Robustness and Reliability of Least Squares Adjustment Algorithms: A Quantitative Evaluation for Geodetic Survey Networks

Abstract

The integrity of geodetic network adjustment is frequently compromised by gross errors and measurement anomalies, necessitating robust estimation strategies beyond classical ordinary least squares (OLS). This study presents a systematic evaluation of OLS alongside robust alternatives, including Iteratively Reweighted Least Squares (IRLS), Least Median of Squares (LMS), Least Trimmed Squares (LTS), and a reweighted LTS variant (LTS-RC), using Monte Carlo simulations under varying levels of data contamination. Performance was assessed through four dimensions: robustness to outliers, internal and external reliability indices, hypothesis testing power, and computational efficiency. Results reveal that while OLS provides minimal runtimes (~0.02 s per adjustment), its vulnerability to gross errors severely undermines reliability and detection capability, restricting its applicability to clean and low-risk data environments. Robust estimators substantially enhanced both internal redundancy and minimal detectable biases (MDBs), with IRLS offering a balanced trade-off between robustness and computational cost. LMS and LTS achieved superior error detection rates but at higher runtimes (0.20–0.35 s). Notably, LTS-RC consistently delivered the strongest overall performance, maintaining coordinate integrity under severe contamination while achieving acceptable computational feasibility (~0.15 s). These findings corroborate prior work in geodesy and statistics while extending their relevance to modern survey network configurations. The study recommends prioritizing robust estimators, particularly LTS-RC, for high-stakes applications such as deformation monitoring, GNSS-based engineering surveys, and critical infrastructure projects. Integrating robust adjustment methods into technical standards and professional training will enhance the resilience and reliability of geodetic practice.