基于X-11-ARIMA模型在GNSS定位数据后处理的应用

匡宇龙; 雷孟飞

doi:10.12265/j.gnss.2021051201

基于X-11-ARIMA模型在GNSS定位数据后处理的应用

doi: 10.12265/j.gnss.2021051201

匡宇龙^,,
雷孟飞

湖南联智科技股份有限公司, 长沙 410200

详细信息

作者简介:
匡宇龙：（1994—），男，硕士，工程师，研究方向为高精度北斗卫星定位算法

雷孟飞：（1991—），男，硕士，工程师，研究方向为高精度北斗卫星定位算法

通讯作者:
匡宇龙 E-mail：yulongkuang@qq.com

中图分类号: P228.4
计量
- 文章访问数: 241
- HTML全文浏览量: 144
- PDF下载量: 12
- 被引次数: 0
出版历程
- 收稿日期: 2021-05-12
- 网络出版日期: 2021-11-02

Application of X-11-ARIMA model in post-processing of GNSS positioning data

KUANG Yulong^,,
LEI Mengfei

Hunan Lianzhi Monitoring Technology Co.Ltd., Changsha 410200, China

摘要

摘要: 定位数据分析及后处理是卫星导航定位系统在测绘和地灾监测应用中的关键环节. 通常，在卡尔曼滤波处理定位数据后得到的平滑数据，能够剔除噪声干扰得到贴近真值的数据. 但在长时间跨度的情况下，周期性发生的干扰难以在短时间内被识别和滤除，从而反映为一种频率较低的噪声波动. 假设该波动干扰存在周期性，以X-11分解时间序列分析方法进行数据处理，平滑后定位数据的方差从4.733减小至2.683，精度提高了43.3%. 并对拆分数据进行差分自回归移动平均模型(ARIMA)建模预测. 还原数据对比直接预测数据的分析结果表明：拆分后分别预测再整合还原精度高于直接预测5%～10%，可以应对平滑处理实时性差的问题.
- 全球卫星导航系统(GNSS) /
- 后处理 /
- 差分自回归移动平均模型(ARIMA) /
- X-11分解 /
- 时间序列分析 /
- 季节性
Abstract: Positioning data analysis and post-processing is essential part in the application of Global Navigation Satellite System in S/M and geological hazard monitoring and forecast project. Generally, the smooth data obtained after the Kalman filter processes the positioning data can eliminate noise interference and obtain data close to the true value. However, in the case of a long-term span, the periodic interference is difficult to identify and filter out in a short time, which is reflected as a kind of lower frequency noise fluctuation. This paper assumes that the fluctuation interference is periodic, and uses the X-11 decomposition time series analysis method for data processing. After smoothing, the variance of the positioning data is reduced from 4.733 to 2.683, and the accuracy is increased by 43.3%. And perform autoregressive integrated moving average mode (ARIMA) modeling and prediction on the split data. When compare the restored data with the direct prediction data, we can draw the conclusion that the accuracy of the separate prediction and integration restoration is basically higher than that of the direct prediction by 5% to 10%, so as to deal with the problem of poor real-time smoothing.
- Global Navigation Satellite System (GNSS) /
- post-processing /
- autoregressive integrated moving average mode (ARIMA) /
- X-11 decompose /
- time series /
- seasonal.

HTML全文

图 1 数据“波动”的时间跨度

下载: 全尺寸图片幻灯片

图 2 算法原理

下载: 全尺寸图片幻灯片

图 3 坐标残差数据ACF分析

下载: 全尺寸图片幻灯片

图 4 数据预测结果

下载: 全尺寸图片幻灯片

表 1 数据样本分类

数据来源	数据总量	日期
串丝斜坡	369	2021-02-17—2021-02-24
遵义边坡	2816	2019-05-22—2019-07-01
贵黄边坡	2600（截取）	2018-01-07—2021-01-07

下载: 导出CSV

表 2 预测模型

数据样本	原始数据	趋势项	不规则项
串丝斜坡	(1, 1, 2) (2, 0, 2, 13)	(3,1,3)	(0,0,2)
遵义边坡	(3, 1, 1) (3, 0, 0, 13)	(3,1,1)	(0,0,3)
贵黄边坡	(3, 1, 1) (3, 0, 0, 13)	(3,1,0)	(0,0,2)

