利用最小二乘直接法反演卫星重力场模型的MPI并行算法

doi:10.11947/j.AGCS.2015.20140396

测绘学报 ›› 2015, Vol. 44 ›› Issue (8): 833-839.doi: 10.11947/j.AGCS.2015.20140396

利用最小二乘直接法反演卫星重力场模型的MPI并行算法

周浩¹, 罗志才^1,2, 钟波^1,2, 陆飚¹

1. 武汉大学测绘学院, 湖北武汉 430079;
2. 地球空间环境与大地测量教育部重点实验室, 湖北武汉 430079

收稿日期:2014-07-23 修回日期:2015-04-20 出版日期:2015-09-20 发布日期:2015-09-02
作者简介:周浩(1987-),男,博士生,主要从事物理大地测量和卫星重力学研究。E-mail:zhouhao2013@whu.edu.cn
基金资助:
国家973计划(2013CB733302);国家自然科学基金(41104014;41131067);地理信息工程国家重点实验室开放基金(SKLGIE2013-M-1-3);大地测量与地球动力学国家重点实验室开放基金(SKLGED2015-1-3-E);地球空间环境与大地测量教育部重点实验室开放基金(13-02-05)

MPI Parallel Algorithm in Satellite Gravity Field Model Inversion on the Basis of Least Square Method

ZHOU Hao¹, LUO Zhicai^1,2, ZHONG Bo^1,2, LU Biao¹

1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
2. Key Lab of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China

Received:2014-07-23 Revised:2015-04-20 Online:2015-09-20 Published:2015-09-02
Supported by:
The National Basic Research Program of China(973 Program)(No. 2013CB733302);The National Natural Science Foundation of China(Nos. 41104014;41131067);The Open Research Fund Program of the State Key Laboratory of Geo-information Engineering(No. SKLGIE2013-M-1-3) The Open Research Fund Program of the State Key Laboratory of Geodesy and Earth's Dynamics(No. SKLGED2015-1-3-E) The Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy, Ministry of Education(No. 13-02-05)

摘要/Abstract

摘要： 针对海量卫星重力数据反演高阶次地球重力场模型的密集型计算任务与高内存耗用问题,基于MPI实现了最小二乘直接法恢复高阶次位系数的并行算法。引入并行读写、分块存储与分块计算等方式完成了设计矩阵的构建、法方程的形成与求解等密集型计算任务的并行算法,数值计算结果表明三者的并行相对效率峰值可分别达到95%、68%、63%。利用GOCE轨道跟踪和径向扰动重力梯度数据(共518 400个历元)分别反演了120、240阶次地球重力场模型,计算时间仅为40 min、7 h,内存耗用峰值仅为290 MB、1.57 GB;采用与GOCE同等噪声水平的观测数据恢复的重力场模型精度与GOCE已发布模型的解算精度相一致,联合GRACE和GOCE的解算模型能够实现二者独立信息的频谱互补,表明本文方法可高效稳定地恢复高阶次地球重力场模型。

关键词: MPI, 并行算法, 卫星重力场模型, Gauss-Jordan算法, GOCE

Abstract: In order to solve the intensive computing tasks and high memory demand problem in satellite gravity field model inversion on the basis of huge amounts of satellite gravity observations, the parallel algorithm for high truncated order and degree satellite gravity field model inversion with least square method on the basis of MPI was introduced. After analyzing the time and space complexity of each step in the solving flow, the parallel I/O, block-organized storage and block-organized computation algorithm on the basis of MPI are introduced to design the parallel algorithm for building design matrix, establishing and solving normal equation, and the simulation results indicate that the parallel efficiency of building design matrix, establishing and solving normal equation can reach to 95%, 68%and 63% respectively. In addition, on the basis of GOCE simulated orbits and radial disturbance gravity gradient data(518 400 epochs in total), two earth gravity models truncated to degree and order 120, 240 are inversed, and the relative computation time and memory demand are only about 40 minutes and 7 hours, 290 MB and 1.57 GB respectively. Eventually, a simulation numerical calculation for earth gravity field model inversion with the simulation data, which has the equivalent noise level with GRACE and GOCE mission, is conducted. The accuracy of inversion model has a good consistent with current released model, and the combined mode can complement the spectral information of each individual mission, which indicates that the parallel algorithm in this paper can be applied to inverse the high truncated degree and order earth gravity model efficiently and stably.

Key words: MPI, parallel algorithm, satellite gravity field model, Gauss-Jordan method, GOCE

中图分类号:

P223

周浩, 罗志才, 钟波, 陆飚. 利用最小二乘直接法反演卫星重力场模型的MPI并行算法[J]. 测绘学报, 2015, 44(8): 833-839.

ZHOU Hao, LUO Zhicai, ZHONG Bo, LU Biao. MPI Parallel Algorithm in Satellite Gravity Field Model Inversion on the Basis of Least Square Method[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(8): 833-839.

