Protection Level Calculation Using Measurement Residuals: Theory and Results-猫眼课题宝

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2005-09

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作者：

J. Blanch;T. Walter;P. Enge

在卫星导航的生命安全应用中，保护水平(PL)方程将已知的伪距误差转化为对定位误差的可靠限制。目前的星载增强系统的概率谱方程都是基于高斯统计的：所有的误差都服从零均值高斯分布，在某种意义上它是真实分布的上界。该方法计算简单，接收端计算量小，具有很强的实用性。然而，当真实分布远不是高斯分布时，这种特征会迫使保护水平膨胀，从而损害性能。这尤其发生在具有重尾分布的误差或没有足够的数据来评估直到小分位数的分布密度的误差的情况下。由于接收器级别的计算能力预计会增加，因此值得探索计算完整性误差界的新方法。给出了伪距误差为混合高斯模式时最优保护电平的计算方法。首先，我们展示了这种错误表征增加了新的灵活性，并有助于在不损失紧凑核心分发的好处的情况下解决繁重的尾部。然后，我们使用贝叶斯方法来描述定位问题。最后，我们将该方法应用于广域增强系统(WAAS)接收机的实际数据保护水平计算。结果非常有希望：垂直保护级别降低了50%，而不会损害完整性。未来十年，用于卫星导航的伪距信号源的数量和质量预计将大幅增加：美国将在现代化的GPS中增加两个新的民用频率(L5和L2C)，欧洲计划发射伽利略卫星，它应该在2015年前全面运行，也具有多个频率。通过组合两个频率，用户将能够消除电离层延迟，这是目前最大的误差，从而将名义误差范围减少50%以上。特别是，使用增强系统的生命安全应用程序将大大增强。然而，提供小的硬误差界限保护级别--以满足严格的导航要求--仍将是一个挑战。机载多路径、星历误差、(赤道区)闪烁造成的信号损失仍然是提供Cat III全球导航卫星系统增强系统路径上的一个挑战。例如，即使使用双频，仅带有GPS的广域增强系统(WAAS)在美国也不能100%满足APV II(垂直20米)的可用性[1]。有许多方法可以在不改变报文标准的情况下提高SBAS的性能[2]：通过增加卫星、通过增加参考站、通过改进主站的算法(特别是时钟和星历算法)。然而，现在正在开发新的L5 MOPS，探索对消息内容进行可能的修改以提高性能是值得的。当前为增强系统用户提供完整性的方法是基于高斯上界技术的。对于每个误差源，用户都会收到对应于误差的高斯上界的标准偏差。因此，在某种意义上，每个伪距误差源都需要在危险误检概率(10)[3]的数量级上被高斯分布约束到非常小的分位数。这是一项非常困难的任务：例如，由于条件和环境总是在变化，因此不可能具有误差的实验平稳分布。此外，所有的错误都混在一起，所以很难将它们分离出来。因此，有必要增加高斯上界，以确保覆盖各个误差分布的尾部。然而，通过这样做，我们忽略了这样一个事实，即分布的核心通常比过界(大因素)紧得多，从而放弃了性能[4]、[5]。在这篇文章中，我们提出了一种用高斯混合来表征误差的估计方法。通过使用贝叶斯方法，该技术最佳地利用了误差分布的紧密核心，而

In safety-of-life applications of satellite navigation, the Protection Level (PL) equation translates what is known about the pseudorange errors into a reliable limit on the positioning error. The current PL equations for Satellite based augmentation systems are based on Gaussian statistics: all errors are characterized by a zero mean Gaussian distribution which is an upper bound of the true distribution in a certain sense. This approach is very practical: the calculations are simple and the receiver computing load is small. However, when the true distributions are far from Gaussian, such characterization forces an inflation of the protection levels that damages performance. This happens in particular with error with heavy tail distributions or errors for which there is not enough data to evaluate the distribution density up to small quantiles. Because the computing power is expected to increase at the receiver level, it is worthwhile exploring new ways of computing integrity error bounds. We present a way of computing the optimal protection level when the pseudorange 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 protection level calculations for the Wide Area Augmentation System (WAAS) using real data from WAAS receivers. The results are very promising: Vertical Protection Levels are reduced by 50% without damaging integrity. INTRODUCTION In the next ten years the number of pseudorange sources for satellite navigation and their quality is expected to increase dramatically: The United States is going to add two new civil frequencies (L5 and L2C) in the modernized GPS, and Europe is planning to launch Galileo which should be fully operative before 2015, also with multiple frequencies. By combining two frequencies, users will be able to remove the ionospheric delay which is currently the largest error, thus reducing nominal error bounds by more than 50%. In particular, safety-of-life applications using augmentation systems will be greatly enhanced. However, it will remain a challenge to provide small hard error bounds Protection Levels – to meet stringent navigation requirements. Airborne multipath, ephemeris error, loss of signal due to scintillation (in equatorial regions), are still a challenge in the path to provide Cat III GNSS augmentation systems. For example, even with dual frequency, it is not obvious that the Wide Area Augmentation System (WAAS) with GPS alone would meet 100% APV II (20 meters vertical) availability over the United States [1]. There are many ways to improve the performance of an SBAS without changing the message standards [2]: by adding satellites, by adding reference stations, by improving the algorithms at the master station (specially the clock and ephemeris algorithms). It is worthwhile however, now that the new L5 MOPS is being developed, to explore possible modifications to the message content to improve performance. The current methodologies to provide integrity to augmentation system users are based on Gaussian overbounding techniques. For every source of error, the user receives a standard deviation that corresponds to the Gaussian overbound of the error. For this reason, every source of pseudorange error needs to be overbound, in a certain sense, by a gaussian distribution up to very small quantiles on the order of the probability of hazardously misdetection (10) [3] This is a very difficult task: for example, it is not possible to have experimental stationary distributions for the errors because the conditions and environment are always changing. Also, the errors are all mixed together so it is hard to isolate them. As a result, it is necessary to increase the Gaussian overbound to be sure to cover the tails of the individual error distributions. However, by doing so, we ignore the fact that the core of the distribution is usually much tighter than the overbound (by a large factor), thus giving up performance [4], [5]. In this paper, we present an estimation technique where errors are characterized by Gaussian mixtures. By using a bayesian approach, this technique optimally takes advantage of the tight core of the error distributions while

Protection Level Calculation Using Measurement Residuals: Theory and Results

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