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

Abstract There are many methods for outlier detection and robust estimation in the field of geodesy, but most of them are based on the additive random error model (AREM). In the multiplicative random error model (MREM) or mixed additive and multiplicative random error model (MAMREM), outlier detection or robust estimation is less studied. Based on the bias-corrected weighted least squares (bcWLS) iteration solution of the MAMREM, combined with the conventional M robust estimation in the AREM, this paper proposes an M robust bcWLS iteration solution suitable for the MAMREM. The analysis of the examples shows that the proposed method can obtain better parameter estimation and more reasonable mean square error of unit weight when the observations contain outliers, which verifies the feasibility and preponderance of the proposed method.