Total least squares adjustment in inequality constrained partial errors-in-variables models: optimality conditions and algorithms

Abstract

The partial errors-in-variables (PEIV) model is a structured form of errors-in-variables (EIV) model reformulated by collecting all the independent random elements of the coefficient matrix. When some reliable inequality constraints are taken into account, the adjustment results of inequality constrained PEIV (ICPEIV) model are probably improved. In this contribution, we first present the optimality conditions for inequality constrained weighted total least squares (ICWTLS) solution in ICPEIV model. Then we modified the existing linear approximation (LA) approach to make it suitable for cross-correlated data. The sequential quadratic programming (SQP) method is proposed based on the optimality conditions. Since the Hessian matrix is difficult to compute in the SQP algorithm and it converges slowly or even not converges when the Hessian matrix is indefinite positive, the damped quasi-Newton (DQN) SQP method is proposed. Finally, three examples are given to show the feasibility and performance of the proposed algorithms.