Consistency analysis of global positioning system position errors with typical statistical distributions

Research into statistical distributions of phi, lambda 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 phi and lambda 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 phi and lambda 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 phi and lambda errors for the GPS system are normally distributed. It is proven that phi and lambda errors are more concentrated around the central value than in a typical normal distribution (positive kurtosis) with a low value of asymmetry. Moreover, phi errors are clearly more concentrated than lambda errors. This results in larger standard deviation values for phi errors than lambda 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.

Automated summary

Research on statistical distributions of phi, lambda, and 2D position errors in the GPS system shows that phi and lambda errors are normally distributed with concentrations around central values. The 2D position error, measured by 2DRMS, is slightly higher than R95. Statistical distributions such as beta, gamma, lognormal, and Weibull are found to be the best fit for 2D position errors in the GPS system.