下载: 导出CSV

表 3 直接预测与拆分后预测效果对比

数据来源	误差算法	直接拟合	拆分拟合	改进程度/%	6步直接预测	6步拆分预测	改进程度/%	12步直接预测	12步拆分预测	改进程度/%
串丝斜坡	MAE	0.814	0.649	−20.30	1.159	0.650	−43.9	1.401	0.803	−42.7
	MSE	1.133	0.792	−30.10	1.648	0.493	−70.1	2.295	1.036	−54.9
	RMSE	1.064	0.890	−16.40	1.283	0.702	−45.3	1.515	1.018	−23.8
	MAPE	2.855	2.263	−20.70	4.514	0.602	−86.7	3.545	1.478	−58.3
遵义边坡	MAE	1.900	1.736	−8.63	0.757	1.242	64.1	1.270	1.737	36.8
	MSE	7.421	6.453	−13.04	0.907	1.776	95.8	2.878	4.278	48.6
	RMSE	2.724	2.540	−6.75	0.952	1.332	39.9	1.697	2.068	21.9
	MAPE	0.029	0.026	−10.34	0.403	0.762	89.1	0.644	0.829	28.7
贵黄边坡	MAE	0.976	0.955	−2.15	0.762	0.708	−29.2	1.286	1.469	14.2
	MSE	1.549	1.478	−4.58	1.013	0.791	−21.9	2.922	3.748	28.2
	RMSE	1.245	1.216	−2.33	1.006	0.889	−11.6	1.710	1.936	13.2
	MAPE	0.633	1.450	129.10	0.404	0.382	−5.4	0.652	0.648	−0.4

下载: 导出CSV

参考文献(16)

[1]	何伟, 张伦宁, 贺成成, 等. 地灾监测的大数据信息平台研究及应用[J]. 测绘通报, 2019(1): 127-131.
[2]	刘丹, 王剑, 姜维, 等. 列车组合定位系统定位精度评估方法研究[J]. 铁道学报, 2019, 41(11): 79-87.
[3]	单伟, 何群. 基于非线性时间序列的预测模型检验与优化的研究[J]. 电子学报, 2008, 36(12): 2485-2489.
[4]	游贤菲. X11-ARIMA模型在全国手足口病发病数预测中的应用[J]. 产业与科技论坛, 2020, 19(7): 64-66.
[5]	张立欣, 张艳波, 杨翠芳. 基于X11-ARIMA模型的铁路货运周转量分析[J]. 数学的实践与认识, 2018, 48(17): 154-161.
[6]	LUO X G, MAYER M, HECK B. Verification of ARMA identification for modelling temporal correlations of GNSS observations using the ARMASA toolbox[J]. Studia geophysica et geodaetica, 2011, 55(3): 537-556. DOI: 10.1007/s11200-011-0033-2
[7]	LUO X G, MAYER M, HECK B. Analysing time series of GNSS residuals by means of AR (I) MA processes[C]//The 7th Hotine-Marussi Symposium on Mathematical Geodesy. Springer, Berlin, Heidelberg, 2012: 129-134. DOI: 10.1007/978-3-642-22078-4_19
[8]	ANSARI K, PARK K-D, KUBO N. Linear time-series modeling of the GNSS based TEC variations over southwest japan during 2011–2018 and comparison against ARMA and GIM models[J]. Acta astronautica, 2019(165): 248-258. DOI: 10.1016/j.actaastro.2019.09.017
[9]	HILLMER S C, TIAO G C. An ARIMA-model-based approach to seasonal adjustment[J]. Journal of the american statistical association, 1982, 77(377): 63-70. DOI: 10.1080/01621459.1982.10477767
[10]	JUNAIDI, BULIALI J L, SAIKHU A. Improving ARIMA forecasting accuracy using decomposed signal on PH and turbidity at SCADA based water treatment[C]//The 3rd International Conference on Information and Communications Technology (ICOIACT) IEEE, 2020: 131-136. DOI: 10.1109/ICOIACT50329.2020.9332080
[11]	PENG Y, LEI M, LI J B, et al. A novel hybridization of echo state networks and multiplicative seasonal ARIMA model for mobile communication traffic series forecasting[J]. Neural computing and applications, 2014, 24(3): 883-890. DOI: 10.1007/s00521-012-1291-9
[12]	XIN J Z, ZHOU J T, YANG S X, et al. Bridge structure deformation prediction based on GNSS data using Kalman-ARIMA-GARCH model[J]. Sensors (basel switzerland), 2018, 18(1): 298. DOI: 10.3390/s18010298
[13]	LI Q S, DONG Y, WANG D J, et al. A real-time inertial-aided cycle slip detection method based on ARIMA-GARCH model for inaccurate lever arm conditions[J]. GPS solutions, 2021, 25(1): 1-16. DOI: 10.1007/s10291-020-01077-9
[14]	JANPAULE I, BALODIS J, HARITONOVA D, et al. Geomagnetic storms and their influence on gnss time series[DS/OL]. [2021-05-01]. Ģeodinamika un ģeokosmiskie pētījumi, 2017: 24-26.
[15]	王振龙. 时间序列分析[M]. 北京: 中国统计出版社. 2000.
[16]	雷孟飞, 孔超, 周俊华. 自适应卡尔曼滤波在BDS变形监测数据处理中的应用[J]. 导航定位学报, 2019, 7(4): 75-79.