Robust LS-VCE for the Nonlinear Gauss-Helmert Model: Case Studies for Point Cloud Fitting and Geodetic Symmetric Transformation

Variance component estimation (VCE) is widely applied to adjust random models in the fusion processing of multiple classes of observations. In our previous study, the least-squares VCE (LS-VCE) for the classical Gauss-Markov (GM) model was extended to a universal adjustment model: the nonlinear Gauss-Helmert (GH) model. However, due to its limited ability to resist outliers, the accuracy of the estimated variance components and parameters will be negatively affected in the presence of outliers. In this article, the variance inflation principle of robust estimation is further introduced based on our previous study, and a robust LS-VCE method for the nonlinear GH model is proposed. To avoid the emergence of negative variance components, the nonnegative estimation of the variance components is achieved as well. Unlike the existing studies, the new method can simultaneously mitigate the negative influence of outliers while reasonably adjusting the relative weighting ratios among different classes of observations in the nonlinear GH model. Finally, case studies of point cloud fitting based on original observations and geodetic symmetric transformation are carried out to validate the performance of the proposed method. The results show that when the observations are polluted by outliers, the accuracy of the parameters obtained by the new method has considerable improvement compared with that from the generalized total least-squares and the LS-VCE method for the nonlinear GH model. Since the linear/nonlinear GM and errors-in-variables (EIV) models can be treated as special cases of the nonlinear GH model, the proposed method possesses a wide range of applicability.