RESEARCH ON PERTURBATION ANALYSIS OF THE TOTAL LEAST SQUARES
Wang Leyang1,2)
1)Faculty of Geomatics, East China Institute of Technology, Nanchang 330013;2)Jiangxi Province Key Laboratory for Digital Land,Fuzhou 344000
Abstract On the basis of the condition number definition of coefficient matrix and from the viewpoint of numerical analysis, the perturbation analysis equations of least squares (LS) and data least squares (DLS) are deduced, in following cases when the perturbation is only contained in the observation data, the perturbations are contained in the observation data and coefficient matrix, and the perturbation is only contained in the coefficient matrix. On the basis of the closedform expression of the total least squares (TLS) solution and with the tool of the singular value decomposition (SVD), the perturbation analysis equation of TLS is deduced. Through the analysis, the perturbation analysis equation of TLS is the unified form of the perturbation analysis equation of LS and DLS.
Key words :
total least squares (TLS)
least squares (LS)
data least squares (DLS)
perturbation analysis
condition number
Received: 01 January 1900
Corresponding Authors:
Wang Leyang
[1]
HE Chengwen,YUAN Yunbin,TAN Bingfeng. An Iterative Least Squares Algorithm Based on UWB TDOA Positioning Model [J]. jgg, 2021, 41(8): 806-809.
[2]
ZHAI Xinyi,PAN Guangyong,CHEN Yang,LIU Guolin. L-Curve Characteristic Value Correction Iteration Method for SBAS-InSAR Deformation Inversion [J]. jgg, 2021, 41(4): 403-407.
[3]
ZOU Shilin,WU Xing,WANG Fengwei. Regularized Robust Solution for Ill-Posed Weighted Total Least Squares Model [J]. jgg, 2021, 41(11): 1106-1110.
[4]
YANG Qiuwei,BAI Zhichao,LI Cuihong. Biased Estimation Method Based on Neumann Series [J]. jgg, 2020, 40(5): 512-516.
[5]
LIU Dong,CUI Xingping,WANG Qinghua,MU Baosheng,ZHANG Yong. Influence of Least Squares Weighting Method on Gravity Calculation Results [J]. jgg, 2020, 40(12): 1233-1236.
[6]
SUN Wenzhou,YIN Xiaodong,XIA Wenjie. Analysis of the Influence of Sound Velocity Error on Sailing-Circle Positioning Method for Seafloor Control Points [J]. jgg, 2020, 40(12): 1299-1302.
[7]
WANG Leyang,XU Ranran. Robust Weighted Total Least Squares Algorithm for Three-Dimensional Coordinate Transformation [J]. jgg, 2020, 40(10): 1027-1033.
[8]
ZUO Tingying, CHEN Bangju, SONG Yingchun. Adjustment Algorithm with Spherical Constraint and Application [J]. jgg, 2020, 40(1): 71-76.
[9]
WANG Wei,LI Hongyu,YE Biwen,TIAN Tao. Research on the Method for Annual Period Detection of Variable Amplitude for the Time Series of Deformation [J]. jgg, 2020, 40(1): 7-10.
[10]
WANG Qixin,XU Xiwei,JIANG Zaisen. Strain Characteristics of North-South Seismic Zone and the Analysis of Earthquake Risk [J]. jgg, 2020, 40(1): 23-29.
[11]
WANG Yong,SHI Qiang,LOU Zesheng,HAO Zhenhang,REN Dong. GNSS Vertical Series Noise and Non-Tectonic Deformation RemovalBased on ICEEMDAN and Least Squares [J]. jgg, 2020, 40(1): 39-44.
[12]
. [J]. jgg, 2019, 39(增2): 72-75.
[13]
. [J]. jgg, 2019, 39(增1): 137-141.
[14]
WU Guangming,LU Tieding. New Methods of Ill-Posed Total Least-Squares with Targeting Singular Value Corrections [J]. jgg, 2019, 39(8): 856-862.
[15]
WANG Leyang,ZOU Chuanyi,WU Lulu. The WHP Quasi Newton Correction Method for Inequality Constrained Partial EIV Model and the SUT Method for Its Precision Estimation [J]. jgg, 2019, 39(6): 648-653.