Conditional Adjustment with Parameters Based Solution of EIV Model

Errors-in-Variables (EIV) model is a mathematical model which takes into account the random errors of the design matrix, and it is widely used in the coordinate transformation, linear regression and polynomial fitting. The rigorous solution of EIV model generally requires the total Least-Squares (TLS) estimation, which is comparatively complicated in the calculating process and difficult to be applied in practice than Least-Squares (LS) estimation. In this contribution, the functional model of EIV is transformed into the form of conditional equation with parameters, which provides a novel perspective to understand EIV model. The transformed functional model treats the elements of the design matrix
$A$
as generalized or virtual observations, making the functional model easier to be understood and effortless to be solved. Then, the calculating formulas of the transformed mathematical model are derived by Lagrange Multiplier method combined with the conditions of the convergence point, named conditional adjustment with parameters based solution. Experimental results show that the proposed solution is the same as the existing TLS solution, which proves the feasibility and validity of the proposed solution. In summary, a novel perspective to understand EIV model is provided by transforming EIV model into the form of conditional equation with parameters in this contribution. Then, based on the transformed mathematical model, the calculating formulas equivalent to the classical TLS solution are strictly derived and fully examined.