Bayesian Fault Detection, Identification, and Adaptation for GNSS Applications

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 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 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 enable 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.