A significant anomaly of great importance for ground-based augmentation systems (GBAS) is the steep gradient in ionospheric delays caused by rare ionospheric storms. To avoid such hazardous errors, code–carrier divergence (CCD) monitors have been applied to support the use of GBAS in CAT-I operation. However, to meet the stricter requirements for CAT-II/III operation, it may be necessary to greatly improve the speed with which existing CCD monitors detect ionospheric gradients or develop an innovative divergence monitor. One way of obtaining stricter integrity is to detect anomalous divergence behavior more rapidly than the CCD monitor does. Therefore, we attempted to devise a divergence monitor in which the detection time is reduced by using the Kullback–Leibler information. In simulations and experimental results, we demonstrate that the proposed divergence measure is quite capable of detecting ionospheric anomalies that are hazardous to GBAS and is a very promising alternative for the detection of deviations. A comparison with existing CCD monitors shows its increased fault detectability, which enables it to sense even small ionospheric gradients more rapidly than typical monitors.