An adaptive gyro compassing algorithm is designed based on Unfalsified Adaptive Control Theory (UAC) to solve the in-motion alignment problem of Inertial Navigation System (SINS).The typical way of solving the problem is through filtering,yet the major factor that affects the performance of the filters is the model error as well as the plant properties such as system noise,which make it not optimal as expected.Gyro compassing method is designed based on classical control theory,which can be viewed as a fixed gain PI controller.The control coefficients do not rely on the noise statistics.The problem of gyro compassing is that the controller gain need to be tuned to get good performance and thus is not optimal.Unfalsified Adaptive Control is introduced to fix this problem.UAC belongs to the class of control methods called adaptive supervisory switching control.It selects the best controller from a candidate controller set and switches it into the control loop by calculating the fictitious reference signal of each candidate controller,only using the information from the plant output.In this paper we designed a UAC gyro compassing algorithm which is independent to system model.