参考文献

[1] NING Jinsheng. The Satellite Gravity Surveying Technology and Research of Earth's Gravity Field[J]. Journal of Geodesy and Geodynamics, 2002, 22(1): 1-5. (宁津生. 卫星重力探测技术与地球重力场研究[J]. 大地测量与地球动力学, 2002, 22(1): 1-5.)
[2] NING Jinsheng, LUO Zhicai. The Progress and Application Prospects of Satellite-to-Satellite Tracking Technology[J]. Science of Surveying and Mapping, 2000, 25(4): 1-4. (宁津生, 罗志才. 卫星跟踪卫星技术的进展及应用前景[J]. 测绘科学, 2000, 25(4): 1-4.)
[3] XU Houze. Satellite Gravity Missions-New Hotpoint in Geodesy[J]. Science of Surveying and Mapping, 2001, 26(3): 1-3. (许厚泽. 卫星重力研究: 21世纪大地测量研究的新热点[J]. 测绘科学, 2001, 26(3): 1-3.)
[4] SUN Wenke. Satellitein Low Orbit(CHAMP, GRACE, GOCE) and High Precision Earth Gravity Field: The Latest Progress of Satellite Gravity Geodesy and Its Great Influence on Geoscience[J]. Journal of Geodesy and Geodynamics, 2002, 22(1): 92-100. (孙文科. 低轨道人造卫星(CHAMP、GRACE、GOCE)与高精度地球重力场: 卫星重力大地测量的最新发展及其对地球科学的重大影响[J]. 大地测量与地球动力学, 2002, 22(1): 92-100.)
[5] SANSÒ F, TSCHERNING C C. Fast Spherical Collocation: Theory and Examples[J]. Journal of Geodesy, 2003, 77(1-2): 101-112.
[6] KLEES R, KOOP R, VISSER P, et al. Efficient Gravity Field Recovery from GOCE Gravity Gradient Observations[J]. Journal of Geodesy, 2000, 74(7-8): 561-571.
[7] SNEEUW N. A Semi-analytical Approach to Gravity Field Analysis from Satellite Observations[D].München:University of München, 2000.
[8] LI Xinxing, WU Xiaoping, LI Shanshan, et al. The Application of Block Diagonal Least Squares Methods in Geopotential Model Determination[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(8): 778-785. (李新星, 吴晓平, 李姗姗, 等. 块对角最小二乘方法在确定全球重力场模型中的应用[J]. 测绘学报, 2014, 43(8): 778-785.)
[9] PAIL R, PLANK G. Assessment of Three Numerical Solution Strategies for Gravity Field Recovery from GOCE Satellite Gravity Gradiometry Implemented on a Parallel Platform[J]. Journal of Geodesy, 2002, 76(8): 462-474.
[10] KLEES R, KOOP R,VAN GEEMERT R, et al. GOCE Gravity Field Recovery Using Massive Parallel Computing[C]//SIDERIS M G. Gravity, Geoid and Geodynamics 2000.Berlin Heidelberg: Springer, 2002: 109-116.
[11] WANG Zhengtao. Theory and Methodology of Earth Gravity Field Recovery by Satellite-to-Satellite Tracking Data[D]. Wuhan: Wuhan University, 2005. (王正涛. 卫星跟踪卫星测量确定地球重力场的理论与方法[D]. 武汉: 武汉大学, 2005.)
[12] ZOU Xiancai, LI Jiancheng, WANG Haihong, et al. Application of Parallel Computing with Open MP in Data Processing for Satellite Gravity[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(6): 636-641. (邹贤才, 李建成, 汪海洪, 等. Open MP并行计算在卫星重力数据处理中的应用[J]. 测绘学报, 2010, 39(6): 636-641.)
[13] ZHOU Hao, ZHONG Bo, LUO Zhicai, et al. Application of Parallel Algorithms Based on Open MP to Satellite Gravity Field Recovery[J]. Journal of Geodesy and Geodynamics, 2011, 31(5): 123-127. (周浩, 钟波, 罗志才, 等. Open MP并行算法在卫星重力场模型反演中的应用[J]. 大地测量与地球动力学, 2011, 31(5):123-127.)
[14] LUO Zhicai. The Theory and Methodology for Determining the Earth's Gravity Field Using Satellite Gravity Gradiometry Data[D]. Wuhan:Wuhan Technical University of Surveying and Mapping, 1996. (罗志才. 利用卫星重力梯度数据确定地球重力场的理论和方法[D]. 武汉:武汉测绘科技大学, 1996.)
[15] ZHONG Bo. Study on the Determination of the Earth's Gravity Field from Satellite Gravimetry Mission GOCE[D]. Wuhan:Wuhan University, 2010. (钟波. 基于GOCE卫星重力测量技术确定地球重力场的研究[D]. 武汉:武汉大学, 2010.)
[16] University of Tennessee. Message Passing Interface Forum[EB/OL].[2012-09-21]. http://www.mpi-forum.org/.
[17] ZHANG Linbo,CHI Xuebin, MO Zeyao, et al. Introduction to Parallel Computing[M]. Beijing:Tsinghua University Press, 2006. (张林波,迟学斌, 莫则尧, 等. 并行计算导论[M]. 北京:清华大学出版社,2006.)
[18] [JP+4] CHEN Guoliang, AN Hong, CHEN Ling, et al. The Practical Study of Parallel Algorithm[M]. Beijing:Higher Education Press,2004. (陈国良, 安虹, 陈崚, 等. 并行算法实践[M]. 北京:高等教育出版社,2004.)
[19] [JP+4] MO Zeyao, YUAN Guoxing. Message Passing Parallel Programming Environment MPI[M]. Beijing:Science Press, 2001. (莫则尧, 袁国兴. 消息传递并行编程环境MPI[M]. 北京:科学出版社,2001.)
[20] DU Zhihui, LI Sanli. High Performance Parallel Programming with MPI[M]. Beijing:Tsinghua University Press, 2001. (都志辉, 李三立. 高性能计算之并行编程技术-MPI并行程序设计[M]. 北京:清华大学出版社,2001.)
[21] ZHOU Hao,LUO Zhicai, ZHONG Bo. Design and Analysis of MPI Parallel Algorithm for Large-scale Matrix Inversion[J]. Journal of Geodesy and Geodynamics,2014, 34(5):120-124.(周浩, 罗志才, 钟波. 大规模矩阵的MPI并行求逆算法设计与分析[J].大地测量与地球动力学, 2014, 34(5):120-124.)

