Enhancing the Reliability of M-Estimation through Redundancy Design

Abstract

Outlier detection is a crucial aspect of model fitting, particularly in geodetic applications where data reliability is paramount. The traditional least squares estimation method, while optimal under ideal conditions, is highly sensitive to deviations caused by outliers. This study proposes a robust M-estimation method by incorporating a redundancy design to enhance the reliability of outlier detection. An iterative weight adjustment method is developed by changing the partial redundancy values of the observations, thereby improving the sensitivity of residuals to outliers. The proposed method was evaluated through extensive Monte Carlo simulations using a simple regression model and leveling network for a small outlier. The results demonstrate that the proposed method outperforms conventional techniques such as the Baarda's and Pope's tests, particularly when multiple outliers are present. While the method slightly reduces detection power for observations initially exhibiting high redundancy, it significantly enhances the detection rate for low-redundancy observations. In addition, the method was applied to uncorrelated observations. The overall findings highlight the importance of redundancy management in robust estimation processes and suggest that the proposed method offers a viable alternative for outlier detection in adjustment models.