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This paper presents two alternative methods for moving long baseline (MLBL) navigation of autonomous underwater vehicles (AUVs). In both methods 13-bit messages are broadcasted from transponders on the moving target ship to the AUV. These messages provided both range and state information about the target ship. The first method uses an extended Kalman filter (EKF) based on a relative coordinate system fixed to a moving target ship. The second method uses two EKFs, one to estimate the state of the target ship, and a second to estimate the state of the AUV itself. Both methods performed similarly in simulation. Further simulations utilizing field test data showed the global approach to be more robust to the target ship dynamics and message broadcast timing cycle.