This paper addresses the problem of error correction of AIS messages by using the a priori knowledge of some information in the messages. Indeed, the AIS recommendation sets a unique value or a range of values for certain fields in the messages. Moreover, the physics can limit the range of fields, such as the speed of the vessel or its position (given the position of the receiver). The repetition of the messages gives also some information. Indeed, the evolution of the ship position is limited between messages and the ship ID is known. The constrained demodulation algorithm presented in this article is an evolution of the constrained Viterbi algorithm (C-VA). It is based on a modified Viterbi algorithm that allows the constraints to be considered in order to correct transmission errors by using some new registers in the state variables. The constraints can be either a single value or a range of values for the message fields. Simulation results illustrate the algorithm performance in terms of bit error rate and packet error rate. The performance of the proposed algorithm is 2 dB better than that obtained with the receiver without constraints.