﻿ 基于CMONOC GPS数据的SSA电离层预测模型研究
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 大地测量与地球动力学  2019, Vol. 39 Issue (11): 1153-1158, 1177  DOI: 10.14075/j.jgg.2019.11.011

### 引用本文

SHI Kunpeng, GUO Jinyun, ZHANG Yongming, et al. Ionospheric Prediction of SSA Model Based on CMONOC GPS[J]. Journal of Geodesy and Geodynamics, 2019, 39(11): 1153-1158, 1177.

### Foundation support

National Natural Science Foundation of China, No. 41374009; Natural Science Foundation of Shandong Province, No.ZR2013DM009; Science and Technology Innovation Fund of Postgraduates of Shandong University of Science and Technology, No. SDKDYC180207.

### Corresponding author

GUO Jinyun, PhD, professor, PhD supervisor, majors in space geodesy, marine geodesy and physical geodesy, E-mail: jinyunguo1@126.com.

### 第一作者简介

SHI Kunpeng, postgraduate, majors in space geodesy, E-mail: 514026949@qq.com.

### 文章历史

1. 山东科技大学测绘科学与工程学院, 青岛市前湾港路579号，266590;
2. 山东科技大学矿山灾害预防控制省部共建国家重点实验室，青岛市前湾港路579号，266590

1 方法介绍 1.1 SSA预测模型

SSA可以分析时间序列的周期振荡行为，将时间序列周期分解与时间尺度密切关联，从而较好地从含噪声的有限尺度时间序列中提取主要信息[9]

 $\boldsymbol{X}=\left[\begin{array}{cccc}{x_{1}} & {x_{2}} & {\cdots} & {x_{N-M+1}} \\ {x_{2}} & {x_{3}} & {\cdots} & {x_{N-M+2}} \\ {\cdots} & {\cdots} & {\cdots} & {\cdots} \\ {x_{M}} & {x_{M+1}} & {\cdots} & {x_{N}}\end{array}\right]$ (1)

 $\boldsymbol{T}_{x}=\left[\begin{array}{cccc}{S_{(0)}} & {S_{(1)}} & {\cdots} & {S_{(M-1)}} \\ {S_{(1)}} & {S_{(0)}} & {\cdots} & {S_{(M-2)}} \\ {\cdots} & {\cdots} & {\cdots} & {\cdots} \\ {S_{(M-1)}} & {S_{(M-2)}} & {\cdots} & {S_{(0)}}\end{array}\right]$ (2)

 $a_i^k = \sum\limits_{j = 1}^M {{x_{i + j}}} \mathit{\boldsymbol{E}}_j^k, 0 \le i \le N - M$ (3)

 $x_i^k = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{M}\sum\limits_{j = 1}^M {a_{i - j}^k} \mathit{\boldsymbol{E}}_j^k, }\\ \begin{array}{l} M \le i \le N - M + 1\\ \begin{array}{*{20}{c}} {\frac{1}{i}\sum\limits_{j = 1}^M {a_{i - j}^k} \mathit{\boldsymbol{E}}_j^k, }\\ \begin{array}{l} 1 \le i \le M - 1\\ \frac{1}{{N - i + 1}}\sum\limits_{j = i - N + M}^M {a_{i - j}^k} \mathit{\boldsymbol{E}}_j^k, \\ N - M + 2 \le i \le N \end{array} \end{array} \end{array} \end{array}} \right.$ (4)

 $w_{i}=\left\{\begin{array}{l}{i, 1 \leqslant i 式中，$ {M^*} = \min (M, K), {K^*} = \max (M, K), K = N - M + 1$。假设RC为Yk，且其相应的元素为y1k, y2k, …, yNk，任意2个RC间的自相关系数可以表示为： $ \rho_{i, j}^{w}=\frac{\left(\boldsymbol{Y}^{(i)}, \boldsymbol{Y}^{(j)}\right)}{\left\|\boldsymbol{Y}^{i}\right\|_{w}\left\|\boldsymbol{Y}^{j}\right\|_{w}}, 1 \leqslant i, j \leqslant N $(6) 式中，${\left\| {{\mathit{\boldsymbol{Y}}^i}} \right\|_w} = \sqrt {\left( {{\mathit{\boldsymbol{Y}}^{(i)}}, {\mathit{\boldsymbol{Y}}^{(i)}}} \right)} , {\left\| {{\mathit{\boldsymbol{Y}}^j}} \right\|_w} = \sqrt {\left( {{\mathit{\boldsymbol{Y}}^{(j)}}, {\mathit{\boldsymbol{Y}}^{(j)}}} \right)} , \left( {{\mathit{\boldsymbol{Y}}^{(i)}}, {\mathit{\boldsymbol{Y}}^{(j)}}} \right) = \sum\limits_{l = 1}^N {{w_l}} y_l^iy_l^j $。如果RC的相关系数趋近于1，说明相关性越大，合并w-correlation值较大的RC就可以充分反映原始数据的主要信息；反之则代表噪声信号的RC相互之间不能很好地分离。 本文有关预测期的数据被认为是缺失数据，而SSA可以用来预测TEC数据的主成分。根据w-correlation选择合适的阶次，即RC的个数K确定之后，在原始数据后面添加缺省数据，重复迭代过程直到收敛。更多详细的描述可以参阅文献[11]。 1.2 ARMA预测模型 ARMA模型是目前应用最为广泛、最基本的时序模型，ARMA(p, q)[12]模型可表示为: $ \begin{aligned} \boldsymbol{X}_{t} &=a_{1} \boldsymbol{X}_{t-1}+\cdots+a_{p} \boldsymbol{X}_{t-p}+\\ \varepsilon_{t} &+b_{1} \varepsilon_{t-1}+\cdots+b_{q} \varepsilon_{t-q} \end{aligned} \$ (7)

