Time synchronization is a fundamental requirement for many services provided by a distributed system. Clock calibration through the time signal is the usual way to realize the synchronization among the clocks used in the distributed system. The interference to time signal transmission or equipment failures may bring about failure to synchronize the time. To solve this problem, a clock bias prediction module is paralleled in the clock calibration system. And for improving the precision of clock bias prediction, the first-order grey model with one variable (GM
Time synchronization technology has been widely used in the distributed system [
In order to guarantee the distributed system work normally and add anti-interference ability of the synchronization system, clock bias prediction module is paralleled in the clock calibration system. In this parallel module, clock bias could be acquired through the prediction module, when the system cannot get clock bias. And system uses the predicted clock bias to generate a control signal, which is used to adjust the local clock. Above all, the performance of clock bias prediction has a direct impact on synchronization precision when accidents occur. At present, the clock bias prediction is an important work in GNSS; researchers have put forward several prediction models [
Aiming at this problem, we introduce the particle swarm optimization (PSO) algorithm to optimize GM
The rest of this paper is organized as follows. The mechanism that clock bias module is paralleled in clock calibration system is described in the next section. In Section
Figure
Workflow of clock calibration.
As shown in Figure
Clock error prediction in calibration.
In Figure
The GM
For demonstrating that parameters obtained by LSC are not optimal, clock bias of satellite PG01 provided by the international GNSS service (IGS) in June 10 of 2012 is selected; the sampling interval is 15 min. GM
The values of ME and MSE are got through using different combinations of parameters. In these different models, the optimal combination of
Prediction errors of different models.
In Figure
PSO algorithm is widely used as a global optimization algorithm, which has the characteristics of simple programming, high efficiency, and fast computing speed [
During iterative procedure, these particles fly through the problem space following the current optimum particle and corporate with each other to find the global optimum. The algorithm updates velocity and position of each particle as follows:
After each cycle is complete, these two subgroups will compare with each other. This mechanism can make the algorithm avoid local optimization on the basis of not increasing the optimal algebra obviously.
In the time synchronization system, channel interruption or equipment failure will lead to a failure to get clock bias. Under these negative circumstances, clock bias acquired through a prediction model can guarantee the distributed system work normally. We use GM
Flow of the improved model.
As shown in Figure
The parameters of IPSO are firstly initialized, including
IPSO algorithm establishes two subgroups, which search in opposite direction according to (
Velocity and position of particles are updated, and the
In order to find the optimal combination of parameters, fitness of two subgroups is compared.
IPSO algorithm continues to find the relative optimal combination of parameters, until it reaches the maximum number of circulating times or the value of fitness meets the threshold.
After IPSO algorithm finishes, GM
In order to evaluate the performance of GM
Clock calibration through wired channel.
As shown in Figure
Clock bias acquired by wired channel.
Devices are also used to design the clock calibration experiment that time signal is transmitted through radio channel. Layout is shown in Figure
Clock calibration through radio channel.
The sampling interval of this experiment is also 10 seconds. Figure
Clock bias acquired by radio channel.
As shown in Figures
In order to get the accuracy of GM
Individual atomic clocks have different frequency offset characteristic, the relationship between order of polynomial and atomic clock is defined as
Considering that Rb atomic clock is used in these experiments, polynomial with one order is used. Figure
Errors of different prediction models.
Data 1
Data 2
In Figure
Statistics of the different models (ns).
Clock bias | Polynomial model | GM | IPSO-GM | ||||||
---|---|---|---|---|---|---|---|---|---|
| ME | SD | | ME | SD | | ME | SD | |
Data 1 | 1.543 | −0.414 | 0.641 | 0.822 | 0.383 | 0.325 | 0.544 | 0.127 | 0.301 |
Data 2 | 3.247 | −1.776 | 0.850 | 2.758 | −1.248 | 0.799 | 1.614 | −0.323 | 0.623 |
Figure
Also, the limitation of parameters selection range at the beginning can not only overcome the blindness in IPSO but also reduce the calculation time in a certain degree. The simulation process on PC platform indicates that running time of improved prediction model is less than 5 s, which concludes that the improved prediction model can completely match the real-time requirement.
At the same time, the accuracy of all prediction models built using data 1 is better than using data 2. The noises in clock bias have negative effect not only on performance of clock calibration, but also on the accuracy of clock bias prediction.
The failure to transfer time signal and equipment’s breakdown will bring the failure to time synchronization system. Aiming at this problem, we parallel the clock bias system with clock calibration system. Also, GM
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Grant no. 61571459. The authors also would like to thank IGS for granting access to satellite clock bias data.