Weighted total least squares: necessary and sufficient conditions, fixed and random parameters
By X. Fang. Journal of Geodesy, 2013
132 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Oceanography
View Paper: https://www.semanticscholar.org/paper/409baf698d9f87653de4f9aaa11ddd999a948ec8
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In Applied Mathematics
In Computer Vision and Pattern Recognition
In Oceanography
Citations in the corpus
- A structured and constrained Total Least-Squares solution with cross-covariances (2013, background): “In terms of the admissibleness of weights, the differences in these TLS solutions vary from special to fairly general to general to very general as in Schaffrin and Felus (2008), Schaffrin and Wieser (2008), Mahboub (2012) and Fang (2011, 2013), respectively.”
- On non-combinatorial weighted total least squares with inequality constraints (2014, methodology): “…for cross-correlations between the cofactor matrices for the random coefficient matrix A and the observation vector y. Matrix B is defined in Fang (2013a) as Bn×n(u+1) := [ξT ⊗ In,−In], where the symbol ⊗ denotes the Kronecker product, and In is the identity matrix of size of n × n.…”
- Weighted total least-squares with constraints: a universal formula for geodetic symmetrical transformations (2015, methodology): “The increment of the parameterdξ canbeobtainedbymultiplying the gradient vector by the negative inverted Hessian matrix (Fang 2013):”
- A total least squares solution for geodetic datum transformations (2014, methodology): “Although proof of the QIEA is presented only for 3D datum transformations in this paper, the 2D symmetrical transformation problem can be also represented by an unconstrained optimization (Schaffrin and Felus 2008; Fang 2011, 2013), which is categorized as QIEA as a consequence.”
- 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.”