Generalized ridge estimation method for morbid weighted total least squares
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Graphical Abstract
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Abstract
For the variable error (EIV) model in the weighted case, the generalized ridge estimation method is used to deal with the morbid problem of the total least squares adjustment. Combined with optimization criterion and covariance propagation rate, the correction formula of unknown parameters is derived. Accordsing to the principle of minimizing mean square error of parameter estimation, the iterative solution of ridge parameter in generalized ridge estimation is given by solving partial derivative, and the meaning and function of generalized ridge parameter are discussed. The weighted least squares estimation, total least squares estimation, the weighted least squares ridge estimation, total least squares ridge estimation, generalized ridge estimation of the weighted least squares and generalized ridge estimation of total least squares are compared and analyzed by examples. The advantages and disadvantages of generalized ridge estimation of weighted total least squares are described.
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