Article
Total LeastSquares Adjustment of Condition Equations
Studia Geophysica et Geodaetica (Impact Factor: 0.98). 01/2011; 55(3). DOI: 10.1007/s1120001100323

Article: Weighted total least squares: necessary and sufficient conditions, fixed and random parameters
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ABSTRACT: A standard errorsinvariables (EIV) model refers to a Gaussâ€“Markov model with an uncertain model matrix from a geodetic perspective. Least squares within the EIV model is usually called the total least squares (TLS) technique because of its symmetrical adjustment. However, the solutions and computational advantages of the weighted TLS problem with a general weight matrix (WTLS) are mostly unknown. In this study, the WTLS problem was solved using three different approaches: iterative methods based on the normal equation, the iteratively linearized Gaussâ€“Helmert model with algebraic Jacobian matrices, and numerical analysis. Furthermore, sufficient conditions for WTLS optimization were investigated systematically as proposed solutions yield only necessary conditions for optimality. A WTLS solution was considered to treat random parameters within the EIV model. Last, applications to test these novel algorithms are presented.Journal of Geodesy 08/2013; 87(8). · 2.81 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A new proof is presented of the desirable property of the weighted total leastsquares (WTLS) approach in preserving the structure of the coefficient matrix in terms of the functional independent elements. The WTLS considers the full covariance matrix of observed quantities in the observation vector and in the coefficient matrix; possible correlation between entries in the observation vector and the coefficient matrix are also considered. The WTLS approach is then equipped with constraints in order to produce the constrained structured TLS (CSTLS) solution. The proposed approach considers the correlation between the observation vector and the coefficient matrix of an ErrorInVariables model, which is not considered in other, recently proposed approaches. A rigid transformation problem is done by preservation of the structure and satisfying the constraints simultaneously.Studia Geophysica et Geodaetica 01/2014; · 0.98 Impact Factor
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