地球物理学进展 ›› 2019, Vol. 34 ›› Issue (4): 1323-1327.doi: 10.6038/pg2019CC0255

• 固体地球物理及空间物理学(大气、行星、地球动力学、重磁电及地震学、地热学) • 上一篇    下一篇

卫星重力梯度数据确定地球重力场的正则化方法研究

梁勇1,朱广彬2,*(),刘洪涛1,朱娅男3,瞿庆亮2,4   

  1. 1. 济南市勘察测绘研究院,济南 250000
    2. 自然资源部国土卫星遥感应用中心,北京 100048
    3. 济南市城市规划咨询服务中心,济南 250000
    4. 山东科技大学测绘科学与工程学院,山东青岛 266590
  • 收稿日期:2018-09-21 修回日期:2019-05-10 出版日期:2019-08-20 发布日期:2019-08-30
  • 通讯作者: 朱广彬 E-mail:sasmac_zgb@163.com
  • 作者简介:梁勇,男,1980年8月生,山东人,工程师,主要从事大地测量、地理信息系统等方面的研究与应用工作.(E-mail:ly-0708@163.com)
  • 基金资助:
    民用航天预先研究项目:重力梯度测量卫星系统技术和国家高分专项“GF-7卫星高程基准转换模型构建与应用技术”联合资助.

Regularization of the earth gravity field determination using satellite gravity gradiometry data

LIANG Yong1,ZHU Guang-bin2,*(),LIU Hong-tao1,ZHU Ya-nan3,QU Qing-liang2,4   

  1. 1. Jinan Geotechnical Investigation and Surveying Research Institute,Jinan 250000,China
    2. Land Satellite Remote Sensing Application Center,NASG,Beijing 100048,China
    3. Jinan City Planning Advisory Service Center,Jinan 250000,China
    4. College of Geomatics,Shandong University of Science and Technology,Shandong Qingdao 266590,China
  • Received:2018-09-21 Revised:2019-05-10 Online:2019-08-20 Published:2019-08-30
  • Contact: Guang-bin ZHU E-mail:sasmac_zgb@163.com

摘要:

在卫星重力梯度数据确定地球重力场时,观测数据有色噪声及极空白问题导致法方程呈现病态性.本文基于严密的卫星重力梯度数据确定地球重力场的直接解法,对零次、一次Tikhonov正则化和Kaula正则化等多种正则化技术,以及用于确定正则化参数的L曲线法、GCV法、MSE法等三种方法进行了适用性分析.研究结果表明,Tikhonov正则化和Kaula正则化方法能够有效改善法方程求解的稳定性,提高大地水准面的恢复精度,Kaula正则化方法较之Tikhonov正则化要稍优.以大地水准面误差均方差最小为标准,GCV方法的精度要优于L曲线法,更适于卫星重力梯度实测数据的解算.

关键词: 卫星重力梯度, 地球重力场, 直接解法, 正则化, 广义交叉检验

Abstract:

When determining the earth’s gravity field using the satellite gravity gradiometry data, the normal equation is ill-conditioned because of the colored noise and the polar gaps in the observation data. In the paper, using the direct approach of the earth’s gravity field determination with satellite gravity gradiometry data, the zero-order, the first-order Tikhonov regularization and Kaula regularization, as well as the three methods of determining the regularization parameter including L-curve method, GCV method and MSE method are compared and analyzed in numerical simulation. The results show that, both Tikhonov regularization and Kaula regularization could effectively improve the solution stability of the normal equation and the recovery accuracy of the geoid. The solution after Kaula regularization is slightly better than that after Tikhonov regularization. According to the minimum mean square error of the geoid, the accuracy of the GCV method is better than the L-curve method, which is more suitable for the processing of the real satellite gravity gradiometry data.

Key words: Satellite gravity gradiometry, The earth gravity field, The direct approach, Regularization, Generalized cross-validation

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