Position-Domain Integrity Analysis for Generalized Integer Aperture Bootstrapping

A full analysis of position-domain integrity is carried out for the recently introduced generalized integer aperture bootstrapping (GIAB) technique, a data-driven method for resolving and validating global navigation satellite system carrier-phase integer ambiguities suitable for high-integrity safety-critical systems. The analysis can be extended to all integer aperture (IA) techniques that are generalized in the sense of allowing partial integer fixing. It is shown that generalized IA methods produce relative position (baseline) estimates that suffer from nonnegligible biases. Key conditional distributions of the baseline computed from GIAB-validated ambiguities are rigorously derived for both full and partial ambiguity resolution. These distributions enable evaluation of the a posteriori risk from bias in the GIAB baseline estimate. Compared to enforced position-domain integrity risk of cycle resolution, the state-of-the-art high-integrity algorithm, GIAB is shown to satisfy tighter integrity requirements for the same measurement model.