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Position error bound calculation for GNSS using measurement residuals

机译：使用测量残差计算GNSS的位置误差范围

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摘要

In safety-of-life applications of satellite navigation, the protection level (PL) equation translates what is known about the pseudo-range errors into a reliable limit on the positioning error. The current PL equations for satellite-based augmentation systems (SBAS) rely on Gaussian statistics. This approach is very practical: the calculations are simple and the receiver computation load is small. However, when the true distributions are far from Gaussian, such a characterization forces an inflation of the PLs that degrades performance. This happens in particular with errors with heavy tail distributions or for which there is not enough data to evaluate the distribution density up to small quantiles. We present a way of computing the optimal protection level when the pseudo-range errors are characterized by a mixture of Gaussian modes. First, we show that this error characterization adds a new flexibility and helps account for heavy tails without losing the benefit of tight core distributions. Then, we state the positioning problem using a Bayesian approach. Finally, we apply this method to PL calculations for the wide area augmentation system (WAAS) using real data from WAAS receivers. The results are very promising: vertical PLs are reduced by 50% without degrading integrity.
机译：在卫星导航的生命安全应用中，保护等级（PL）方程将有关伪距误差的已知信息转换为对定位误差的可靠限制。当前基于卫星的增强系统（SBAS）的PL方程依赖于高斯统计。这种方法非常实用：计算很简单，接收机的计算量很小。但是，当真实分布远离高斯分布时，这种表征会导致PL膨胀，从而降低性能。这种情况尤其发生在尾部分布较重的错误中，或者没有足够的数据来评估分布密度直至小分位数的情况。当伪距误差以高斯模式混合为特征时，我们提出了一种计算最佳保护等级的方法。首先，我们证明了这种错误特征描述增加了新的灵活性，并有助于解决粗尾问题而又不会失去紧密堆芯分布的好处。然后，我们使用贝叶斯方法陈述定位问题。最后，我们使用来自WAAS接收器的真实数据将此方法应用于广域增强系统（WAAS）的PL计算。结果非常令人鼓舞：垂直PL减少了50％，而不会降低完整性。

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