A method of aligning an inertial navigation system or gyrocompass, including executing real-time navigation software on real-time inertial data to generate real-time navigation data, executing real-time Kalman filter software on the real-time navigation data and real-time aiding data, recording the real-time inertial data and the real-time aiding data as real-time input data in a buffer, initializing a playback process, executing playback navigation software on buffered inertial data to generate playback navigation data, and executing playback Kalman filter software on the playback navigation data and buffered aiding data. The execution of the real-time navigation software and the real-time Kalman filter software effect a real-time alignment process. The playback navigation software and the playback Kalman filter software effect an alignment process executed at a faster rate than the real-time navigation software and real-time Kalman filter software.