In order to suppress the random drift and zero bias of the Hemispherical Resonator Gyro(HRG),and improve the azimuth self-alignment accuracy of the HRG inertial navigation platform，a four-position self-alignment method with drift compensation was designed for the HRG inertial navigation platform.An ARMA model of the HRG random drift was constructed for filtering the signal output from the gyro,thus to decrease the influence of the random drift and noise to the azimuth self-alignment accuracy.Experiments were made to the two-position and four-position schemes separately.The experiment result shows that,the alignment time of our four-position drift detecting scheme is equivalent to that of the traditional four-position scheme,but the accuracy of this scheme is 15.78′,which is better than that of the traditional two/four-position scheme ignoring the gyroscope drift.