“…In general, the relationships between alignment errors and sensor errors are often expressed in the navigation frame because only the analysis of alignment errors in the navigation frame is meaningful, since the final results of alignment need to be expressed in the navigation frame. For many alignment approaches (for instance, gyrocompass alignment and optimum alignment), the relationships can be written as [ 16 , 17 , 18 , 19 ]: where is the east alignment error, is the north alignment error, is the up alignment error, represents the east accelerometer error, represents the north accelerometer error, and represents the east FOG error. By utilizing the perturbation method, the correlation between and in this paper can be described as: where is the error matrix related to , , and , and denotes the error matrix of .…”