<div>This research investigates the detection and exclusion of faulty global navigation satellite system (GNSS) measurements using a parameterized quadratic programming formulation (PQP) approach. Furthermore, the PQP approach is integrated with the integrity risk and continuity risk bounds of the Chi-squared advanced receiver autonomous integrity monitoring (ARAIM). The integration allows for performance evaluation of the PQP approach in terms of accuracy, integrity, continuity, and availability, which is necessary for the PQP approach to be applied to the vertical navigation in the performance-based navigation (PBN). In the case of detection, the PQP approach can also be integrated with the vertical protection level and the associated lower and upper bounds derived for the solution separation ARAIM. While there are other computationally efficient and less computationally efficient fault detection and</div><div>exclusion methods to detect and exclude faulty GNSS measurements, the strength of the PQP approach can summarized from two different perspectives. Firstly, the PQP</div><div>approach belongs to the group of the computationally efficient methods, which makes the PQP approach more favorable when it comes to detect and exclude multiple simultaneous faulty GNSS measurements. Secondly, because of the integration of the PQP approach with the integrity risk and continuity risk bounds of the Chi-squared</div><div>ARAIM, the PQP approach is among the first computationally efficient fault detection and exclusion methods to incorporate the concept of integrity, which lies in</div><div>the foundation of PBN. Despite the PQP approach not being a practical integrity monitoring method in its current form because of the combinatorial natural of the integrity risk bound calculation and the rather conservative integrity performance, further research can be pursued to improve the PQP approach. Any improvement on the integrity risk bound calculation for the Chi-squared ARAIM can readily be</div><div>applied to the integrity risk bound calculation for the PQP approach. Also, the connection between the PQP approach and the support vector machines, the application of the extreme value theory to obtain a conservative tail probability may shed light upon the parameter tuning of the PQP approach, which in turn will result in tight integrity risk bound.</div>