The ARS(Attitude Reference System) calculates an attitude of a vehicle using inertial angular rate sensors and acceleration sensors. The attitude error of ARS increases due to the integration of angular rate sensor output. To reduce the attitude error an acceleration of sensor is used similar to leveling method of INS(Inertial Navigation System). When an acceleration of vehicle is increased, it is difficult to calculate the attitude error using acceleration sensor output. In this paper the estimation method of acceleration due to the attitude error only is proposed. Two methods of the attitude calculation depending on vehicle dynamics and the integration method of these two methods are proposed. To verify its performance the monte carlo simulation is performed and shows that it bounds attitude error of ARS to reasonable level.