Linearization Estimation Algorithm for Universal EIV Adjustment Model

The universal EIV model extends the EIV model to the most general form, and the weighted total least squares (WTLS) algorithm is proposed to take into account the random errors in observation vector, observation vector coefficient matrix and parameter coefficient matrix. In this paper, the nonlinear universal EIV function model is expanded, and the second-order term is included into the constant term of the model, so the universal EIV model is represented as Gauss-Helmert model in linear form, and the Linearized total least squares algorithm and approximate precision estimation formula of the universal EIV model are derived. Through the simulation data and examples, this algorithm is consistent with the estimation results of the WTLS algorithm of the universal EIV model, which verifies the correctness and feasibility of this algorithm. When the model contains a large number of estimators, the linearized estimation algorithm of the universal EIV model significantly improves the computational efficiency and converges faster.