| Summary: | This contribution introduces a Bayesian framework of
fault detection, identification, and adaptation (Bayesian DIA)
methods for Global Navigation Satellite System (GNSS)
applications. It provides an alternative to the classical DIA
approach, which allows for leveraging the prior information
about faults to enhance the robustness of DIA estimators and
subsequently use posterior information to implement quality
control. In this framework, the Bernoulli-Gaussian (BG)
model is first used to construct the prior distribution of
faults describing prior information about the mode and size
of faults. Next, a DIA method based on Bayesian hypotheses
testing (DIA-BHT) is proposed to process the additive faults
in linear observation systems. Finally, the Bayesian DIA
probability and credibility levels are introduced as measures
for quality control. These probability levels describe the
probabilities of decisions conditioned on the realities, which
enables the prediction of the possibility of making a correct
decision. The credibility levels denote the probabilities of
realities conditioned on the decisions, which is helpful for the
assessment of decision correctness. GNSS examples verified
that the proposed Bayesian DIA method is robust for
detecting and identifying faults with different modes and
sizes.
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