Optimized Integer Aperture Bootstrapping for High-Integrity CDGNSS Applications

Integer Aperture Bootstrapping (IAB) is a crucial method for testing ambiguity acceptance in carrier-phase differential global navigation satellite system (CDGNSS) positioning. It has the advantage that integrity parameters, such as the failure rate, can be analytically calculated, which is essential in safety-of-life applications. Although the IAB methods have been extensively studied, their threshold-determining method is still not well explained, theoretically. In this study, a new method, named Analytical Integer Aperture Bootstrapping (AIAB), is theoretically derived to determine the optimal IAB threshold. AIAB is novel in that: (1) a precise and easy-to-compute expression has been developed to describe the relationship between the IAB threshold and the failure rate, (2) an analytical function model has been derived from the expression to determine the IAB threshold; moreover, the function model is simplified, and (3) a data-constraint approach has been proposed to reduce the complexity of IAB. In the global CDGNSS simulations, AIAB is shown to outperform the existing IAB methods under both strong and weak models, particularly at low fix rates, which are 23% to 40% higher than the basic IAB method. The Monte Carlo simulation results show that AIAB can obtain almost theoretically the same performance as Optimal Integer Aperture (OIA).