An iterative solution of weighted total least-squares adjustment

By Yunzhong Shen, Bofeng Li, Yi Chen. 2011

139 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/56ed539aa73dcf2c669b6e150ebd1ec4c4fc32c4

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Environmental Engineering

Citations in the corpus

On non-combinatorial weighted total least squares with inequality constraints (2014, methodology): “…adjust the univariate EIV model (see e.g., Markovsky et al. 2006; Schuermans et al. 2007; Schaffrin and Wieser 2008; Neitzel 2010; Fang 2011, 2013a; Shen et al. 2011; Amiri-Simkooei and Jazaeri 2012; Grafarend and Awange 2012; Snow 2012; Jazaeri et al. 2013) including its variance components…”
Application of least squares variance component estimation to errors-in-variables models (2013, background): “We may for instance refer to Schaffrin and Wieser (2008), Schaffrin and Felus (2009), Schaffrin and Wieser (2009), Schaffrin and Wieser (2011), Tong et al. (2011) and Shen et al. (2011).”
Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis (2012, methodology): “…step, the approach to using the method of Lagrange multipliers to solve EIV models, as developed by Deming (1931), has been followed by almost all the works on weighted TLS (see e.g. Gerhold 1969; Schaffrin and Wieser 2008; Felus and Burtch 2009; Schaffrin and Felus 2009; Shen et al. 2011).”
Iterative algorithm for weighted total least squares adjustment (2014, methodology): “[23] proposed an iterative method to perform a WTLS adjustment for an EIV model based on the Gauss– Newton approach of non-linear weighted least squares adjustment.”
Data-snooping procedure applied to errors-in-variables models (2013, methodology): “Eqs (5) and (6) are used to compute ye and Ae in our algorithm, while Shen et al. (2011) use, in addition, the nonlinear Gauss-Newton increment ˆδx in their formulation.”
Weighted total least squares formulated by standard least squares theory (2012, methodology): “Equation (20) is then written as x̂ = ( ÃT Q−1ỹ Ã )−1 ÃT Q−1ỹ ỹ (21) This formulation is similar to that of Shen et al. (2011).”
Weighted total least squares: necessary and sufficient conditions, fixed and random parameters (2013, methodology): “Such an investigation for the effect of the random coefficient matrix on the estimate was mentioned in Xu (2004), which is related to TLS but without using the terminology of TLS.”