Carrier phase error overbounding using Gaussian mixture model for high-precision air navigation integrity monitoring

Carrier phase measurements play a pivotal role in enabling high-precision positioning within future air traffic systems and autonomous vehicles. Current aviation navigation integrity monitoring, primarily using pseudorange measurements, cannot meet system positioning accuracy and integrity requirements, leading to limitations and false alarm risks, especially in complex urban canyons with signal reflections. This work presents a carrier phase-based positioning integrity monitoring algorithm, utilizing the expectation–maximization algorithm to compute parameters for the Gaussian mixture model (GMM) and nonparametric bootstrapping to construct an overbounding model of carrier phase residuals. It establishes a precise protection level (PL) calculation method, which is validated with static and flight data, demonstrating accurate overbounding of carrier phase residuals using GMM. Protection levels during testing remain below the alarm limit and exceed system positioning error, ensuring normal system operation without false or missed alarms, confirming the effectiveness of the established carrier phase error overbounding model.