Weighted total least squares for solving non-linear problem: GNSS point positioning

摘要

In this contribution, two algorithms are developed for parameter estimation in a non-linear measurement error model with errors in both the coefficient matrix and the vector of measurement. They are based on the complete description of the variance-covariance matrices of the observation errors and of the coefficient matrix errors without any restriction. The paper reinvestigates the nonlinear measurement model associated with GNSS point positioning. Various simulation experiments indicate that GNSS point positioning is much better formulated as a nonlinear WTLS problem with errors in both the coefficient matrix and measurement variables. The efficacy of the proposed algorithms is verified through the numerical results.