An Improved Weighted Total Least-Squares for Condition Equation and Corresponding Bias-Corrected Method

Weighted total least-squares for condition equation (WTLSC) is a method to solve the problem that random errors exist in both observation vector and coefficient matrix of condition equation. WTLSC takes into account the case that the elements in the observation vector and coefficient matrix are independent. But in some problems, the coefficient matrix and the observation vector have common elements. Therefore, this study extends the WTLSC into IWTLSC (improved WTLSC), to deal with the case that the elements in the observation vector and coefficient matrix are dependent. The derivation process of solutions, variance-covariance matrices and bias-corrections of IWTLSC are given. A simulated experiment is applied to illuminate the proposed IWTLSC method. Considering the dependent and independent condition respectively, two group simulated data are implemented. The results show that the IWTLSC method can obtain stable solution. The bias can be corrected effectively, and the IWTLSC method is an alternative strategy to solve the nonlinear problems without linearizing.