Advanced Receiver Autonomous Integrity Monitoring (ARAIM) is a further extension of the existing RAIM to provide vertical services using dual-frequency and multi-constellation satellite signals. It compares the difference between solutions of subsets in a monitoring list and those of all satellites and then judges whether the difference is within the theoretical error model. From the principle of the ARAIM algorithm, it can be seen that a priori fault probability generating a monitoring list and the error model of the measurements, collectively referred to as the model parameters, are crucial to ARAIM. However, the model parameters of ARAIM are set based on historical data in advance and completely independent of current measurements or data in the receiver. Once the model parameters dictating the ARAIM results are not conservative enough, additional potential integrity risks may be imposed, thus challenging the trust in ARAIM. For example, accidental multipath interference makes actual faults out of the monitoring list or fails the pseudorange error model to overbound the actual error. In order to solve this problem, this paper proposes a measurements-assisted ARAIM using a posteriori information of observed pseudoranges. Since measurement failures are extremely rare in stable GNSS, sparse estimation methods can be adopted to obtain possible pseudorange bias. Based on the posterior bias estimate, we supplement the monitoring list and validate the error models. This paper describes in detail how to construct the LASSO algorithm to estimate the pseudorange deviations, and simulations show that the proposed method detects faults more sensitively, thus satisfactorily supporting ARAIM.