<p>The aviation community is actively pursuing the multi-constellation advanced receiver autonomous integrity monitoring (ARAIM) to ensure the safety of aircraft navigation services. The fault detection and exclusion (FDE) is of significance for ARAIM because it improves the integrity and continuity of navigation services. However, the traditional FDE method in current multi-constellation ARAIM is primarily challenged by maintaining a high success rate of fault exclusion and low computational burden, simultaneously. In response, a maximum a posteriori probability (MAP) approach is proposed for the multi-constellation ARAIM FDE framework, and a fault exclusion method based on MAP (FE-MAP) is proposed. The FE-MAP employs a statistical approach known as the maximum likelihood estimation to analyze the error characteristics of measurements. Based on the posterior error distribution, the hypothesis with the maximum posterior probability is chosen to rapidly isolate faulty measurements. Meanwhile, an existing integrity risk evaluation model for fault exclusion is used to verify the correctness of exclusion. The advantages of the proposed method in avoiding the wrong exclusion have been comprehensively analyzed from both the theoretical and the simulation perspectives. The experimental results demonstrate that the proposed method can greatly enhance the success rate performance of fault exclusion while maintaining a high efficiency of ARAIM fault exclusion establishment.</p>