Research into statistical distributions of φ, λ and two-dimensional (2D) position errors of the global positioning system (GPS) enables the evaluation of its accuracy. Based on this, the navigation applications in which the positioning system can be used are determined. However, studies of GPS accuracy indicate that the empirical φ and λ errors deviate from the typical normal distribution, significantly affecting the statistical distribution of 2D position errors. Therefore, determining the actual statistical distributions of position errors (1D and 2D) is decisive for the precision of calculating the actual accuracy of the GPS system. In this paper, based on two measurement sessions (900,000 and 237,000 fixes), the distributions of GPS position error statistics in both 1D and 2D space are analysed. Statistical distribution measures are determined using statistical tests, the hypothesis on the normal distribution of φ and λ errors is verified, and the consistency of GPS position errors with commonly used statistical distributions is assessed together with finding the best fit. Research has shown that φ and λ errors for the GPS system are normally distributed. It is proven that φ and λ errors are more concentrated around the central value than in a typical normal distribution (positive kurtosis) with a low value of asymmetry. Moreover, φ errors are clearly more concentrated than λ errors. This results in larger standard deviation values for φ errors than λ errors. The differences in both values were 25–39%. Regarding the 2D position error, it should be noted that the value of twice the distance root mean square (2DRMS) is about 10–14% greater than the value of R95. In addition, studies show that statistical distributions such as beta, gamma, lognormal and Weibull are the best fit for 2D position errors in the GPS system.

中文翻译：

---

全球定位系统位置误差与典型统计分布的一致性分析

统计分布研究φ,λ全球定位系统 (GPS) 的二维 (2D) 位置误差可以评估其准确性。基于此，确定可以使用定位系统的导航应用。然而，对 GPS 精度的研究表明，经验φ和λ误差偏离典型的正态分布，显着影响二维位置误差的统计分布。因此，确定位置误差（一维和二维）的实际统计分布对于计算 GPS 系统实际精度的精度具有决定性意义。在本文中，基于两个测量会话（900,000 和 237,000 次定位），分析了 GPS 位置误差统计在 1D 和 2D 空间中的分布。统计分布测量是使用统计检验确定的，关于正态分布的假设φ和λ误差进行验证，并评估 GPS 位置误差与常用统计分布的一致性，并找到最佳拟合。研究表明，φ和λGPS 系统的误差呈正态分布。事实证明φ和λ与具有低不对称值的典型正态分布（正峰度）相比，误差更集中在中心值附近。而且，φ错误显然比λ错误。这导致更大的标准偏差值φ错误比λ错误。两个值的差异为 25-39%。关于 2D 位置误差，需要注意的是两倍距离均方根 (2DRMS) 的值比 R95 的值大 10-14% 左右。此外，研究表明，β、伽马、对数正态和 Weibull 等统计分布最适合 GPS 系统中的二维位置误差。