2 数据来源

CMONOC是一个以GNSS系统为主的国家级地球科学综合监测网络，其连续运行基准站达260个，在全国范围内分布较均匀，为反演高精度的电离层模型提供了很好的数据基础，可以有效弥补GIM在中国大陆区域上空精度较低、实效性较差的缺点[13]。本文利用CMONOC网260个测站的GPS双频观测数据，基于球谐函数拟合区域电离层。考虑到解算精度和速度，将解算阶次设置为5阶，参考系为日固-地磁坐标系[14]，最后生成以2 h为时间间隔，跨度为70°~140°E、15°~55°N，空间分辨率为1°×1°的RIM。

 图 1 两种电离层模型RMS分布 Fig. 1 The distribution of RMS based on two ionospheric models
3 实验分析

 图 2 不同序列长度预测的相对精度对比 Fig. 2 Comparison of relative accuracy of different sequence length prediction

 图 3 不同窗口长度的前15阶RC w-correlation值 Fig. 3 The first 15 order RC w-correlation values of different window length

3.1 中心网格点TEC预测

 图 4 TEC预测结果 Fig. 4 Predicted results of TEC

 图 5 不同模型预测7 d的精度 Fig. 5 7-day accuracy of different models

Dst指数表示中低纬度区的地磁活动状况，可以较好地反映中国地区的地磁活动[17]。本文通过统计4个时段的ARMA模型和SSA模型的平均预测相对精度和平均|Dst|信息，观察地磁活动对预测结果的影响。从图 6表 2可以看出，地磁活动和模型预测结果有一定的相关性，根据两种预测模型所有预测结果的相关精度和对应时刻的Dst指数绝对值计算其相关系数，判断地磁活动对预测结果的影响，SSA模型的TEC预测结果和Dst的相关系数为－0.69，ARMA模型的TEC预测结果和Dst的相关系数为－0.89。可以看出，SSA模型在地磁场平静期的预测精度更高，抗干扰能力也似乎更强。本文仅作初步探索，未来会对磁暴时段的电离层预测展开更多分析。

 图 6 不同时段的平均|Dst|和两种方法的相对误差 Fig. 6 Average |Dst| and relative errors of the two methods at different time periods

3.2 中国大陆上空TEC预测

 图 7 RMSE中国大陆及周边区域分布 Fig. 7 RMSE distribution in mainland China and surrounding regions

 图 8 Prel中国大陆及周边区域分布 Fig. 8 Prel distribution in mainland China and surrounding regions
4 结语

1) 总体来看，SSA模型的预测精度在短期(7 d)内相比于ARMA模型有明显的提高，利用SSA模型不仅可以较好地预测TEC整体变化趋势，同时也可以较好地体现TEC日变化特征。

2) 以本文的4个分析时段为基础，在地磁平静时期，|Dst|和SSA模型的TEC预测值的相关性为－0.69，低于|Dst|和ARMA模型预测值的相关性－0.89。后续工作将对地磁扰动时期进行统计，判断SSA模型在不同地磁条件下的预测精度。

3) 对比两种模型预报结果的RMSE在中国大陆及周边地区的分布情况，发现两者均存在低纬度地区精度低、中高纬度地区精度高的情况，可能与TEC的空间分布有关；同时预测相对精度的空间分布显示出中纬度地区预测精度高、高低纬度地区预测精度较低的特点，这可能与RIM的精度有关。但无论哪种精度指标，SSA模型的预测精度均优于ARMA模型。

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Ionospheric Prediction of SSA Model Based on CMONOC GPS
SHI Kunpeng1     GUO Jinyun1,2     ZHANG Yongming1     DI Wenqiang1
1. College of Surveying and Mapping Science and Engineering, Shandong University of Science and Technology, 579 Qianwangang Road, Qingdao 266590, China;
2. State Key Laboratory of Mining Disaster Prevention and Control Cofounded by Shandong Province and Ministry of Science and Technology, Shandong University of Science and Technology, 579 Qianwangang Road, Qingdao 266590, China
Abstract: Based on GPS observations from CMONOC, the RIM over China is derived precisely. We introduce a new method of singular spectrum analysis(SSA) to estimate the prediction models of TEC extracted from RIM. A suitable length of original TEC time series of 27 days is selected. By the w-correlation, the RC and window size of prediction model can be also determined. It is found that when the size of window is set as 1/3 of original series, the iteration of the first 5 RC decomposed by SSA has the best effects. The TEC data at center grid point of RIM from 1 to 27 d, 101 to 127 d, 201 to 227 d, 301 to 327 d are extracted respectively, to predict TEC for 7 days by SSA method. Meanwhile, the ARMA prediction model is also found and the models are compared. The results show that, compared with the ARMA model, the relative accuracy of SSA model is improved 10% for 7 days, with better long-prediction and anti-magnetic abilities. Furthermore, the TEC data of 2911 points are predicted by both methods. It is found that the RMSE gradually rose along with the decline of latitude, while the relative accuracy of grids over mid-latitude is slightly higher than other regions. However, regardless of the evaluation index, the SSA prediction model is superior to ARMA model.
Key words: CMONOC; TEC; ionosphere prediction; singular spectrum analysis; ARMA model