利用最小二乘直接法反演卫星重力场模型的MPI并行算法

MPI Parallel Algorithm in Satellite Gravity Field Model Inversion on the Basis of Least Square Method

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	潘娟霞, 邹贤才. GOCE引力梯度内部校准方法[J]. 测绘学报, 2022, 51(2): 192-200.
[2]	陈鑑华, 张兴福, 沈云中, 陈秋杰, 李伟超. GOCE卫星重力梯度观测值的时变重力场变化改正及影响分析[J]. 测绘学报, 2021, 50(3): 324-332.
[3]	刘焕玲, 文汉江, 徐新禹, 赵永奇, 蔡剑青. GOCE实测数据反演高阶重力场模型的Torus方法[J]. 测绘学报, 2020, 49(8): 965-973.
[4]	瞿庆亮, 常晓涛, 于胜文, 朱广彬. 利用先验重力场模型求定GOCE卫星重力梯度仪校准参数[J]. 测绘学报, 2019, 48(2): 176-184.
[5]	邹贤才. GOCE卫星重力梯度校准与无阻尼控制效果分析[J]. 测绘学报, 2018, 47(3): 291-297.
[6]	孟祥超, 万晓云, 于锦海, 朱永超, 冯炜. 利用引力梯度数据计算径向梯度的优化方法[J]. 测绘学报, 2016, 45(7): 775-781.
[7]	刘焕玲, 文汉江, 徐新禹, 朱广彬. 利用GOCE模拟观测反演重力场的Torus法[J]. 测绘学报, 2015, 44(9): 965-972.
[8]	叶周润, 柳林涛, 梁星辉. Moho面扰动重力梯度信息的提取[J]. 测绘学报, 2015, 44(6): 609-615.
[9]	苏勇, 范东明, 游为. 利用GOCE卫星轨道数据恢复地球重力场模型方法的分析[J]. 测绘学报, 2015, 44(2): 142-149.
[10]	徐新禹, 赵永奇, 魏辉, 吴汤婷. 利用先验重力场模型对GOCE卫星重力梯度观测值进行校准分析[J]. 测绘学报, 2015, 44(11): 1196-1201.
[11]	范俊甫马廷周成虎季民周玉科许涛. 几何部件缓冲区域合并的Buffer算法及其并行优化方法[J]. 测绘学报, 2014, 43(9): 969-975.
[12]	闫志远孙文彬陈宗娟赵帅阳. PC集群环境下的并行地理网络车辆路径算法[J]. 测绘学报, 2014, 43(7): 753-760.
[13]	高春春陆洋张子占史红岭杜宗亮朱传东. GOCE地球重力场模型在青藏地区的评价及分析[J]. 测绘学报, 2014, 43(1): 21-29.
[14]	沈婕. MPI环境下等高线简化并行计算适宜性研究[J]. , 2013, 42(4): 0-0.
[15]	万晓云于锦海. 极地空白对GOCE引力场恢复的影响研究[J]. , 2013, 42(3): 0-0.