摘要
航空重力梯度测量能获取重力梯度的多个分量,在保证各梯度分量内部固有约束条件下降低测量噪声,是一个巨大的挑战。为提高航空重力梯度测量精度,提出一种基于正则化等效源模型的测量降噪方法。根据矩形棱柱体与重力梯度之间的关系构建了等效源线性方程组,针对该方程组可能存在病态性的问题,引入截断奇异值TSVD和Tikhonov正则化的方法,对等效源模型进行正则化改造。模拟试验表明,正则化方法能够有效抑制病态系数矩阵小奇异值放大噪声对未知参数的污染,提高反演的精度和稳定性,其中基于L曲线确定正则化参数的截断奇异值TSVD法精度较高。实测数据表明,利用正则化等效源滤波转换的垂直梯度与利用傅里叶变换转换的结果吻合。可见,正则化等效源是重力场滤波和分量转换的有效工具。
Airborne gravity gradiometry can obtain multiple gravity gradient components.It will be a great challenge to reduce the surveying noise under the inherent constraints of each gradient component.In order to improve the accuracy of airborne gravity gradient measurement,a method of noise reduction based on regularized equivalent source model is proposed.According to the relationship between the rectangular prism and the gravity gradient,the equivalent source linear equations are constructed.In order to solve the ill-posed problem in the inversion of virtual equivalent source,the truncated singular value TSVD and Tikhonov regularization method are introduced.The simulation results show that the regularization method can effectively suppress the pollution of unknown parameters caused by the small singular value amplification noise of ill conditioned coefficient matrix,and improve the accuracy and stability of inversion,the TSVD method based on L-curve to determine regularization parameters has higher accuracy.The measured data show that the vertical gradient from the regularized equivalent source is in agreement with the results of Fourier transform.The regularized equivalent source is an effective tool for gravity field filtering and component conversion.
作者
赵德军
孙中苗
赵东明
谢心和
ZHAO Dejun;SUN Zhongmiao;ZHAO Dongming;XIE Xinhe(Institute of Geospatial Information,Information Engineering University,Zhengzhou 450001,China;Xi’an Division of Surveying and Mapping,Xi’an 710054,China;State Key Laboratory of Geo-Information Engineering,Xi’an 710054,China;Xi’an Research Institute of Surveying and Mapping,Xi’an 710054,China)
出处
《中国惯性技术学报》
EI
CSCD
北大核心
2021年第1期69-76,共8页
Journal of Chinese Inertial Technology
基金
国家自然科学基金(41774018,41674082,41574020)
国家社会科学基金(2020-SKJJ-C-043)。
