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Considering the methods of variance components estimation (VCE) in Partial errors-in-variables (Partial EIV) model have not considered the effect of the bias of parameter estimates, the formulas of bias and second-order covariance matrix of parameter estimates are presented with the Partial EIV model regarded as a non-linear function and the parameter estimates after bias-correct are calculated. Combining the VCE method, the matrix variable influenced by the parameter estimates is updated, and an iterative method of variance components estimation based on bias-correct is given. The experiments show that the reasonable parameter estimates and its second-order approximate covariance results are affected by the bias of parameter estimates. The reasonable parameter estimates and variance components estimates can be obtained through the bias-correct and the second-order information obtained can reasonably evaluate precision of parameter estimates.

The weighted total least-squares (WTLS) estimate for the partial errors-in-variables (EIV) model is very susceptible to outliers. Because the observations and coefficient matrix in the partial EIV model may be contaminated with outliers simultaneously, a total robustified least squares (TRLS) estimation for the partial EIV model is proposed by combining a two-step iterated algorithm of the WTLS estimate with the equivalent weight method of robust M-estimation. And the uniformly most powerful test statistics are constructed to determine the down-weighting factors. For the characteristics of the two-step iterated method, two different down-weighting schemes are presented. In the first scheme down-weighting is only implemented for the coefficient matrix and not for the observations when some elements of the coefficient matrix are estimated, and the second scheme is contrary. A simulated two-dimensional affine transformation and a linear fitting with real data are analyzed. The results show that the TRLS with the first scheme is superior to one with the second scheme, and it outperforms the existing robust methods with residual and posterior estimate of variance of unit weight and existing robust methods for the general EIV model.