Objectives  In October 2011 the Russian GLONASS(global navigation satellite system) orbital constellation of 24 satellites is restored, enabling global coverage for positioning, navigation and timing for civil users once again. It plays key roles in navigation system performance evaluation, integrity monitoring, determination and prediction of satellite clock correction. To analyze the time-frequency characteristics of GLONASS in-flight satellite clocks, GLONASS satellites are equipped with cesium clocks, which are different from GPS, Galileo and BDS(BeiDou navigation satellite system) satellites, so GLONASS in-flight Cesium clock may have quite different time-frequency characteristics. However, analysis and evaluation are rarely reported about GLONASS satellite clocks.

  Methods  In order to estimate the behavior and state of GLONASS in-flight satellite clocks, the long-term characterization of the GLONASS in-orbit Cesium clocks is carried out in terms of the long-term variations of the five indices, namely clock phase, frequency, frequency drift, frequency stability and clock model noise. In view of the availability and accuracy of GLONASS satellite clock data, the precise GLONASS satellite clock products from Jan. 1, 2016 to May 11, 2019 with 5-minute interval released by the Russian GLONASS Information and Analysis Center for Positioning, Navigation and Timing are used as data base to derive the clock phase, frequency, frequency drift and clock model noise from the quadratic polynomial model, as well as calculate the clock frequency stability at the short interval according to the classical Hadamard deviation.

  Results  It is clearly shown that the phase and frequency of the GLONASS on-board Cesium clocks are very stable. The average values of the model noise and frequency drift of the GLONASS in-orbit clocks are 0.7 ns and 5.94×10^-15/d, respectively. The results demonstrate that GLONASS Cesium clocks have good physical characteristics.The frequency stability of the GLONASS satellite clocks in orbit is at the 10^-13 level at short interval, and there is noticeable relationship between the frequency stability and clock model noise, which will be needed to clarify further.

  Conclusions  The results show that the physical characteristics of new satellite clocks are better than that of older clocks, and the clock model noise are also substantially lower.