Optimization of Protection Level of GBAS with Gaussian Mixture Model

Abstract

The Gaussian mixture model (GMM) is commonly used to model the heavy tail of the ground-based augmentation system (GBAS) range error distribution. In practice, Gaussian over-bounding based on a GMM is used to over-bound the heavy tail of the ranging errors, but the GBAS protection levels (PLs) based on the Gaussian over-bounding tend to be overestimated. Based on the idea of solution separation and overcoming the shortcoming of its direct reference to GBAS, this paper analyses the constraint conditions and objective functions of the optimal protection level based on solution separation under a GMM distribution, and proposes that multi-hypothesis solution set classification can effectively reduce the computational complexity. At the same time, least squares optimization and dynamic allocation of integrity risk are used to further reduce the protection level. This paper verifies the validity of the parameters of the GMM based on actual airport GBAS data, performs simulation verification of the typical scenarios of CAT I and CAT II/IIIa global GBAS under the Beidou 3 constellation, and analyses the performance improvement effect under different solution set traversal depths. The results show that when the traversal depths of CAT I and CAT II/IIIa are 4 and 6, the vertical protection level component of the ground ranging error is reduced by 14% and the total vertical protection level is reduced by 10%.