A novel position domain overbounding method using pseudorange error model based on extreme value theory

In the protection level calculation of Ground Based Augmentation System (GBAS), overbounding method is employed to maintain distribution stable when mapping from pseudorange domain to position domain, for the real distribution of error may not be Gaussian. According to different order of overbounding and mapping, there are two ways to overbound position domain error. The one is overbounding pseudorange error by Gaussian distribution at first, and then mapping the Gaussian distribution to position domain by linear combination. The other is mapping the pseudorange error distribution to position domain by convolution, and then overbound. Limited by computing power of receiver onboard, the former one is commonly used, which avoid from convolution. However, the core of the distribution is usually much tighter than the overbound, and the availability is reduced. To obtain higher availability without consuming large amounts of computing resources, a novel position domain overbounding method is proposed in this paper. Pseudorange error is modeled on the base of extreme value theory at first, and the pseudorange error model is mapped to position domain to be overbounded without convolution. Experimental results show that, the vertical protection level of current GPS constellation is reduced without damaging integrity, while the computing resource consumption is acceptable.