To enhance the safety of marine navigation, one needs to consider the involvement of the automatic identification system (AIS), an existing system designed for ship-to-ship and ship-to-shore communication. Previous research on the quality of AIS parameters revealed problems that the system experiences with sensor data exchange. In coastal areas, littoral AIS does not meet the expectations of operational continuity and system availability, and there are areas not covered by the system. Therefore, in this study, process models were designed to simulate the tracking of vessel trajectories, enabling system failure detection based on integrity monitoring. Three methods for system integrity monitoring, through hypotheses testing with regard to differences between model output and actual simulated vessel positions, were implemented, i.e., a Global Positioning System (GPS) ship position model, Dead Reckoning and RADAR Extended Kalman Filter (EKF)—Simultaneous localization and mapping (SLAM) based on distance and bearing to navigational aid. The designed process models were validated on simulated AIS dynamic data, i.e., in a simulated experiment in the area of Gdańsk Bay. The integrity of AIS information was determined using stochastic methods based on Markov chains. The research outcomes confirmed the usefulness of the proposed methods. The results of the research prove the high level (~99%) of integrity of the dynamic information of the AIS system for Dead Reckoning and the GPS process model, while the level of accuracy and integrity of the position varied depending on the distance to the navigation aid for the RADAR EKF-SLAM process model.