In the present disclosure, an error in the velocity and position computed from a three dimensional IMU measurement is reduced confined by computing an auxiliary speed in a drive direction of a vehicle from an angular velocity measurement and a lateral acceleration measurement. The auxiliary speed is then compared with the speed computed from the acceleration measurement. The auxiliary speed is provided as the speed of the vehicle mounted with the IMU when the absolute difference between the auxiliary speed and the speed computed from the acceleration measurement in the drive direction is above a threshold. The auxiliary speed is computed when the vehicle is detected to be in a curved motion. According to another aspect of the present disclosure, the bias errors are determined when the vehicle is in a steady state, at rest or in a straight line motion. The bias errors are used to obtain the accurate auxiliary measurement.