Systems and Methods for Attitude Propagation for a Slewing Angular Rate Vector

Computer-based systems and methods for determining attitude of a moveable object. Attitude is determined by a transformation matrix {right arrow over (U)} from a body coordinate frame of the moveable object to an inertial reference frame. The transformation matrix is determined by: (i) determining a slew rate vector, {right arrow over (.alpha.)}, for time t.sub.N for the moveable object that represents a change in direction of an angular rate vector, {right arrow over (.omega.)}, for the moveable object over the time interval from t.sub.N-1 to t.sub.N in the body coordinate frame; (ii) determining an update to the transformation matrix for time t.sub.N that is based on a product of two matrices, the first matrix being related to a sum of {right arrow over (.omega.)} and {right arrow over (.alpha.)}, and the second matrix being related to -{right arrow over (.alpha.)}; and (iii) multiplying a transformation matrix for time t.sub.N-1 and the update to the transformation matrix for time t.sub.N to obtain the transformation matrix for time t.sub.N.