This paper presents a demodulation algorithm for automatic identification system (AIS) signals received by a satellite. The main contribution of this work is to consider the phase recovery problem for an unknown modulation index, coupled with a time-varying phase shift. The proposed method is based on a demodulator introduced in a previous paper based on a Viterbi-type algorithm applied to an extended trellis. The states of this extended trellis are composed of a trellis-code state and of a cyclic redundancy check state. The bit stuffing mechanism is taken into account by defining special conditional transitions in the extended trellis. This algorithm estimates and tracks the phase shift by modifying the Euclidean distance used in the trellis. Simulation results obtained with and without phase tracking are presented and compared in the context of the AIS system.