Mathematical Problems in Engineering

Volume 2016, Article ID 1813403, 6 pages

http://dx.doi.org/10.1155/2016/1813403

## High Precision Clock Bias Prediction Model in Clock Synchronization System

^{1}Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China^{2}Unit 95425 of the Chinese People’s Liberation Army, Qujing 655000, China

Received 19 July 2016; Revised 18 October 2016; Accepted 23 October 2016

Academic Editor: Magdi S. Mahmoud

Copyright © 2016 Zan Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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) model is proposed. In the traditional GM model, the combination of parameters determined by least squares criterion is not optimal; therefore, the particle swarm optimization (PSO) is used to optimize GM model. At the same time, in order to avoid PSO getting stuck at local optimization and improve its efficiency, the mechanisms that double subgroups and nonlinear decreasing inertia weight are proposed. In order to test the precision of the improved model, we design clock calibration experiments, where time signal is transferred via radio and wired channel, respectively. The improved model is built on the basis of clock bias acquired in the experiments. The results show that the improved model is superior to other models both in precision and in stability. The precision of improved model increased by 66.4%~76.7%.

#### 1. Introduction

Time synchronization technology has been widely used in the distributed system [1–4], such as global navigation satellite system (GNSS) and multistatic radar and electric network. Clock calibration is that devices of distributed system use reference time to synchronize the local clock. Hence, process of clock calibration determines the accuracy of time synchronization [5–7]. Nowadays, the way to calibrate local clock is that finite impulse response (FIR) filter uses the bias between local and remote clock measured by time interval counter (TIC) or discriminator to get a control signal [8–10], which is used to regulate clock until the clocks are synchronized. In the distributed system with far distance, time signal is always conveyed by electric cable, satellite, or microwave. Recently, troposphere scatter has also been proposed to transfer the time signal [6]. In a process of time signal’s transmission, channel interruption or equipment failure will lead to the failure to get clock bias, and the absence of clock bias can make synchronization system abnormal.

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 [8, 9], such as first-order grey model with one variable (GM) model, artificial neutral network (ANN) model, and least squares support vector machine (LSSVM) model. The sampling interval of satellite clock bias is generally 15 min, which lead to a relatively low real-time requirement. Nevertheless, in the clock calibration system, the short sampling time puts forward a great requirement for real-time performance. GM model needs less data sample and has better real-time than artificial intelligence algorithms, which need more data to train themselves. However, parameters of GM model are usually determined by the least square criterion (LSC), which cannot guarantee the parameters are optimal.

Aiming at this problem, we introduce the particle swarm optimization (PSO) algorithm to optimize GM model. Also, in order to avoid the PSO getting stuck at local optimization and improve its efficiency, the mechanisms that double subgroups and nonlinear decreasing inertia weight are proposed.

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 3, GM model optimized by improved particle swarm optimization (IPSO) is introduced. In Section 4, we design two clock calibration experiments that time signal is transferred via wired and radio channel, respectively. And the improved model is built through clock bias acquired by these calibration experiments. Finally, some conclusions are drawn in Section 5.

#### 2. Clock Bias Prediction in Clock Calibration

Figure 1 shows the workflow of the clock calibration model in time synchronization system.