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This paper introduces a method of detecting atomic clock anomalies for Global Navigation Satellites System (GNSS) satellites in real-time mode and presents some results obtained by monitoring actual GNSS satellite clocks. The method employs a Kalman filter formulation which facilitates the real-time processing of GNSS carrier-phase measurements. Judgment regarding clock anomalies is made using the prediction interval approach and actual distribution of predicted phase and frequency error is replaced by overbounding Gaussian distribution. Results show that the method could be a suitable method to detect GNSS clock events.