Overbounding SBAS and GBAS Error Distributions with Excess-Mass Functions
Overbounding SBAS and GBAS Error Distributions with Excess-Mass Functions
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发表时间：
2004
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通讯作者：
J. Rife;T. Walter;J. Blanch
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作者：
J. Rife;T. Walter;J. Blanch
生命安全 GNSS 增强系统必须限制危险导航错误发生的概率。本文通过使用过剩质量函数，为天基增强系统（SBAS）和地基增强系统（GBAS）开发保守边界方法。超额质量概念采用积分密度大于统一的保守边界函数，用于开发两种新的边界策略，其中第一个侧重于概率密度函数（EMP 超界），第二个侧重于累积分布函数（EMC 超界）。这些策略可以限制任意误差分布，甚至是不对称、多峰或非零均值的误差分布。为了相互比较这两种策略以及与配对 CDF 越界和矩越界等现有方法，引入了一组指标来评估实际误差分布中给定异常的越界性能。这些性能指标为特定于应用程序的权衡研究提供了基础，该研究将平衡各种越界方法的可用性优势与广播信号和保护限制所需的修改。在一般情况下，假设所有卫星的误差源相同并忽略广播消息带宽限制，性能指标有利于 EMC 方法，该方法严格限制未知偏差和重尾误差。 EMC 方法的主要缺点是它对采样误差分布中的异常值敏感。
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.