Outlier detection in multiplicative error models

Multiplicative error models have become increasingly vital in geodesy because observations based on electromagnetic wave measurement techniques are often disturbed by multiplicative errors. Currently, research on multiplicative error models primarily focuses on accuracy evaluation, equation or inequality constraints, coefficient matrix pathology, and variance component estimation; however, the issue of outliers has yet to be systematically addressed. In light of this, this study addresses the outliers problem in multiplicative error models. Initially, we analyzed the impact of outliers on least squares and bias-corrected weighted least squares; the findings indicated that the impact on bias-corrected weighted least squares propagates via the least squares solution. Subsequently, we proposed an algorithm for detecting outliers in multiplicative error models. Finally, we statistically analyzed the algorithm's accuracy through simulation cases; the results confirm its feasibility and superiority.