An Error Overbounding Method Based on a Gaussian Mixture Model with Uncertainty Estimation for a Dual-Frequency Ground-Based Augmentation System

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To ensure the integrity of a ground-based augmentation system (GBAS), an ionosphere-free (Ifree) filtering algorithm with dual-frequency measurements is employed to make the GBAS free of the first-order ionospheric influence. However, the Ifree algorithm outputs the errors of two frequencies. The protection level obtained via the traditional Gaussian overbound is overconservative. This conservatism may cause false alarms and diminish availability. An overbounding framework based on a Gaussian mixture model (GMM) is proposed to handle samples drawn from Ifree-based GBAS range errors. The GMM is employed to model the single-frequency errors that concern the uncertainty estimation. A Monte Carlo simulation is performed to determine the accuracy of the estimated GMM confidence level obtained by using the general estimation approach. Then, the final GMM used to overbound the Ifree error distribution is analyzed. Based on the convolution invariance property, vertical protection levels in the position domain are explicitly derived without introducing complex numerical calculations. A performance evaluation based on a real-world road test shows that the Ifree-based vertical protection levels are tightened with a small computational cost.