An inertial ("INS")/GPS receiver uses injected alignment data to determine the alignment of the INS sub-system when the receiver is in motion during start-up. The alignment data is determined from parameterized surface information, measured GPS velocity, and a known or predetermined angular relationship between the vehicle on which the receiver is mounted and an inertial measurement reference, or body, frame associated with the accelerometers and gyroscopes of the inertial measuring unit ("IMU"). The parameterized surface information, which provides a constraint, may be the orientation of the surface over which the vehicle that houses the receiver is moving. The receiver uses the initial GPS position to determine the location of the vehicle on the parameterized surface, and thus, the known surface orientation. The receiver then determines the roll, pitch and heading of the vehicle on the surface using the associated GPS velocity vector. Thereafter, the receiver uses the calculated roll, pitch and heading of the vehicle and the known or predetermined angular relationship between the vehicle and the IMU body frame to determine a rotation matrix that relates the IMU body frame to a computation or referenced frame used by the receiver.