The hemispherical resonator gyroscope is a type of vibratory gyroscope, which can measure angle or angular rate, based on its operating mode. This paper deals with the case when the hemispherical resonator gyroscope is operated in angle measurement mode. In angle measurement mode, the resonator pattern angle precesses, with respect to the external rotation input, by the principle of the Coriolis effect, so that the external rotation can be estimated, by measuring the amount of precession angle. However, this pattern angle drifts, due to the manufacturing error of the resonator. Since the drift effect causes degradation of the angle estimation performance of the resonator, the corresponding drift compensation control should be performed, to enhance the estimation performance. In this paper, a mathematical model of the hemispherical resonator gyro is first introduced. By using the mathematical model, a nonlinear observer for imperfection parameter estimation, and the corresponding compensation controller are designed to operate hemispherical resonator gyros, as angle measurement sensors.