Total Least Squares Adjustment of Partial Errors-in-Variables Model with Weight Scaling Factor

As a prior stochastic model contains inaccurate information, the weight matrices of observation and coefficient matrix are unreasonable. To address this problem, we investigate the total least squares adjustment of partial errors-in-variables(PEIV)model with a weight scaling factor that adaptively adjusts the contribution of the observation and coefficient matrix to parameter estimation. A prior unite weight variance and minimum discriminate function method are deduced, so the proposed method is valid for a structured coefficient matrix. Some conclusions are drawn from simulations of straight line fitting and coordinate transformation. When the prior unit weight variances of observation and coefficient matrix are known and accurate, the prior unit weight variance method is very effective; the minimum discriminate function method with the \overline\mathit\mathit\Phi _1\left( \boldsymbol\hat\varepsilon ,\boldsymbol\hat\varepsilon _a \right)=\boldsymbol\hat\varepsilon ^\textT\boldsymbol\hat\varepsilon +\boldsymbol\hat\varepsilon _a^\textT\boldsymbol\hat\varepsilon _a as its discriminate function to determine weight scaling factor yielded the best performace.