Extreme Value Overbounding With the Aid of Samples From Distribution Core in GNSS Augmentation System

In GNSS augmentation system, the error distribution model is established to characterize the real error distribution. By the character of approximating the real distribution, Extreme Value Theory (EVT) can be utilized to analyze and model the distribution tail. Nevertheless, only a little part of samples, which are from the distribution tail, is used by EVT. The variation caused by statistical uncertainty is big on the condition that the sample space is limited. For this reason, it is difficult to estimate model parameters with high precision. An extreme value overbounding method with the aid of samples from distribution core is proposed in this paper to establish error distribution model precisely. By the assumption that the CDF of the model is continuous and derivable, the relationship between distribution core and tail is established. Profile likelihood estimation is used to estimate model parameters, and the confidence upper bound of quantile, which is corresponding to the required integrity risk, is calculated by delta method. Experimental results show that, with the method mentioned above, the standard deviations of estimated model parameters are reduced, the accuracy of model is increased, and the error distribution can be overbounded more precisely.