An Ionosphere Estimation Algorithm for WAAS Based on Kriging
An Ionosphere Estimation Algorithm for WAAS Based on Kriging
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发表时间：
2002-09
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通讯作者：
J. Blanch
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作者：
J. Blanch
全球定位系统本身无法提供空中导航所需的完整性。几个误差源恶化的位置估计的精度。对于单频用户来说，最大和更不可预测的误差来源之一是电离层。因此，电离层行为驱动广域增强系统（WAAS）的性能。在任何给定的时间，我们对电离层的唯一信息是有限数量的总电子含量（TEC）测量。因此，为了估计电离层延迟并得到这样的估计的置信限，我们需要了解感兴趣区域上方电离层的空间结构。使用薄壳模型框架，其中每个TEC测量值被识别为薄壳上的一个位置，标记为电离层皮尔斯点（IPP），问题被简化为一个二维问题。一旦我们有一个很好的描述名义电离层，有两个问题，需要回答之前，估计在一个给定的IPP的延迟：IPP测量与假设的名义模型的电离层兼容？IPP测量与我们需要估计的位置有多大相关性？为了回答第一个问题，需要在标称条件下准确描述电离层的特性。大量观察到的平稳性违反使得后一个问题非常困难。提出了一种基于最坏情况的方法来确定标称电离层的空间结构的变异函数，或等效地，协方差。这种称为“克里金法”的技术在每个位置产生一个估计值和估计值的置信区间，即克里金方差。克里金方差在覆盖范围边缘的特殊行为使我们能够直观地定义“良好采样”区域。我们表明，一个精心设计的估计算法的基础上克里金可以提供电离层延迟校正的置信区间，使WAAS，以满足GNSS着陆系统的要求。
GPS alone cannot provide the integrity needed for air navigation. Several error sources deteriorate the precision of the position estimate. One of the largest and more unpredictable sources of error for single frequency users is the ionosphere. For this reason, ionospheric behavior drives the performance of the Wide Area Augmentation System (WAAS). At any given time, the only information we have of the ionosphere is a limited amount of Total Electron Content (TEC) measurements. As a consequence, in order to estimate the ionospheric delay and get a confidence bound on such an estimate, we need to understand the spatial structure of the ionosphere over the region of interest. Using the thin shell model framework, where each TEC measurement is identified as a location on the thin shell, labeled the Ionospheric Pierce Point (IPP), the problem is reduced to a 2-dimensional problem. Once we have a good description of a nominal ionosphere, there are two questions that need to be answered before estimating the delay at a given IPP: Are the IPP measurements compatible with the assumed nominal model of the ionosphere? How relevant are the IPP measurements to the location we need to estimate? To answer the first one, an accurate characterization of the ionosphere in nominal conditions is needed. The large observed stationarity violations make this latter question very difficult. A worst case based method to determine the spatial structure of the nominal ionosphere in terms of the variogram, or, equivalently, the covariance is presented. The technique called "kriging" produces at each location an estimate and a confidence bound on the estimate, the kriging variance. The particular behavior of the kriging variance at the edge of coverage allows us to intuitively define the "well sampled" region. We show that a carefully designed estimation algorithm based on kriging could provide confidence bounds on the ionospheric delay corrections allowing WAAS to meet the GNSS Landing System requirements.