Space qualified atomic clocks are fundamental in Global Navigation Satellite Systems, but they can suffer from different types of anomalies, like phase and frequency jumps, frequency drift changes and variance changes. Different solutions have been proposed for an automated on-board detection of clock anomalies, among which a frequency jump detector based on a recursive exponential filter, with soft requirements in terms of memory and computational power and hence particularly useful for on-board applications. Here, we propose a generalization of this recursive detector, based on double exponential smoothing: it properly takes into account the frequency drift and also detects drift and variance changes. Then, we test a first version of our detector on simulated and real data, and we discuss the results.