Accurate detection and exclusion of faulty measurements is the key for advanced receiver autonomous integrity monitoring (ARAIM) to ensure the safety of navigation service in the aviation field. With the deployment of new constellations such as Beidou and GLONASS, the number of fault modes to be monitored increases sharply, and it is difficult for traditional ARAIM to take into account the success rate and computational efficiency at the same time by using recursive search method. This paper presents a multi-constellation ARAIM fault exclusion method based on maximum a posteriori probability (MAP). On the one hand, this method realizes the risk control of misarrangement of healthy satellites by combining the prior probability information of faulty measurements. On the other hand, the posterior probability distribution model of faulty measurements under the hypothesis of potential failure mode is accurately constructed based on the maximum likelihood estimation to avoid the occurrence of incomplete exclusion events of faulty measurements. Additionally, this article incorporates the suggested MAP fault exclusion approach with the fault feature judgment of faulty measurements to create an ARAIM fault exclusion framework that enhances fault exclusion efficiency. Simulation and experimental results show that, compared with the traditional ARAIM fault exclusion method, the proposed method can improve ARAIM fault exclusion efficiency and ensure the accuracy of fault exclusion in both single-satellite and multi-satellite fault scenarios.