A note on Constrained Total Least-Squares estimation

Schaffrin, Burkhard

doi:10.1016/j.laa.2006.03.044

Cited by 90 publications

(40 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, and n m  (Annan et al, 2016a;Schaffrin, 2006). B is the design matrix, X is the matrix of the unknown parameters, and L is the observation matrix.…”

Section: Ordinary Least Square (Ols) and Total Least Square (Tls)mentioning

confidence: 99%

Performance evaluation of the Ordinary Least Square (OLS) and Total Least Square (TLS) in adjusting field data: an empirical study on a DGPS data

Peprah¹,

Mensah²

2017

SA J of Geomatics

View full text Add to dashboard Cite

show abstract

“…, and n m  (Annan et al, 2016a;Schaffrin, 2006). B is the design matrix, X is the matrix of the unknown parameters, and L is the observation matrix.…”

Section: Ordinary Least Square (Ols) and Total Least Square (Tls)mentioning

confidence: 99%

Performance evaluation of the Ordinary Least Square (OLS) and Total Least Square (TLS) in adjusting field data: an empirical study on a DGPS data

Peprah¹,

Mensah²

2017

SA J of Geomatics

View full text Add to dashboard Cite

show abstract

“…Furthermore, constraints on the unknown parameters have been often introduced in geodetic applications. Schaffrin [15] solved a TLS problem with linear constraints, whereas the TLS solution of [16] can be applied with arbitrary constraints.…”

Section: Errors-in-variables Model and Total Leastmentioning

confidence: 99%

Errors-in-Variables Anisotropic Extended Orthogonal Procrustes Analysis

Maset

Crosilla

Fusiello

2017

IEEE Geosci. Remote Sensing Lett.

View full text Add to dashboard Cite

Abstract-This paper presents a novel total least squares solution of the anisotropic row-scaling Procrustes problem. Ordinary least squares Procrustes approach finds the transformation parameters between origin and destination sets of observations minimizing errors affecting only the destination one. In this study, we introduce the Errors-In-Variables model in the anisotropic Procrustes analysis problem and present a solution that can deal with the uncertainty affecting both sets of observations. The algorithm is applied to solve the image exterior orientation problem. Experiments show that the proposed total least squares method leads to an accuracy in the parameters estimation that is higher than the one reached with the ordinary least squares anisotropic Procrustes solution when the number of points, whose coordinates are known in both the image and the external systems, is small.

show abstract

“…In recent years, the TLS method has been developed further. For example, Schaffrin (2006) investigated the Constrained TLS (CTLS) method; Schaffrin and Wieser (2008) analyzed the Weighted TLS (WTLS) adjustment for linear regression; Schaffrin and Felus (2009) developed the TLS problem with linear and quadratic constraints; Neitzel (2010) solved the TLS within the EIV model as a special case of the method of LS within the nonlinear Gauss-Helmert (GH) model. Only a few authors described estimation of parameters of camera calibration within the EIV model, and none have presented the straightforward algorithm as in the following sections.…”

Section: Introductionmentioning

confidence: 99%

Performing Improved Two-Step Camera Calibration With Weighted Total Least-Squares

2012

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

View full text Add to dashboard Cite

ABSTRACT:In order to improve the Tsai's two-step camera calibration method, we present a camera model which accounts for major sources of lens distortion, namely: radial, decentering, and thin prism distortions. The coordinates of principle points will be calculated at the same time. In the camera calibration model, considering the errors existing both in the observation vector and the coefficient matrix, the Total Least-Squares (TLS) solution is preferred to be utilized. The Errors-In-Variables (EIV) model will be adjusted by the solution within the nonlinear Gauss-Helmert (GH) model here. At the end of the contribution, the real experiment is investigated to demonstrate the improved two-step camera calibration method proposed in this paper. The results show that using the iteratively linearized GH model to solve this proposed method, the camera calibration parameters will be more stable and accurate, and the calculation can be preceded regardless of whether the variance covariance matrices are full or diagonal.

show abstract

A note on Constrained Total Least-Squares estimation

Cited by 90 publications

References 3 publications

Performance evaluation of the Ordinary Least Square (OLS) and Total Least Square (TLS) in adjusting field data: an empirical study on a DGPS data

Performance evaluation of the Ordinary Least Square (OLS) and Total Least Square (TLS) in adjusting field data: an empirical study on a DGPS data

Errors-in-Variables Anisotropic Extended Orthogonal Procrustes Analysis

Performing Improved Two-Step Camera Calibration With Weighted Total Least-Squares

Contact Info

Product

Resources

About