A novel theoretical analysis of fault detection for atomic clock

The Generalized Likelihood Ratio Test (GLRT) is a fault detection technique usually employed for revealing faulting behavior by analyzing a finite length sequence of data. This technique is largely employed in many engineering applications and recently its effectiveness has been proved for detecting anomalies also in on-board atomic clocks. Although the large number of scientific publications allows a simple interpretation of the GLRT outcome, the application of the GLRT to frequency data acquired from atomic clocks still need to be properly customized and metrologically characterized. In particular, by considering Global Navigation Satellite Systems (GNSS), the most effective application where atomic clocks are used, a faulting clock behavior should be recognized fast and efficiently in order to guarantee the system target accuracy. In this paper, a novel theoretical analysis of the GLRT is performed for revealing frequency jumps and variance changes. An application example shows how the presented analysis can be used for deriving practical criteria that simplify the application of the fault detection procedure based on the GLRT to atomic clock frequency data.