Vibratory gyroscopes can work as an angle sensor as well as an angular rate sensor by changing the operating algorithm without hardware modification. Angle sensor has advantages over rate senor in that it does not have numerical divergence issue when we want to obtain angle information. While an ideal vibratory sensor will output perfect information of rotational angle, real vibrator has natural frequency split and asymmetric quality factor (Q-factor). For working as an angle sensor, an algorithm for parameter estimation and compensation of vibratory gyros with these non-ideal parameters is proposed. For initialization of the gyro, rate sensor mode is adopted in the initial stage and the control mode switches to angle measurement mode. Simulation model is set up and numerical simulation is performed to verify proposed algorithm.