Overbounding SBAS and GBAS Error Distributions with Excess-Mass Functions

Safety-of-life GNSS augmentation systems must provide bounds on the probability with which hazardous navigation errors occur. This paper develops conservative bounding methods both for space-based augmentation systems (SBAS) and for ground-based augmentation systems (GBAS) by using excess-mass functions. The excess-mass concept, which employs conservative bounding functions with integrated density greater than unity, is applied to develop two new bounding strategies, of which the first focuses on probability density functions (EMP overbounding) and the second on cumulative distribution functions (EMC overbounding). These strategies can bound arbitrary error distributions, even those that are asymmetric, multimodal, or non-zero mean. To compare the two strategies to each other, and to existing methods such as paired-CDF overbounding and moment overbounding, a set of metrics are introduced to evaluate overbound performance given anomalies in the actual error distribution. These performance metrics provide a basis for application-specific trade studies that would balance the availability benefits of various overbounding methods against required modifications to the broadcast signal and protection limits. In the generic case, assuming identical error sources for all satellites and neglecting broadcast-message bandwidth constraints, the performance metrics favour the EMC approach, which tightly bounds unknown biases and heavy-tailed errors. The major drawback of the EMC approach is its sensitivity to outliers in sampled error distributions.