In a long baseline (LBL) acoustic positioning system, a navigation subject estimates its own position at a time based on the ranges between itself and the LBL transponders. To obtain the ranges, each transponder sends acoustic wave to the subjects receiver. Here, a range equals to time required by the wave to travel between these two points multiplied by the wave propagation speed. This method is known as the time of flight (ToF) measurement. One of the ideals in carrying out a ToF is that the navigation subject would remain still throughout the measurement. Corollary, position estimation based on the ToF holds on the same ideal. However, an acoustic wave propagates in a very low speed. Due to this characteristic, the displacement of a moving navigation subject like an autonomous underwater vehicle (AUV) may not be negligible and becomes a source of bias for the range estimations. The AUV motion would also lead to asynchronous ToFs, i.e. acoustic waves sent by transponders arrive at the AUV in different time epochs. In this paper, we present LBL navigation for an AUV that deals with uncertainty due to motion of the AUV. Here, state estimator is modeled while considering the bias for each ToF. Once we obtain the state space representation, we apply Kalman filter to estimate the AUV position and speed. By simulation, we demonstrate that the estimator follows the actual states with good accordance.