﻿ 时频传递的改进整数相位钟方法
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1. 国防科技大学电子对抗学院, 安徽 合肥 230037;
2. 中国洛阳电子装备试验中心, 河南 洛阳 471000

Time and frequency transfer based on modified integer phase clock method
LÜ Daqian1, ZENG Fangling1, OUYANG Xiaofeng1, YU Heli2
1. College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China;
2. Luoyang Electronic Equipment Test Center of China, Luoyang 471000, China
Abstract: The integer phase clock method is one of the most widely used integer ambiguity resolution method in precise point positioning (PPP). The stability of frequency transfer based on integer phase clock method is better than that of the conventional PPP. However, the clock offsets calculated by integer phase clock method contain the systematic biases, which affect the accuracy of time transfer. In this paper, we introduce the integer phase clock method, and analyze the origin of this systematic bias. Then based on single-difference ambiguity resolution method and atomic-clock refinement, a modified integer phase clock method is proposed. And some experiments are carried out to assess the modified integer phase clock method for ambiguity resolution and time-frequency transfer. The experiment results prove that the modified algorithm can eliminate the systematic bias effectively. The accuracy of time transfer can reach 0.1~0.2 ns, and the stability of frequency transfer can achieve 1.1×10-15/d.
Key words: precise point positioning    integer phase clock method    integer ambiguity resolution    time and frequency transfer    atomic clock model

1 整数相位钟法基本原理 1.1 观测值组合模型

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1.2 非差模糊度固定原理

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2 利用整数相位钟法进行时频传递存在的问题

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 图 1 不同卫星IGS最终产品卫星钟差与GRG相位钟产品卫星钟差的双差结果 Fig. 1 The double difference between IGS satellite clock offsets and the GRG satellite clock offsets for different satellites

(1) 如果用户采用与服务端相同的模糊度固定策略，同样需要将某个窄巷模糊度任意固定为基准值，以确保相位钟和模糊度参数能够直接分离。此时接收机相位钟差具有和式(7)相似的形式

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(2) 在用户端参数估计时，传统整数相位钟法将测站钟差建模为历元间独立的高斯白噪声，这种建模策略会导致GRG相位钟产品所包含的系统性偏差被测站钟差吸收，同样会影响IPPP时间传递精度。本文通过3组时间传递试验，计算GRG产品传递结果与IGS最终产品传递结果的差值。

 图 2 GRG产品时间传递结果与IGS最终产品差值 Fig. 2 The difference of time transfer results between GRG products and the IGS final products

3 改进整数相位钟法 3.1 星间单差模糊度固定方法及质量控制策略

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 图 3 模糊度固定质量控制策略 Fig. 3 The flow chart of IPPP quality control strategy

(1) 模糊度浮点解阶段：首先进行传统PPP计算，当卡尔曼滤波的位置方差平方根Q3D小于0.05 m时[21]，模糊度收敛精度较高，转入IPPP计算。

(2) 固定宽巷模糊度阶段：剔除高度角低于16°的卫星观测数据(避免质量较差观测数据影响模糊度固定，阈值可视观测环境情况调整)，并对MW组合观测值进行历元间平滑，确保模糊度准确固定。采用宽巷模糊度取整后剩余偏差小于0.25周和模糊度Bootstrapping检核成功率大于0.999 9两项条件作为固定成功判据。在单差基准星的选择上，本文参考文献[20, 22]的做法，构建所有可能的卫星对组成星间单差，并固定通过检验的模糊度参数。

(3) 固定窄巷模糊度阶段：以取整后剩余偏差小于0.25周和LAMBDA算法结果通过ratio-test作为窄巷模糊度固定成功判据。

(4) 参数更新阶段：当连续多个历元通过以上检验且前后固定一致时，认为固定结果趋于稳定，此时将传统PPP估计参数更新为IPPP参数；为防止模糊度固定错误，在状态更新前进行Q3D检验，若固定解Q3D大于传统PPP的Q3D，模糊度存在固定错误的可能，则该历元以传统PPP结果为准。

3.2 扩展原子钟模型

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4 算例分析 4.1 改进整数相位钟法模糊度固定性能分析

 图 4 星间单差窄巷模糊度参数 Fig. 4 The single-difference narrow-lane ambiguity parameters between satellites

 图 5 Ratio-test模糊度检验成功率 Fig. 5 The success rate of ratio-test for ambiguity validation

 图 6 小于0.15周窄巷残差所占百分比 Fig. 6 The percentage of narrow-lane ambiguity residuals within 0.15 cycles

4.2 改进整数相位钟法频率传递性能分析

 图 7 改进整数相位钟算法与IGS最终产品和GRG产品修正阿伦偏差比较 Fig. 7 The modified Allan deviation of modified integer phase clock method compared with IGS final products and GRG products

 图 8 改进整数相位钟算法与IGS最终产品修正阿伦偏差比较 Fig. 8 The Modified Allan Deviation of modified integer phase clock method compared with IGS final products

4.3 改进整数相位钟法时间传递性能分析

 图 9 单天M-IPPP时间传递结果与IGS产品参考值差值 Fig. 9 The difference between M-IPPP time transfer results and IGS products for one day

 图 10 10 d M-IPPP时间传递结果与IGS产品参考值差值 Fig. 10 The difference between M-IPPP time transfer results and IGS products for ten days

5 结论

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http://dx.doi.org/10.11947/j.AGCS.2019.20180248

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#### 文章信息

LÜ Daqian, ZENG Fangling, OUYANG Xiaofeng, YU Heli

Time and frequency transfer based on modified integer phase clock method

Acta Geodaetica et Cartographica Sinica, 2019, 48(7): 889-897
http://dx.doi.org/10.11947/j.AGCS.2019.20180248