| Tikhonov正则化法在重力场最小二乘配置逼近理论中的应用 |
| |
| 引用本文： | 邓凯亮,黄谟涛,暴景阳,刘传勇.Tikhonov正则化法在重力场最小二乘配置逼近理论中的应用[J].海洋测绘,2010(Z1):18-24. |
| |
| 作者姓名： | 邓凯亮 黄谟涛 暴景阳 刘传勇 |
| |
| 作者单位： | 海军大连舰艇学院 海测工程系,辽宁 大连 116018 ；海军海洋测绘研究所,天津 300061 |
| |
| 基金项目： | 国家863 计划项目(2006AA06A202)；国家重大海洋勘测专项项目(4200301)；国家自然科学基金(41074002) |
| |
| 摘 要： | 最小二乘配置法由于其能融合不同种类重力观测数据进行局部重力场逼近的特性而受到广泛关注,但最小二乘配置结果的不稳定严重影响该方法的推广应用。 基于对重力观测量协方差矩阵的谱分解,分析出该协方差矩阵存在病态性,协方差矩阵的求逆过程是信号放大的非平稳过程,微小的观测误差会被协方差矩阵的小奇异值放大,从而导致配置结果的不稳定且精度偏低。 引入 Tikhonov 正则化算法,通过 L 曲线法选择正则化参数,利用正则化参数修正重力观测量协方差矩阵的小奇异值,能抑制其对观测误差的放大影响。 通过以 EGM2008 重力场模型分别计算的山区、丘陵和海域重力异常作为基础数据确定相应区域大地水准面的实验,验证了本文算法的有效性。
|
| 关 键 词： | 最小二乘配置理论 Tikhonov 正则化法 L 曲线法 |
Application of Tikhonov Regulation Algorithm to the Theory of Least-squares Collocation of Gravity Field |
| |
| DENG Kai-liang,HUANG Mo-tao,BAO Jing-yang,LIU Chuan-yong.Application of Tikhonov Regulation Algorithm to the Theory of Least-squares Collocation of Gravity Field[J].Hydrographic Surveying and Charting,2010(Z1):18-24. |
| |
| Authors: | DENG Kai-liang HUANG Mo-tao BAO Jing-yang LIU Chuan-yong |
| |
| Abstract: | Based on the characteristics combing heterogeneous gravity data to approach local gravity field,the method of LSC ( Least-squares combination) is investigated widely. Because of the instability and the low- accuracy of the combination results,the method of LSC is limited to apply more broader. According to the spectral decomposition of the covariance matrix of the gravity observations,the covariance matrix is found ill-posed,its inverse approach is a non-stationary magnifying process,and the observation errors are magnified by the small singular values of the covariance matrix,so the collocation result is unsteady and low-accuracy. The method of LSC is imported the Tikhonov regulation algorithm. Using the L-curve method to choose the regulation parameter, and the small singular values of the covariance matrix are corrected by the regulation parameter. The magnifying effect that the relative small singular values give to the observation errors is suppressed. Based on the EGM2008 gravity model,the gravity anomalies are calculated in three different regions such as mountainous region,hill and ocean region. According to this gravity anomaly,the local Geoids in corresponding regions are determined. The simulation results have clearly shown significant quality advantages of this method. |
| |
| Keywords: | |
|
| 点击此处可从《海洋测绘》浏览原始摘要信息 |
| 点击此处可从《海洋测绘》下载免费的PDF全文 |
|
