A Tutorial Review of Statistical Snapshot Detectors for GNSS/RAIM Fault Detection: Unified Derivations and Detector Relationships

The receiver autonomous integrity monitoring (RAIM) and Global Navigation Satellite System (GNSS) fault detection literature uses a group of statistical detectors that are often introduced with different names, coordinate systems, and derivation styles. This makes it difficult for new researchers to determine whether two methods use different information or only express the same inconsistency through different statistics. This paper provides a detector-centered tutorial review of statistical snapshot fault detection with a unified whitened linearized model. The chi-squared detector, parity-space detector, Baarda w-test, range comparison detector, jackknife detector, solution separation detector, and generalized likelihood-ratio test are derived with consistent notation. For each detector, the statistic construction, null and alternative distributions, threshold rule, and minimum detectable bias (MDB) are presented. A relationship map was developed to distinguish exact equivalence, projection relations and linear transformations among these detectors. An illustrative validation was then conducted with a real satellite geometry collected in an urban environment and synthetic Gaussian faults. The results verify the relationship checks, detection-probability behavior, and MDB calculations in a reproducible setting.