Abstract The accuracy of solutions for ill-posed equations can be significantly improved by using the reasonable equality constraint between the adjustment parameters. In this paper, an ill-posed total least squares model with equality constraints is proposed by applying equality constraints to an ill-conditioned total least squares model. The regularization criterion for constrained ill-posed total least squares is established, and the iterative solution of parameters and its variance-covariance matrix are obtained according to the Lagrangian multiplier method. Finally, numerical examples and ill-posed trilateration network example are used to verify the correctness of the formula. The results show that new method not only improves the ill-posedness of normal matrix by regularization criteria, but also complies with error of coefficient matrix according to EIV criteria. At the same time, it also considers reasonable prior information between parameters; therefore, the accuracy of solution is significantly improved.
JI Kunpu. A Regularized Solution and Accuracy Evaluation of Ill-PosedTotal Least Squares Problem with Equality Constraints[J]. jgg, 2019, 39(12): 1304-1309.
JI Kunpu. A Regularized Solution and Accuracy Evaluation of Ill-PosedTotal Least Squares Problem with Equality Constraints[J]. jgg, 2019, 39(12): 1304-1309.