Abstract:The coefficient matrix of the error-in-variables (EIV) model is ill-posed, and the precision of the coefficient matrix and the observation are not equal, so we derive the regularized solution of the ill-posed weighted total least squares model using the Lagrangian multiplier method. We prove the existing regularized solution of the ill-posed total least squares model to be a special case of the new model. On this basis, we propose the regularized robust solution based on the median method for ill-posed weighted total least squares model, and the effectiveness of the new algorithm is verified by two examples of the first kind Fredholm integral equation and ill-posed trilateration network. The results show that the least squares solution and the total least squares solution have poor accuracies and seriously deviate from the true value due to the influence of ill-posedness and the outliers of the model, while the accuracy of the regularized solution has been improved for weakening the ill-posedness of the model taking into account the errors of coefficient matrix and the observations. On the basis of regularized solution, the regularized robust solution reconstructs the weight matrix using the equivalent weight function, which can effectively resist the influence of gross error and has the highest accuracy.