inertial sensors biases cannot get full observability except the upaxis accelerometer. However, the full skewed redundant SINS(RSINS) can not only enhance the reliability of the system, but also improve the accuracy of the system, such as the initial alignment. Firstly, the observability of the system state includes attitude errors and all the inertial sensors biases are analyzed with the global perspective method: any three gyroscopes and three accelerometers can be assembled into an independent subordinate SINS(subSINS); the system state can be uniquely confirmed by the coupling connections of all the subSINSs; the attitude errors and random constant biases of all the inertial sensors are observable. However, the random noises of the inertial sensors are not taken into account in the above analyzing process. Secondly, the fullobservable Kalman filter which can be applied to the actual RSINS containing random noises is established; the system state includes the position, velocity, attitude errors of all the subSINSs and the random constant biases of the redundant inertial sensors. At last, the initial selfalignment process of a typical fourredundancy full skewed RSINS is simulated: the horizontal attitudes(pitch, roll) errors and yaw error can be exactly evaluated within 80 s and 100 s respectively, while the random constant biases of gyroscopes and accelerometers can be precisely evaluated within 120 s. For the full skewed RSINS, the selfalignment accuracy is greatly improved, meanwhile the selfalignment time is widely shortened. Traditional orthogonal strapdown inertial navigation system (SINS) can not achieve perfectly self-alignment accuracy in the stationary base: taking more than 5 minutes and all the inertial sensors biases can not get full observability except the upaxis accelerometer. However, the full skewed redundant SINS (RSINS) can not only enhance the reliability of the system, but also improve the accuracy of the system, but also improve the accuracy of the system, but also improve the accuracy of the system, but also improve the accuracy of the system, but also improve the accuracy of the system three gyroscopes and three accelerometers can be assembled into an independent subordinate SINS (subSINS); the system state can be uniquely confirmed by the coupling connections of all the subSINSs; the attitude errors and random constant biases of all the inertial sensors are observable. However, the random noises of the inertial sensors are not taken into account in the above analyzing process Secondly, the fullobservable Kalman filter which can be applied to the actual inerted sensors, RSINS containing random noises is established; the system state includes the position, velocity, attitude errors of all the subSINSs and the random constant biases of the redundant inertial sensors. At last, the initial selfalignment process of a typical fourredundancy full skewed RSINS is simulated: the horizontal attitudes (pitch, roll) errors and yaw errors can be precisely evaluated within 80 s and 100 s respectively, while the random constant biases of gyroscopes and accelerometers can be precisely as within 120 s. For the full skewed RSINS, the selfalignment accuracy is greatly improved, meanwhile the selfalignment time is widely shortened.