Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis

By Peiliang Xu, Jing-nan Liu, Chuang Shi. Journal of Geodesy, 2012

167 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3a0704ae58eb4f3a7cc3634ed8b671306a78fa28

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. X. Fang
2. Alireza Amiri-Simkooei
3. Guobin Chang
4. S. Jazaeri
5. Jing-nan Liu
6. Mahdi Sharifi
7. Peiliang Xu

In Statistics and Probability

1. X. Fang
2. Alireza Amiri-Simkooei
3. Guobin Chang
4. S. Jazaeri
5. Jing-nan Liu
6. Mahdi Sharifi
7. Peiliang Xu

Citations in the corpus

• On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model (2015, methodology): “…method, the GHM can also be safely treated as a nonlinear LS problem and solved iteratively, maybe with more general weighting strategies, see, e.g., Fang (2013); Mahboub (2012); Xu et al. (2012), or maybe with some kind of equality (Mahboub and Sharifi 2013) or inequality (Fang 2014a) constraints.”
• Variance components in errors-in-variables models: estimability, stability and bias analysis (2014, methodology): “…more than one century and found a wide variety of applications, either from the point of view of approximation (see, e.g., Golub and Loan 1980; Huffel and Vandewalle 1991) or from the statistical point of view (see, e.g., Pearson 1901; Deming 1931, 1934; Schaffrin and Wieser 2008; Xu et al. 2012).”
• On non-combinatorial weighted total least squares with inequality constraints (2014, methodology): “…Fang 2011, 2014b; Li et al. 2012, 2013), the structured EIV model (see e.g., Markovsky and Van Huffel 2006; Schaffrin et al. 2009; Mahboub 2012; Xu et al. 2012; Schaffrin et al. 2012), the equality-constrained EIV model (see e.g., Sima et al. 2004; Schaffrin and Felus 2005, 2009; Fang 2011,…”
• Iterative algorithm for weighted total least squares adjustment (2014, methodology): “[26] formulated WTLS as a nonlinear adjustment model without constraints and further extended it to a partial EIV model.”
• Weighted total least squares: necessary and sufficient conditions, fixed and random parameters (2013, background): “…multipliers to rearrange the specially weighted TLS problem as a constrained minimization optimization in which the weight matrix is fairly general (Schaffrin and Wieser 2008) or the weighted matrix of the model matrix is perfectly described (Shen et al. 2010; Mahboub 2012; Xu et al. 2012).”
• Weighted total least squares formulated by standard least squares theory (2012, methodology): “Xu et al. (2012) formulated WTLS as a nonlinear adjustment model without constraints and further extended it to a partial EIV model.”
• A total least squares solution for geodetic datum transformations (2014, methodology): “Secondly, it can also be seen in the complexity of each iteration that in the BFGS 3u2 + O (u) is required, where u is the number of unknown parameters (see Fletcher 1987, p. 54), whereas the methods of the Gauss–Newton class need O ( u3 ) or even O ( u3n3 ) multiplications (see Xu et al. 2012).”
• A structured and constrained Total Least-Squares solution with cross-covariances (2013, background): “Amiri-Simkooei and Jazaeri (2012) and Xu et al. (2012) formulated WTLS based on the well-known nonlinear least squares theory allowing one to directly use the existing body of statistical knowledge of the least squares theory.”