On weighted total least-squares for geodetic transformations

By V. Mahboub. Journal of Geodesy, 2012

114 citations recorded by the source corpus.

Subfields: Applied Mathematics, Environmental Engineering, Oceanography

View Paper: https://www.semanticscholar.org/paper/60d4bd0f7b3e84aa4a9f56104de764a3793ccee1

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. Guobin Chang
3. Alireza Amiri-Simkooei
4. S. Jazaeri

In Environmental Engineering

1. Guobin Chang
2. X. Fang
3. S. Jazaeri
4. Alireza Amiri-Simkooei

In Oceanography

1. Guobin Chang
2. S. Jazaeri
3. Alireza Amiri-Simkooei
4. X. Fang

Citations in the corpus

• Weighted total least squares: necessary and sufficient conditions, fixed and random parameters (2013, methodology): “To address the straight-line problem, the cofactor matrix should be preserved correctly as follows (Mahboub 2012):”
• A structured and constrained Total Least-Squares solution with cross-covariances (2013, methodology): “, Felus and Schaffrin, 2005; Mahboub, 2012). However, the symmetrical adjustment of rigid transformations, which should be formulated as the STLS problem with constraints, has rarely been treated. Furthermore, this contribution provides a reasonable stochastic model and target function to treat a ST”
• Weighted total least squares formulated by standard least squares theory (2012, methodology): “…a few simple mathematical operations, the estimated unknown vector follows directly from the preceding equation as x̂ = (( A−ẼA )T Q−1ỹ A )−1( A−ẼA )T Q−1ỹ y (18) This formulation is indeed a different appearance (but equivalent) of the Tong et al. (2011) and Mahboub (2012) formulations.”
• 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.”
• On non-combinatorial weighted total least squares with inequality constraints (2014, background): “Our ICWTLS solution can also treat the structured TLS with inequalities if the structure of the coefficient matrix is preserved according to Mahboub (2012).”