Least trimmed squares estimator with redundancy constraint for outlier detection in GNSS networks

Global navigation satellite system (GNSS) networks facilitate accurate positioning over short and long distances on the surface of the Earth and expand the range of high-precision measurement. These networks are the basis not only for mapping activities, geoinformation, land registry and other location-based services, but also provide an important role in society as infrastructure works (roads, bridges, tunnels, water supply, sewage, electricity networks, telecommunications, etc.) which are directly dependent on highly accurate three-dimensional control points. Constituted by a predetermined number of points, the GNSS networks have their points' coordinates estimated from the relative distances between them, called observations, through adjustment processes. Given the importance of this information, a precise adjustment is highly necessary. The least squares (LS) method is often applied because it is the best linear unbiased estimator, assuming that no outliers and/or systematic errors exist. Outliers may occur in practice, however, and cause such estimation to fail and leading to unprecedented errors over many points in the network. Therefore, in this study, we propose a new approach for detecting small and large outliers in observations by examining the residuals' vector. For this purpose, we apply a metaheuristic method along with a novel robust estimator, called the Least Trimmed Squares with Redundancy Constraint (LTS-RC). We also propose a definition of the search space for metaheuristics in order to attain the desired results at lower computational cost. Experiments confirmed the effectiveness of the proposed approach, even in the presence of correlated observations in GNSS networks. Furthermore, the robust estimator yielded a significant improvement in comparison with the classic LTS technique. The proposed method correctly detected all outliers with no false positives in most established scenarios, even with a reduced number of cycles in the metaheuristic algorithm, and recorded better detection accuracy for moderate and large outliers than for small errors.