Robust solution of coordinate transformation parameters with a high breakdown point

Abstract

Because the M estimation method may lead to poor robustness or even failure owing to excessive outliers, a robust algorithm with a high breakdown point was proposed and applied to the estimation of coordinate transformation parameters. Firstly, the sampling method was used to calculate multiple sets of model parameters, and some sampling results were sifted according to posterior information. Then, the samples were sorted according to their number in the sampling results, and the F-test was adopted to screen and reserve valid information. Finally, the initial values of the reliable parameters were computed using the valid information, and the final parameters were obtained by the Institute of Geodesy and Geophysics (IGG) III scheme. Monte Carlo method was adopted for the simulation test, and a case analysis was chosen for verification. The results show that the proposed method can identify and process outliers more accurately than those of Rousseeuw [22] and Tao et al. [25]. When the proportion of outliers exceeded 50%, the proposed algorithm maintained a strong robustness and had a high breakdown point.

M robust bias-corrected weighted least squares iteration solution of mixed additive and multiplicative random error model

“…The ρ and φ in the M estimation are arbitrarily chosen functions, and by choosing different ρ and φ , there will be different equivalent weight functions, and there will be different M estimations with different robustness. The equivalent weight function selected in this paper is the IGG III weight function [31][32][33]:…”